# The Vested Parimutuel — supporting articles

Companion essays to the Vested Parimutuel whitepaper (Hunch Research).
The paper is the specification; these are the explanations, comparisons,
and operator guides that hang off it. Full paper:
https://www.playhunch.xyz/vpm-whitepaper.md

Text CC BY 4.0, code MIT. Every number quoted here is the paper's;
where an article states a figure, the paper's section is cited beside it.

## Contents

**Foundations**

- [What a Vested Parimutuel actually does](https://www.playhunch.xyz/vpm-whitepaper/articles/what-is-a-vested-parimutuel) — Two rules, one worked example, and what happens to your money — the whole mechanism in plain language, before any notation.
- [The lock window, and what it costs to keep](https://www.playhunch.xyz/vpm-whitepaper/articles/the-lock-window) — Every parimutuel venue closes entry before the event. Here is the free-ride that forces it, the handle it burns, and why this mechanism deletes it as an identity rather than a policy.
- [Who funds the first counterparty](https://www.playhunch.xyz/vpm-whitepaper/articles/the-cold-start-problem) — No market structure has a first bettor. Four structures, four answers, and what each one costs the party who pays it.
- [What a stake is worth when it arrives](https://www.playhunch.xyz/vpm-whitepaper/articles/the-vesting-yield) — The pricing formula, the belief it implies, the two-sided band that proves the pool ratio is not a probability, and the winner's curse that halves the number you thought you had.
- [Capacity, κ, and the market that freezes](https://www.playhunch.xyz/vpm-whitepaper/articles/capacity-and-kappa) — The matching rule that makes vesting sound, the partial fills it causes, and the absorbing n-way failure that makes finite κ a binary-market instrument.

**Comparisons**

- [Four ways to make a market](https://www.playhunch.xyz/vpm-whitepaper/articles/four-ways-to-make-a-market) — Order books, CFMMs, scoring rules, pools — what each one needs before it can quote, what it costs to run, and where each one stops working.
- [Against the classic parimutuel](https://www.playhunch.xyz/vpm-whitepaper/articles/vpm-vs-classic-parimutuel) — The strongest adoption case in the paper: same pool, same plumbing, one moment moved — and the free-ride, the lock window, and the dilution all go with it.
- [Against AMMs and scoring rules](https://www.playhunch.xyz/vpm-whitepaper/articles/vpm-vs-amms) — LMSR, Maniswap, pm-AMM, Azuro: every one funds its first counterparty with a negative-EV position. The comparison is about incidence, not about who is cleverer.
- [Against order books](https://www.playhunch.xyz/vpm-whitepaper/articles/vpm-vs-order-books) — Polymarket and Kalshi solved the head of the market properly. Why this mechanism does not compete with them there, and what it is actually offering instead.

**Adoption**

- [Should your venue adopt this?](https://www.playhunch.xyz/vpm-whitepaper/articles/should-you-adopt-vpm) — A decision guide with the disqualifications first: five venue shapes that should not adopt it, four that should, and the three questions that separate them.
- [Migrating a pool venue, step by step](https://www.playhunch.xyz/vpm-whitepaper/articles/migrating-a-parimutuel-venue) — λ = 0 is the rule you already run. The staged path from there to a vested pool, what to publish at each stage, and the two things that break if you skip one.
- [What it saves, what it costs](https://www.playhunch.xyz/vpm-whitepaper/articles/venue-economics) — The revolving float, the recovered lock-window handle, and the honest cost column: carry, resolution risk, a worse late price, and a secondary layer you now owe your users.
- [Choosing λ, market class by market class](https://www.playhunch.xyz/vpm-whitepaper/articles/choosing-lambda) — No point on the dial gives you all four properties. A table of market types with the setting each one wants and what it gives up to get it.

**Building**

- [Implementing it](https://www.playhunch.xyz/vpm-whitepaper/articles/implementing-vpm) — The O(1) accumulator, the fixed-point scale you must choose correctly, four settlement-path MUSTs, and the conformance suite that tells you whether you got it right.
- [Resolution when the claims are already accrued](https://www.playhunch.xyz/vpm-whitepaper/articles/resolution-under-vested-claims) — Vesting changes the resolver's incentives in three specific ways, two of them for the worse. Delay farming, stall-into-void, and the direction premium — with the fixes.
- [MEV, vintages, and the price of one block](https://www.playhunch.xyz/vpm-whitepaper/articles/mev-vintages-and-block-time) — Batching by block removes the ordering game inside a block and prices it exactly between blocks. The capture formula, and every mitigation with its cost.
- [Where the late price comes from](https://www.playhunch.xyz/vpm-whitepaper/articles/where-the-late-price-comes-from) — If late pool entry is supposed to die, something else has to carry the last hour's information. The measured bound on what a thin transaction layer delivers — and the cheaper repair that does not exist.

**Ecosystem**

- [Why there are only a few thousand prediction markets](https://www.playhunch.xyz/vpm-whitepaper/articles/the-long-tail-ceiling) — The count is not a demand problem. It is a per-market cost problem, and the cost has a name in every structure that exists.
- [Agents as market makers](https://www.playhunch.xyz/vpm-whitepaper/articles/agents-as-market-makers) — Seeding is the first market-making job with a closed-form value and a floor. It is also the one where a naive growth estimate loses 11.5% per entry.
- [The objections, answered honestly](https://www.playhunch.xyz/vpm-whitepaper/articles/honest-objections) — Is it a Ponzi, can a whale take it over, can you wash-trade it, does it worsen the favorite-longshot bias — the structural questions, with the ones that land conceded.

---
# What a Vested Parimutuel actually does

There is a version of this mechanism that takes an hour to explain and a version that takes ninety seconds. This is the ninety-second one, written out.

A parimutuel is the oldest way to run a market that nobody is making. Everyone's money goes into a pot, the event happens, and the winners split the pot. No market maker, no quotes, no counterparty to find — it works from the first dollar, which is why racetracks, lotteries and every prediction market operating past its first few hundred listings end up running one.

It has exactly one flaw, and it is a bad one. **A pool pays the same multiple to everyone who was right, regardless of when they were right.** Someone who took a position an hour before the event and someone who took it three seconds before the whistle collect the identical return. The second person took almost no risk, contributed nothing anyone needed, and is paid out of the first person's winnings.

The Vested Parimutuel changes one thing about that. Not the pot, not the plumbing, not the payout arithmetic. One moment.

## The change, in one sentence

> In a classic pool, the losing money is divided among the winners **at resolution**. Here, it is assigned to them **at the moment it arrives**.

That is the entire idea. Everything else in the [whitepaper](/vpm-whitepaper) is the consequences of that sentence and the one guardrail it needs.

Think about what it means to be on the other side of a bet. If you are on YES and someone stakes $100 on NO, that $100 is *yours if YES wins* — that is what having a counterparty is. The classic pool agrees, but waits until the end to say so, and by then more people have joined your side, so you share it with them. The vested rule says it immediately and never revisits it. The $100 is split among whoever was standing on YES **at that instant**, pro-rata by how much they had at stake, and no one who arrives afterwards can touch it.

## Rule 1: money vests to the other side, on arrival

Formally, from [§4.1](/vpm-whitepaper#41-the-two-rules):

> When a stake arrives on an outcome, it is assigned — immediately and irrevocably — pro-rata by principal to the positions already standing on each of the other outcomes.

Two words in there are load-bearing.

**Already.** People who join your side after that moment share in nothing that came before them. They share only in what arrives after *them*. Your accrued claim is fixed the instant it accrues.

**Irrevocably.** Nothing in the mechanism ever decrements a claim. There is no rule anywhere that takes something back. The only condition is that the market actually resolves; if it voids, everyone refunds at principal ([§12](/vpm-whitepaper#12-resolution)).

The direct consequence: **a minimum payout that is set the moment you enter and can only go up.** Not a guaranteed profit — if your outcome loses you get zero, exactly as in any market — but on your winning branch, a floor that ratchets. In the paper this is P2, and its proof is one line: a sum of non-negative increments, and nothing subtracts.

## Rule 2: only as much as the other side can cover

Rule 1 alone would be broken, and it breaks in an entertaining way. If there is no limit on how much a book can absorb, then the *first* position on an empty book collects 100% of all opposing inflow until a second one joins. Make that position one cent and it earns an unbounded multiple. In the design-phase measurements a seeding straddle returned +155% at $50 a leg and **+82,037% at one cent a leg** ([Appendix A.1](/vpm-whitepaper#appendix-a-design-alternatives-and-how-they-fail)). The optimal strategy would be to post dust on every new market and collect a toll while supplying no liquidity at all.

So there is a second rule:

> Each position grants its own book `κ · s` of matching capacity. A stake is accepted only up to the capacity remaining in every opposing book. The rest is refused at entry and returned in the same transaction.

`κ` (kappa) is a single published number — a maximum-odds cap, the same object every betting exchange already publishes. That is all. No decay schedule, no bonus bucket, no parameters to tune.

What it does: it constrains **acceptance**, never **distribution**. The split stays pure pro-rata, which means return on capital is scale-invariant — a $1 position earns exactly the same multiple as a $10,000 position entering at the same moment, never more. Dust has nothing to dominate. And the multiple everyone shares is bounded at `1 + κ(1 + ln g)`, where `g` is the book's later growth.

The familiar consequence of a matching constraint is the **partial fill**, which is why the answer to "can I bet $500 here?" is sometimes "you can bet $400 of it."

## What $500 into a fresh market actually looks like

Take the paper's reference parameters: a binary market, `κ = 9`, seeded with $50 on each side.

A symmetric seed of `S` per leg leaves each book exactly `S(κ − n + 1)` of headroom, so at `S = 50`, `κ = 9`, `n = 2` that is **$400**.

You offer $500 on YES. The market accepts $400 and returns $100 in the same transaction. Nothing is held, nothing is escrowed, nothing is pending — the $100 is simply back in your wallet, and the refusal is telling you something true: there is only $50 of NO money in this market, and $400 at nine-to-one is everything that $50 can honestly stand behind.

Your $400 now sits on YES. Two things are true about it:

- **If YES wins**, you get at least your $400 back, plus your pro-rata share of every NO dollar that arrives from now on. Right this second that share is 100%, because you are the only non-seed position on YES.
- **If NO wins**, you get nothing, and your $400 belongs to the NO seed. Which is exactly the deal you took.

Then the market fills up. Every NO dollar that arrives vests partly to you, forever. Every *YES* dollar that arrives dilutes only your share of *future* NO flow — it cannot reduce a cent of what you have already accrued.

And if you had wanted the whole $500 in, you had two options: wait for someone to take the other side, or bring the other side yourself. Which brings us to the thing most people ask second.

## The first bettor can be the seeder

A market opens when someone stakes **every** outcome, in a reserved slot the paper calls vintage 0. This is usually described as "the creator seeds it," which makes it sound like a chore imposed on whoever wrote the question.

It is better read as a directional first bet with a floor. The seed does not have to be balanced — [§4.4](/vpm-whitepaper#44-creation-entry-exit) accepts any legs satisfying `a_o ≤ κ · min_{w≠o} a_w`, so at `κ = 9` a **$450 / $50 straddle** is a perfectly valid opening. That is a nine-to-one directional bet that happens to leave on the table exactly what the second bettor needs in order to exist.

And whoever posts it recovers at least what they staked, in every branch, under every continuation ([P6](/vpm-whitepaper#5-properties)). The proof is trivial once you see it: immediately after seeding, you own every position in the market, and every branch pays the whole pool to its owners. Later flow only adds.

That property is what makes the seat worth taking, and [the cold-start article](/vpm-whitepaper/articles/the-cold-start-problem) is about why it matters more than it sounds.

## The worked example

Here is the paper's [§4.2](/vpm-whitepaper#42-a-worked-example) log — a $25/$25 seed, five ordinary stakes, $1,050 accepted, no fees, machine-checked as the first pair of conformance vectors.

| # | time | who | outcome | stake |
|---|---|---|---|---|
| 0 | 0 | creator | YES / NO | $25 / $25 |
| 1 | 10 | A | YES | $100 |
| 2 | 30 | B | NO | $200 |
| 3 | 60 | C | YES | $300 |
| 4 | 90 | D | NO | $200 |
| 5 | 99 | E | YES | $200 |

If YES realizes, the classic parimutuel pays every YES holder a flat **1.680×**. Here:

| position | staked | payout | multiple | classic |
|---|---|---|---|---|
| creator (YES leg) | $25 | $101.76 | **4.070×** | 1.680× |
| A (t=10) | $100 | $307.06 | **3.071×** | 1.680× |
| C (t=60) | $300 | $441.18 | **1.471×** | 1.680× |
| E (t=99) | $200 | $200.00 | **1.000×** | 1.680× |

Read three things off it.

**The point of the whole exercise is the last two rows.** A carried the risk for 89% of the market's life. E arrived after the last opposing dollar. The classic column pays them the same. This one pays 3.071× and 1.000×, out of the identical pool.

**Payouts still total $1,050 exactly**, in both branches, in integer units. Nothing is created and nothing is skimmed. This is P1, and it is an accounting identity rather than a solvency claim someone tested — the conservation is a bijection between accepted units and payout units.

**E is not being punished; E is being told the truth.** Under classic rules E takes $136 of profit, every cent of it out of A, C and the creator, for arriving late and bearing no risk. Here, E gets its money back. That is not a penalty. That is what a bet with no counterparty is worth.

## What follows for free

Because these are consequences of the two rules rather than features bolted on, they come with proofs rather than promises:

- **No lock window.** Because a stake arriving after the last opposing dollar pays exactly 1×, the buzzer-beating strategy that forces every parimutuel venue to close entry early has nothing to aim at. Measured across 20 seeds × 2,000 markets: unconditional expected value of the snipe is **−1.05% here against +25.27% under classic rules**. [More on that here.](/vpm-whitepaper/articles/the-lock-window)
- **Dilution protection is exact.** Under a snipe worth 50% of the pool, early winners' total payouts fall 0.19% on average here, against 13.6% under classic rules.
- **Settlement is O(1).** The rule reads like a loop over every opposing position, but it collapses to one running accumulator per outcome — two scalars per position, updated in constant time. That is the difference between implementable on-chain and not ([§6](/vpm-whitepaper#6-settlement-in-constant-time)).
- **Your payout depends on nobody else's record.** It is a function of two numbers: your outcome's accumulator when you entered, and at resolution.

## What it does not do

The paper is unusually direct about this, and an explainer that skipped it would be selling something.

- The floor is **conditional on your outcome winning.** It is not downside protection. Wrong side, zero.
- **You cannot get out.** Positions are transferable in principle, but the mechanism itself offers no exit, no cash-out, and no hedge. Something else has to provide that ([§8](/vpm-whitepaper#8-the-separation-principle)).
- **The late price gets worse.** With rational late entry gone, the pool ratio stops tracking probability near the end: final-phase Brier 0.174, against 0.150 for a classic pool that simply locks. That is a measured cost, paid deliberately.
- **A big enough early position squeezes everyone else.** A seed three times the organic pool takes ordinary early winners from 1.70× to 1.09×. Nothing prevents it.
- **There is no equilibrium theorem.** The incentive arguments are arguments, and the paper labels them as such.

---

*Next: [The lock window, and what it costs to keep](/vpm-whitepaper/articles/the-lock-window) — why every pool venue closes early, and what deleting that rule is worth.*


---

# The lock window, and what it costs to keep

Go to a racetrack and try to bet ninety seconds after the gates open. You can't. Betting closed at the off. Go to a sports pool and try to enter at half-time on a 3–0 scoreline. You can't. Entries closed at kick-off. Go to a prediction market running a pool and try to buy the obvious answer thirty seconds before the announcement. Most of the time, you can't.

Every venue that runs a parimutuel closes it early. This is so universal that it reads as a fact of nature, like a market having opening hours. It isn't. It is a patch for a specific defect, and the patch is expensive.

## The defect

A classic pool pays a flat multiple. If the winning side holds $10,000 out of a $25,000 pool, everyone on that side is paid 2.5× — the person who committed at the open, and the person who committed after the outcome was effectively known.

That second person has a strategy. Wait until the event is nearly decided, identify the side that is now overwhelmingly likely to win, and put money on it. You are buying a near-certainty at pool odds set when it was still uncertain. Your money joins the winning book, which *reduces* everyone else's multiple, and you collect a return you took no risk to earn.

This is not a theoretical exploit; it is the dominant strategy, and it has been studied experimentally since [Plott, Wit & Yang (2003)](/vpm-whitepaper#references). The paper measures it directly. A sniper stakes 50% of the gross pool on a leader above 85% at `t = 0.95T`, across 20 seeds × 2,000 markets ([§13.1](/vpm-whitepaper#131-the-main-study)):

| | classic pool | this mechanism |
|---|---|---|
| sniper's multiple, restricted to wins | 1.273× ± 0.003 | **1.005× ± 0.00006** |
| leader actually wins | 98.42% ± 0.13 | 98.42% ± 0.13 |
| **unconditional EV, pre-fee** | **+25.27% ± 0.33** | **−1.05% ± 0.13** |
| unconditional EV, post-fee | +22.76% | −3.03% |
| early winners' payouts fall by | 13.64% avg, 64.4% worst | **0.19% avg, 4.9% worst** |

A +25% expected-value strategy available to anyone with a clock is not a thing a venue can leave open. So it doesn't.

## What the patch costs

**Handle.** The most obvious cost, and the one an operator feels in the P&L. Every minute of closure is a minute of volume the venue does not take. In sports this is the *worst* possible window to be shut: interest peaks near the event, and the venue is dark for exactly that peak. In the paper's behavioural study the lock arm loses 5.0% of its total volume relative to the unlocked arm — and that is with an artificial crowd. Real venues close for far longer than the final 5% of a market's life.

**A closed market is a dead market.** The lock does not just stop the snipe. It stops the hedger with real exposure, the trader whose thesis matured late, the person who only just heard about it. Everyone gets locked out to stop one strategy.

**It is a policy, not a property.** Someone has to choose the window, defend it, and adjust it per market class. It is a parameter with a business case attached, and it is the venue's fault when it is wrong in either direction.

**It does not actually fix dilution.** This is the part usually missed. The lock stops the *buzzer* snipe. It does nothing about ordinary late money. Look at the classic row of the paper's payout-by-decile table, 20 seeds × 2,000 markets:

| decile | 1st | 2nd | 3rd | 5th | 8th | 10th |
|---|---|---|---|---|---|---|
| classic | 1.40 | 1.37 | 1.36 | 1.36 | 1.39 | 1.42 |
| **this mechanism** | **2.54** | 1.76 | 1.45 | 1.20 | 1.06 | **1.004** |

The classic row is flat, and *slightly rising* at the end. Being early is worth nothing at all — and the last decile of entrants captures **13.20% ± 0.07** of the losing pool. That transfer is happening inside every locked market, every day, below the level the lock operates at.

## What replaces it

The vested rule makes the snipe pointless rather than illegal, and it does so as an identity rather than as a measure.

Here is [P4](/vpm-whitepaper#5-properties) in full:

> A stake accepted after the last opposing inflow is paid exactly its principal; for a trader with belief `p < 1`, its expected value is `−(1−p)s < 0`.

The proof is two clauses. Vesting only ever adds increments from *opposing* inflow, so if there is no opposing inflow after you, you accrue nothing and are paid your stake back. And under the capacity rule there is no unmatched residue to recover — a classic pool's late entrant at least gets 1× less takeout on unmatched money, which is a soft floor; here the negativity is unconditional.

So: **1.000× on the win, 0 on the loss.** Any belief short of certainty makes that strictly negative. The strategy has no target, and the venue does not need a rule to stop it.

That is the corollary the paper draws: **no lock window**. Markets can accept entries right up to resolution, because the reason to close them has been removed rather than policed.

## The number that matters is the pair

A single number can be argued with. The paper's approach here is to publish the signed pair on the same triggers: **+25.27% under classic rules, −1.05% under this one.** Same crowd, same markets, same sniper, same 98.42% base rate on the leader.

That pair — not the lock rule, and not a claim about anyone's intentions — is what deletes the strategy.

There is a residual, and the paper does not round it away. Early winners still lose **0.19%** under the snipe. That is not a leak. It is early winners sharing the last 5% of opposing flow with a newcomer who genuinely showed up and genuinely took the other side of it. That is P3 working exactly as specified: your accrued claims are untouched, but a later same-side entrant does share the flow that arrives *after* them.

## What it looks like when the crowd responds

Settling a fixed log under two rule sets proves the arithmetic. It does not tell you whether people change their behaviour. So [§13.2](/vpm-whitepaper#132-what-happens-when-the-crowd-responds) re-runs the experiment with agents deciding for themselves whether to enter, under whichever rule they face.

Share of volume by phase of market life:

| arm | first third | middle third | 67–95% | final 5% |
|---|---|---|---|---|
| classic (no lock) | 32.9% | 33.3% | 28.7% | 5.1% |
| classic + lock | 34.6% | 35.1% | 30.2% | 0.1% |
| **this mechanism** | **43.9%** | 34.7% | 19.7% | **1.7%** |

Late pool volume collapses from 5.1% to 1.7% **without prohibiting anything**, and a third more volume migrates into the market's opening phase. The conservative-estimator arm (agents using a deliberately pessimistic growth assumption) pushes further in the same direction — 48.5% in the first third — so the migration is driven by the incentive, not by a particular estimator.

The residual 1.7% is worth naming honestly. It is not zero, because a market's *last* dollars are not all buzzer snipes; some late entrants still have positive expected value because opposing flow is still arriving behind them.

## What it costs to delete it

This is where an honest article has to turn around, because the trade is real and the paper measures it in the direction that hurts.

If rational late money stops entering the pool, the pool's ratio stops updating near the end. It goes stale. And a stale ratio is a worse forecast:

| Brier score, final 5% of market life | |
|---|---|
| classic, unlocked (the theoretical ideal) | 0.148 |
| **classic + lock (what venues actually deploy)** | **0.150** |
| **this mechanism** | **0.174** |

Lower is better. The fair comparison is the middle row against the bottom: the *deployed* baseline, not the ideal one. The mechanism's late forecast is measurably worse — by 0.024 Brier — and the paper's own summary of the trade is that it "pays forecast quality in the pool's last act to buy dilution protection for everyone before it."

Two things soften that, neither of which is a dismissal.

**The information still exists; it just stops showing up in the pool.** Adding a stylized dealer — every late informed arrival prints a transaction at its belief, shaded by half a spread — produces a composite forecast with a final-phase Brier of **0.054–0.057, at every spread from 2% to 20%**. Better than the locked classic pool by a wide margin. That is an upper bound on what a thin transaction layer could deliver, not a design; [the article on the late price](/vpm-whitepaper/articles/where-the-late-price-comes-from) covers what is and is not established there.

**The lock arm has the same problem, one step earlier.** A locked pool's "final" price is simply its price at lock time, frozen. Its 0.150 is a snapshot taken before the last 5% of information existed. The mechanism at least keeps accepting entries; what it loses is the incentive for informed ones.

## The one-line version

A lock window is a venue admitting that its settlement rule pays people for showing up late, and closing the door rather than fixing the rule. Fixing the rule removes the door — and moves where the last hour's price comes from, which is a cost, stated at 0.174 against 0.150.

---

*Next: [Who funds the first counterparty](/vpm-whitepaper/articles/the-cold-start-problem) — the objection at the other end of a market's life.*


---

# Who funds the first counterparty

The first objection this mechanism meets is always the same one, and it is a good objection:

> A market only opens once someone has staked every outcome. But a venue is not going to seed ten thousand markets, and a creator posting a question as an opinion is not going to stake it. Surely a market can just start with its first bettor?

The short answer is that **no market structure has a first bettor**, anywhere, and the objection quietly assumes one exists.

## A bet needs a counterparty

That is not a technicality. It is the definition. So every market structure meets its first arrival with something that is *not yet a bet*, and the four structures differ only in what that something is and who pays for it.

**An order book** holds the first arrival as an unmatched quote. You have placed an order. It binds nobody. It is not a bet until someone takes it, and on a fresh long-tail book, nobody does. What makes an order book *feel* like it works from the first dollar is that on real venues a professional market maker is already standing there — funded, incentivized, and present because the venue arranged for them to be.

**An AMM** meets it with a curve someone funded in advance. Your first trade has a counterparty because a liquidity provider put capital in before you arrived and agreed to lose money to informed flow. The LP is the first counterparty; you just did not have to find them.

**A classic parimutuel** accepts one-sided money outright, which looks like the exception. It isn't. If opposing money never arrives, the pool hands your stake back at resolution at 1×, less takeout. That is an escrow with a fee, dressed as a bet, and you find out at settlement.

**This mechanism** refuses at entry instead. The stake is returned in the same transaction, with the reason: there is nothing on the other side. Same fact, stated immediately and at no cost, rather than discovered later.

So the real question — asked of every structure, not just this one — is never *whether* someone funds the first counterparty. It is **who does, at what expected cost, and holding what guarantee.**

## Three answers, priced

| structure | who funds the first counterparty | their worst case | what it buys |
|---|---|---|---|
| **order book** | a professional market maker, per market | adverse selection loss; venue often pays incentives on top | continuous two-sided quotes, native exit, hedging |
| **AMM / scoring rule** | an LP or the creator, per market | a **funded expected loss** — bounded at `b · ln n` for LMSR; rebalance-into-the-loser for a CFMM on an expiring claim | same three |
| **this mechanism** | the seeder, on all outcomes, in vintage 0 | **nominal recovery in every branch** (P6) | none of those three — see below |

The middle row deserves care, because the one-line dismissal ("a bounded subsidy is still a subsidy") is too quick. The subsidy need not come from the venue. **Manifold runs creator-funded AMM liquidity at scale**, which puts the scoring-rule family in exactly the same funding position as this mechanism's seed: per-market capital at risk, supplied by whoever wants the market to exist.

So the honest comparison is not "subsidy versus no subsidy." It is an **incidence** comparison, and the paper states its own claim narrowly ([§2.2](/vpm-whitepaper#2-related-work)):

> The per-market capital does not disappear here any more than anywhere else. It stops being spent.

A creator-funded LMSR subsidy has a worst case of `−b · ln n` and an expected loss to informed flow that someone chooses to bear. What it buys is continuous quotes, exit, and hedging. The vested seed has a **nominal floor in every branch**, and what it gives up is exactly those three things. Its real costs are fees, carry on locked capital, and resolution risk — none of which is an expected loss to informed flow.

## Why the floor changes the arithmetic of scale

"A platform will not seed every market" has the economics backwards, and the reason is one word: **a subsidy budget is consumed; a floored seed is a revolving float.**

A venue seeding programmatically parks the seed for a market's life, recovers it in every branch, redeploys it, and in the meantime holds the first standing position on every book — collecting a vested share of all subsequent flow.

The arithmetic is smaller than people expect. A symmetric seed of `S` per leg opens `S(κ − n + 1)` of first-vintage headroom per book, so:

- **$50 a side at κ = 9** admits a **$400** first entry.
- **Ten thousand binary markets at $5 a side** is **$100,000** of total float, against zero mechanism-level expected loss.

That is a treasury line, not a marketing line. And the constraint on it is capital *parked*, not capital *spent* — which is the difference between a number that grows with your market count and a number that grows with your market count *and never comes back*.

Then [§9](/vpm-whitepaper#9-incentives) adds a fact that makes small seeds correct rather than merely cheap: growing the seed from $50 to $5,000 a leg — about three times the organic pool — compresses ordinary early winners from **1.70× to 1.09×**, while the seeder sits at its floor. Over-seeding crowds out exactly the participants the venue wanted. So the policy that costs least and the policy the mechanism prefers are the same policy.

## The creator does not have to be the seeder

This is the half of the objection that is genuinely right, and the mechanism accommodates it rather than arguing with it.

In the mechanism's own terms, the **creator** is defined by one act — posting vintage 0 — not by authorship. Whose capital takes that seat is venue policy, not mechanism.

So a venue can carry **unseeded listings**. A market posted as a question, an opinion, a challenge, sitting there un-tradeable until any party posts the all-outcome seed and, with it, takes on the resolution-bond seat that [§12](/vpm-whitepaper#12-resolution) wants filled. If you post an opinion market to your followers and never intend to stake it, that is a valid thing to do; the market opens when a believer opens it.

And the seed need not be balanced. [§4.4](/vpm-whitepaper#44-creation-entry-exit)'s joint acceptance admits any legs satisfying `a_o ≤ κ · min_{w≠o} a_w`. At `κ = 9`, a **$450 / $50 straddle** is a valid opening seed for a binary market. Read that as what it is: a nine-to-one directional first bet that

- carries a floor no ordinary entry gets,
- leaves on the table exactly what the second bettor needs in order to exist, and
- having consumed the whole of the headroom its own side draws on, waits for opposing flow like any first position anywhere.

The demand that "there has to be a first bettor" is met literally. There is one. The mechanism's only requirement is that **the first bet be the one that makes the second bet possible** — and it pays that seat for the wait.

## Why the requirement cannot be softened

It is tempting to treat the seed as deployment guidance — nice to have, enforce it loosely, let markets open unseeded and fill in later. That does not work, and the reason is structural rather than cautious.

P1, the conservation identity, leans on **every book being non-empty for the life of the market**. That is what guarantees an arriving unit always has somewhere to be placed. In the unbounded-κ regime the creation rule alone carries that invariant, which is why the paper treats it as specification rather than policy.

And a market that somehow opened unseeded would not be a *degraded* market. It would be a **dead** one: every book's capacity is zero, so no entry on any outcome at any size is ever acceptable, and no stake can grow a book because no stake can be accepted. It would sit there looking tradeable and refusing everyone.

Which is why [P11](/vpm-whitepaper#52-conformance-cases-beyond-p1-p7) voids such a market **at creation** rather than letting it stand — including the subtle case where integer allocation floors a dust leg to zero. An implementation should treat *every market opens seeded* with the same standing as conservation itself: not because it is prudent, but because without it there is no market to conserve.

## For a venue already running pools

If you already run classic parimutuel pools, this section is the adoption case in miniature — because you have already paid for cold start. Pools work from the first dollar. You pay at the *other* end of the market's life instead, through the lock window, and every closed minute is handle you do not take.

Adopting this rule deletes that window as an identity ([+25.3% buzzer free-ride under your current rule, measured negative here](/vpm-whitepaper/articles/the-lock-window)), and arrives as a settlement-rule change rather than a venue rebuild: **λ = 0 is the rule you already run**, so [the dial](/vpm-whitepaper/articles/choosing-lambda) is a migration path taken at your own pace, and κ is published policy like a fee table.

A venue that today guarantees or tops up thin pools already bears an expected cost for that guarantee. The same commitment, made as a vintage-0 seed, is floored.

What you give up is stated where it is measured, not hidden: **live late pool odds** and **the secondary-layer obligation**. Both have their own articles.

---

*Next: [What a stake is worth when it arrives](/vpm-whitepaper/articles/the-vesting-yield) — the pricing formula, and the correction that halves it.*


---

# What a stake is worth when it arrives

Every market structure has a pricing content — the thing you are actually buying when you put money in. In an order book it is a price. In an AMM it is a point on a curve. In a classic parimutuel it is a *guess at the closing pool ratio*, which is the whole problem with a classic parimutuel: you commit at a price nobody can observe, because it does not exist yet.

Here the pricing content is one formula, and it is the mechanism's central result.

## The formula

A stake `s` on side `o` accrues the path integral of opposing inflow, weighted by your side's principal as it stands:

```
V  =  s · ∫ dΠ_opp / P_o
```

When the pool's composition `q` — your side's share of the pool — is constant over the interval, that closes:

```
V  =  s · ∫ (1−q) dΠ / (qΠ)  =  s · ((1−q)/q) · ln(Π_T / Π_t)
```

Write `L = ln(Π_T / Π_t)` for the pool's **remaining log growth** after you enter, and

```
y  =  ((1−q)/q) · L
```

for the **vesting yield**. Break-even is `p(1 + y) = 1`, which rearranges into the one line an entrant actually needs:

> **An entry is profitable iff `p/(1−p) > [q/(1−q)] / L`.**

Your odds-belief has to beat the pool's current odds, discounted by how much the pool is still going to grow. That is the whole entry rule.

The published script `vpm-yield.mjs` holds composition exactly constant and measures pure discretization error: **0.005%–0.02% relative at 10,000 steps**, across `q ∈ [0.3, 0.9]` and `L ∈ [0.5, 2]`, converging as O(1/steps). The closed form is right; what it does *not* capture is the subject of the second half of this article.

## Three consequences

**You are priced at the ratio you can see.** Under classic rules break-even is `p > q_T` — you are priced at the **closing** ratio, unknowable when you act. Here you are priced at the ratio **prevailing when you enter**, discounted by remaining growth. This is what the paper means by entry-time price integrity, stated precisely: integrity with respect to *pool composition at entry*. It is **not** integrity with respect to the conditional law of future flow, which is the next section's subject and which the paper is careful not to claim.

**`L = 1` is the natural scale.** If the pool will grow exactly e-fold after you, the whole condition collapses to

```
p > q
```

Enter if and only if you are more bullish than the pool is right now. That is textbook aggregation behaviour, and it falls out of the rule rather than being designed into it. It is also the cleanest intuition available for what the mechanism is doing: an e-fold of growth is the unit in which "beating the current pool" is exactly the right test.

**`L > 1` opens a two-sided band — and this one is uncomfortable.** Both sides are simultaneously positive-EV whenever

```
p/(1−p)  ∈  ( [q/(1−q)] / L ,  L · [q/(1−q)] )
```

which is non-empty exactly when `L > 1`. Early in a fast-growing market, the two implied prices **do not sum to one**.

Say it plainly, because the paper does: **the primary pool ratio is not a probability.** It is a pool composition. Anyone reading a VPM market's displayed ratio as "the market thinks 68%" is reading the wrong object. Where a probability actually comes from is [§8](/vpm-whitepaper#8-the-separation-principle) and [its own article](/vpm-whitepaper/articles/where-the-late-price-comes-from).

## What the formula does not price

Two corrections separate the closed form from a usable entry rule. Both are measured in the published suite rather than gestured at, and both cut the same direction: **the naive number is too optimistic.**

### Composition drift

`q` moves after you enter. When it does, your yield is the path integral, not the closed form.

Under the study's crowd the closed form is **roughly unbiased in aggregate** — mean signed error of −0.03 in yield units — but it is poor pointwise. The median absolute gap between realized and predicted yield is **55% of the prediction**, with a mass point at 100% from positions whose side simply receives no further opposing flow at all.

The right reading: the formula is a pricing *model*, not an oracle. An agent's edge in using it is exactly as good as its forecast of future flow, and nothing more.

### The winner's curse

This is the correction that changes decisions, and it is the one most likely to be skipped by someone implementing the entry rule from the formula alone.

The break-even condition treats your yield and your win event as independent. They are **negatively correlated by construction**:

1. Vesting comes from opposing inflow.
2. Opposing inflow is disproportionately informed.
3. Informed opposing flow concentrates in exactly the histories where your side loses.

You are paid contingent on winning, so the decision-relevant quantity is not `E[y]` but `E[y | win]`. In the paper's crowd model:

| | `E[y|win] / E[y]` |
|---|---|
| overall | **0.48** |
| first-tercile entries | 0.57 |
| late entries | 0.40 |

**Roughly half.** For a first-tercile entrant, the naive break-even belief of 0.337 corrects to **0.473** — an understatement of 13.5 percentage points. If you priced off the naive number you would take a large class of entries you should have refused.

The correction shrinks as opposing flow becomes noise, and vanishes entirely for pure-noise flow. So it is not a universal constant; it is a function of how informed the other side is. The paper's instruction to operators is to treat it as a **floor on required edge, not a refinement.**

And the `L = 1` corollary survives only as the zero-drift, uninformed-flow benchmark. That is what "textbook" was doing in that sentence.

## Why this matters more in thin markets

The formula needs `L̂`, an estimate of remaining growth. The obvious estimator is `L̂ = ln(T/t)` — assume the pool grows in proportion to remaining time.

In thick markets that is roughly fine. In thin ones it is a disaster, and the paper measures it in the regime the mechanism is *for*. In the sparse long-tail arm (arrival rate 0.03, roughly 27 stakes a market), agents using the naive estimate realize **−11.5% per entry post-fee**, while the same beliefs under classic rules earn **+11.2%**.

That is not a small miscalibration. The naive estimator wildly overstates growth precisely where flow is thin, and the winner's-curse correction is not optional there.

The prescription from [§10](/vpm-whitepaper#10-agents): form `L̂` from realized per-class growth curves, never from promotional volume — which, as the wash-trading analysis in P5 shows, a book-dominant party can manufacture at near-zero mechanism cost.

There is one piece of good news on the estimator. When [§13.2](/vpm-whitepaper#132-what-happens-when-the-crowd-responds) iterates `L̂` to self-consistency — replacing it with the realized growth curve of the previous round and repeating — it **converges in four iterations rather than unravelling**. Volume contracts about 20%, the first-third share rises to 50.4%, informed PnL improves from +1.3% to +4.6%, and the fixed-point growth curve sits well below the naive one (at `t = 0.1T`: 1.61 against 2.30). That is simulation evidence, not a theorem, and the paper labels it as such.

## The favourite-longshot side effect

Because `y ∝ (1−q)/q`, the mechanism pays **more per winning dollar for backing the minority side**. That is arithmetic, not a policy choice, and it has a consequence the paper takes seriously in [§14](/vpm-whitepaper#14-limitations).

The payment is information-blind. In any crowd where contrarians skew noisy, the minority premium pays noise more per winning dollar than it pays information. The behavioural study measures exactly this: early **noise** winners land at 2.22×, early **informed** winners at 2.10×.

What the corrected calibration shows, though, is *not* a realized-frequency tilt. At `0.95T`, in the 0.2–0.3 pool-implied bin, outcomes realize at 0.02 under classic rules and 0.03 here (binomial SE ±0.002–0.003); in the 0.7–0.8 bin, 0.99 against 0.97. The visible effect is **compression** — the displayed ratio dragged toward the seed's uninformative 50/50 prior as rational late flow stays out, with thinner tail bins. The measured price anomaly is the widening `|q − p|` gap, not a longshot subsidy.

## Using it

If you are writing an entry rule, the honest version is:

1. Estimate `L̂` from **realized growth curves for this market class**, not from `ln(T/t)` and not from observed early volume.
2. Compute `y = ((1−q)/q) · L̂`.
3. **Halve it**, or apply the class-specific `E[y|win]/E[y]` ratio if you have measured one.
4. Require `p̂ · (1 + y_corrected) > 1 + fee + edge`.
5. Accept that step 1 is where your entire edge lives, and that the mechanism gives you no help with it.

Step 5 is the honest summary of the whole formula. The mechanism prices you off something knowable — that is the improvement over a classic pool, and it is real. It does not price you off something *predictable*.

---

*Next: [Capacity, κ, and the market that freezes](/vpm-whitepaper/articles/capacity-and-kappa) — the second rule, and the failure it creates.*


---

# Capacity, κ, and the market that freezes

Rule 1 — money vests to the opposing book on arrival — is the idea. Rule 2 is what makes it a mechanism instead of a toll booth. This article is about Rule 2: what it fixes, what it costs, and the failure mode that makes it unsuitable for anything but binary markets.

It is the least glamorous part of the design and the part most likely to break a deployment.

## Why Rule 1 alone is broken

Distribute each stake pro-rata over the opposing book, with no ceiling on what a book may absorb. Now consider the *first* position on an empty book. Until a second position joins, it receives **100% of every opposing inflow**. Its return on capital diverges as the position shrinks.

The design-phase measurements, preserved in `vpm-edge-tests.mjs`:

| seeding straddle, per leg | return |
|---|---|
| $50 | +155% |
| $1 | +1,104% |
| one cent | **+82,037%** |

The shipped conformance suite pins the same divergence as P5's **200,001×** single-probe comparison.

So the profit-maximizing strategy under Rule 1 alone is to post dust on every new market and toll the organic flow, supplying no liquidity whatsoever. That is the precise opposite of what a cold-start mechanism is for.

## Rule 2

> Each position grants its own book `κ · s_i` of matching capacity. A stake is accepted only up to the capacity remaining in *every* opposing book; the unmatchable remainder is refused at entry and returned in the same transaction.

`κ` (kappa) is one published constant — a **maximum-odds cap**, the same object every betting exchange already publishes. There is no bucket, no decay schedule, no `ρ`, no residual refund. The paper tried the alternative (a metered bootstrap bounty releasing unmatchable flow to later entrants at up to `ρ×`, decaying with market age) and killed it in [Appendix A.2](/vpm-whitepaper#appendix-a-design-alternatives-and-how-they-fail) for three separate reasons — the sharpest being that its decay is indexed to *clock* time while the risk it prices is *informational*, so a market that resolves informationally early reinstates most of the free-ride. A capacity rule has no schedule and therefore has no schedule to mis-index.

## The placement is the whole trick

This sentence from [§4.1](/vpm-whitepaper#41-the-two-rules) is worth reading twice:

> **Capacity constrains acceptance at the book level, never the distribution**, which stays pure pro-rata.

Why it matters:

**Pro-rata distribution makes return scale-invariant.** A dust position earns exactly the multiple that any capital entering at that moment earns — never more. So there is nothing for dust to dominate. The problem was never the pro-rata split; it was that an empty book could absorb unlimited flow.

**The common multiple is then bounded.** While a book's principal is constant, accepted opposing inflow cannot exceed remaining capacity `κ·P − V`, and each new unit of same-side principal adds at most `κ` more, priced at the enlarged book. Integrating gives a winner's multiple of at most `1 + κ(1 + ln(P_T/P_τ))`. Note that this is **not** a flat `1 + κ` except on a static book — it grows with the book's own growth. Verified across 14,520 positions in adversarial random markets, with zero violations, and an ε-position probing a seeded market returns 9.0–9.7× at κ = 9 across stakes from 1 to 10,000 units.

**Constraining acceptance keeps the O(1) form exact.** The obvious alternative fix — cap each *position* at `κ·s_i` — also closes the dust attack, and it is the wrong one. It binds in **87% of test settlements at κ = 3**, and whenever it binds the allocation stops being pro-rata, which breaks the constant-time accumulator in [§6](/vpm-whitepaper#6-settlement-in-constant-time) and with it the property that a payout is a function of two scalars. That failure is pinned as suite case A4.

## What it costs in a binary market

The favoured side receives **partial fills** once the underdog book is saturated. If you try to put $500 on the obvious side of a thin market, you may get $400 of it. That is an honest liquidity signal, and it is the correct answer: there was only ever $400 of honest exposure available at those odds.

The blocking economics deserve stating precisely, because they are asymmetric.

**It is not free to weaponize** if you do not want the position. To exhaust the headroom another buyer needs, you must stake their side yourself, at full risk. Conformance case P10 pins the squatter eating the loss when the blocked side loses.

**It is free at the margin** if you wanted the exposure anyway. By scale-invariance the blocking capital earns the same multiple whether or not it crowds a rival out (case P10b), and seizing the remaining headroom converts *shared* future vesting into an *exclusive* claim on it.

So under a binding κ, entry becomes a race for headroom among same-side traders. The harm is redistributive between them, and informational — the blocked rival's view never enters the pool. The block-vintage rationing rule removes the *within-block* race; per-account acceptance caps are the venue-level mitigation for the rest, at the cost of sybil pressure.

In practice, at sensible κ, none of this touches ordinary flow. Rule 2 refuses **0.10% ± 0.02 of gross stake at κ = 9**. At κ = 3 it refuses 10.1%, with the decile pattern unchanged. From κ = 12 up, measured refusal is zero to two decimals.

## What it costs in an n-way market — the part that matters

Here the constraint **couples across branches**, and the consequence is not a degradation. It is a kill switch.

Acceptance takes the minimum headroom over *every* opposing book. So entry on any outcome requires positive headroom in each opposing book, which means the **thinnest** book gates entry on every outcome that opposes it.

Two measured consequences:

**Liveness.** A three-outcome market with one unloved branch refuses **97.5% of gross volume at κ = 9** (the pinned skewed-book construction, case P9b). Note how far that is from the balanced n = 3 arm's 1.03% refusal — the balanced number is *not representative*, and the paper says so explicitly.

**Griefing.** A **$450** stake on a side outcome blocked a **$2,000** informed entry entirely (case P9). The same entry clears at κ unbounded.

### The absorbing freeze

The sharper statement, and the reason this section exists as its own article. From [§4.3](/vpm-whitepaper#43-capacity-and-why-the-bounty-is-gone), pinned as conformance case **P9c**:

A symmetric seed `S` leaves every book exactly `S(κ − n + 1)` of headroom. One stake of that size on a single outcome consumes the headroom of the `n − 1` books opposing it. Thereafter **every** outcome has a saturated book among its own opponents, so:

> No entry on any outcome at any size is ever accepted again.

Capacity grows only with a book's principal, and principal can no longer grow, because the stake that would replenish a starved book is itself refused. **The market is not throttled. It is dead, and it cannot be revived from inside the mechanism.**

At the paper's own reference parameters — κ = 9, n = 3, a $50 seed per leg — the trigger is **$350**, and the attacker's own accepted stake is capped at exactly that. Worse, the freeze is reachable at any point in a market's life, not just off the seed: after six ordinary entries the same construction costs **$770** and is equally permanent.

**`n = 2` is the sole exception, and it self-heals** — because the single opposing book is precisely the one a recovering entry needs. That asymmetry, not a difference of degree, is what the paper's conclusion rests on.

## The rule for venues

> **Finite κ is a binary-market instrument.**

Markets with three or more outcomes — and ladders with far-out-of-the-money bands especially, since those are exactly the skewed books P9b describes — should run κ **large or unbounded**.

The obvious worry is that this removes the guardrail. It doesn't, and this is the part worth internalizing: **the mechanism's soundness does not depend on the cap.** What holds it up without κ is the pair that Rule 2 arrived with and that stays:

1. **The mandatory all-outcome seed**, so no empty book can ever exist.
2. **Pro-rata scale-invariance**, so dust earns what any same-moment capital earns and P5's dominance analysis needs no cap at all.

With κ unbounded, thin-book multiples are simply long odds — exactly as in a classic parimutuel. What remains bounded is what actually matters: nobody's accrued claim, and nobody's dominance.

## Choosing κ

κ is **venue policy**, published like a fee table before the market opens, not a mechanism identity. A short decision table:

| market shape | κ | why |
|---|---|---|
| binary, ordinary | 9 | 0.10% refusal, cap present for the adversarial case |
| binary, thin or volatile | 12+ | measured refusal falls to zero; still bounds the dust case via the seed |
| binary, aggressive leverage bound wanted | 3 | 10.1% refusal — you are choosing that trade knowingly |
| **n ≥ 3, any shape** | **large or unbounded** | P9c is absorbing and permanent |
| ladders with OTM bands | **unbounded** | worst case of the skewed-book construction |

One arithmetic constraint that catches implementers: `κ ≥ 1` is a **domain requirement**, not a suggestion. Below it, no symmetric seed passes the clamp at all and creation voids.

## The repair that does not exist yet

There is an obvious fix for the freeze, and the paper states it and then declines to design it ([Appendix B.5](/vpm-whitepaper#appendix-b-toward-an-equilibrium-analysis)): a **matched all-outcome top-up**, obeying the vintage-0 rule with legs as counterparties to each other, restores `c(κ − n + 1)` of headroom per book while consuming `(n − 1)c`. It strictly unfreezes.

Three questions block it, and they are real:

- Does a *second* matched vintage preserve P6? The creation floor's proof relies on the creator owning the entire market at a **unique** reserved vintage.
- Does it preserve P3 for holders who entered between the two matched vintages?
- Who may call it? A creator-only top-up is a dilution lever over standing positions. A permissionless one is a new griefing surface, since the same construction that freezes a market is cheap for whoever wants it frozen.

The shipped settler admits no second matched vintage. Until that analysis exists, **large κ is the answer for n-way markets**, and it is a complete answer — it just is not the elegant one.

---

*Next: [Four ways to make a market](/vpm-whitepaper/articles/four-ways-to-make-a-market) — where this sits among the alternatives.*


---

# Four ways to make a market

Anyone can create a prediction market now. Almost nobody can *make* one.

Creation is a database row. Making is the harder thing: standing between two people who want opposite sides at different times, and being willing to be wrong for a living. Every structure in this space is an answer to that problem, and every answer costs someone something.

This is the map. It is the background for every comparison in the rest of the library, and it is deliberately written so that the vested mechanism looks like one column among five rather than the point of the exercise.

## Order books

**How it works.** Buyers post bids, sellers post asks, the venue matches them. The venue takes no position.

**Who makes the market.** A professional market maker, quoting both sides and earning the spread. On real venues they are there because the venue recruited them, and frequently because the venue pays them liquidity incentives.

**What it costs.** For the venue, incentives and integration. For the market maker, adverse selection — the risk of being picked off by someone who knows more.

**What it buys.** Everything, when it works. Continuous two-sided quotes, a real price, native exit at any moment, and hedging. There is a reason the deepest prediction markets in the world are books.

**Where it stops.** It cannot cold-start. An empty book has no price at all — not a bad price, *no* price. And a professional will not quote regional, niche, or machine-made claims, because the expected spread income does not cover the attention. As the paper puts it, Polymarket's order books are "the deployed existence proof of how far books do reach, and their economics still stop well short of the long tail."

The failure is not gradual. Market ten is fine and market ten thousand has a thirty-point spread or nothing at all.

## Constant-function AMMs

**How it works.** A curve holds reserves of both outcomes and quotes a price off their ratio. Trades move along the curve.

**Who makes the market.** A liquidity provider, who deposits before anyone trades.

**What it costs.** On a *persistent* token pair, an LP's problem is impermanent loss, which is unpleasant but symmetric. On an **expiring event contract** it is worse and structurally so: as information arrives, the pool mechanically rebalances *into the losing side*, and at resolution that side is worth zero. The LP absorbs it. Paradigm's [pm-AMM](/vpm-whitepaper#references) (White & Diamandis, 2024) redesigns the curve specifically for expiring claims and reshapes that loss profile — but it still requires a funded liquidity provider per market, which is the constraint that binds.

**What it buys.** Continuous quotes, exit, hedging, and no matching engine to run. Cheap to deploy, easy to reason about.

**Where it stops.** Someone has to fund the curve for every single market, and their expected return on that funding is negative.

## Scoring-rule market makers

**How it works.** The LMSR (Hanson, 2003) and its relatives quote from a cost function rather than an order book. Price emerges from the rule; the market maker is an algorithm.

**Who makes the market.** Whoever funds the liquidity parameter `b`.

**What it costs.** The worst-case loss is **bounded** at `b · ln n`, which is genuinely elegant — you know your maximum downside before you start. But it is still a subsidy, and it is per market.

**What it buys.** The best pricing theory in the space, with utility and axiomatic characterizations behind it. Continuous quotes, exit, hedging.

**Where it stops.** The bound is a ceiling on the loss, not an escape from it. Multiply `b · ln n` by ten thousand markets and you have a budget, not a mechanism.

The paper is careful here, and it is worth repeating the care: the subsidy need not come from the venue. **Manifold runs creator-funded AMM liquidity at scale.** That puts the scoring-rule family in exactly the same funding position as the vested seed — per-market capital at risk, supplied by whoever wants the market to exist. The comparison is therefore about *incidence*, not about whether a subsidy exists.

## The classic parimutuel

**How it works.** Everyone's money goes into a pot. The event resolves. Winners split the pot pro-rata, less takeout.

**Who makes the market.** Nobody. That is the entire appeal.

**What it costs.** No market maker, no LP, no operator risk, no curve. The oldest structure in betting, running at scale on racetracks for a century.

**What it buys.** It works from the first dollar with no counterparty search, which is exactly the property the long tail needs.

**Where it stops.** Two places.

First, **it pays a flat multiple regardless of when you were right.** Someone who committed an hour out and someone who committed three seconds before the whistle are paid identically, and the second is paid out of the first. Measured: the last decile of entrants captures **13.20%** of the losing pool, and the buzzer strategy has an unconditional expected value of **+25.27% pre-fee**.

Second, and consequently, **venues cope by closing entry before the event** — giving up continuous trading, which was one of the things a market was supposed to be. [That patch has its own article.](/vpm-whitepaper/articles/the-lock-window)

There is also a first-dollar subtlety usually glossed over: a classic pool *accepts* one-sided money, but if the other side never arrives it hands your stake back at 1× less takeout. That is an escrow with a fee, discovered at settlement.

## The fifth column

The vested parimutuel keeps the pool and changes one moment: the losing money is assigned to the opposing positions **when it arrives**, not at resolution — with a matching constraint that keeps the assignment sound.

**Who makes the market.** The seeder, who stakes every outcome in a reserved slot and recovers at least that stake in every branch.

**What it costs.** Fees, carry on locked capital, and resolution risk. Not an expected loss to informed flow.

**What it buys.** First-dollar cold start, exact dilution protection, no lock window, and O(1) settlement that runs on-chain.

**Where it stops.** No native exit, no live late price, no hedging, and — with finite κ — [an absorbing failure in n-way markets](/vpm-whitepaper/articles/capacity-and-kappa).

## The whole map

| | order book | CFMM | scoring rule | classic pool | vested pool |
|---|---|---|---|---|---|
| **funds the first counterparty** | market maker | LP | whoever funds `b` | nobody (escrow) | seeder |
| **their worst case** | adverse selection | rebalance into loser | `−b · ln n` | 1× less takeout | **nominal, every branch** |
| **cold-starts from $1** | no | with a funded LP | with a funded `b` | **yes** | **yes** |
| **continuous late trading** | yes | yes | yes | **no — locks** | **yes** |
| **native exit** | **yes** | **yes** | **yes** | no | no |
| **hedging** | **yes** | **yes** | **yes** | no | no |
| **live late price** | **yes** | **yes** | **yes** | frozen at lock | **degraded** |
| **rewards early risk** | via price | via price | via price | **no** | **yes, exactly** |
| **settlement cost** | off-chain matching | O(1) | O(1) | O(1) | O(1) |
| **per-market capital** | recruited | spent | spent | none | **parked** |

Read the bottom three rows together, because they are the actual argument. The three structures that give you exit, hedging and a live price all require per-market capital that is *spent*. The two that need no per-market capital give up all three. The vested pool moves per-market capital from *spent* to *parked*, and pays for it with those same three things.

That is a trade, not a dominance claim. Which side of it you want depends entirely on which markets you are trying to run — which is [the adoption question](/vpm-whitepaper/articles/should-you-adopt-vpm).

## The five requirements, and two more

The Melee Markets litepaper frames five requirements this design adopts without modification:

- **R1** continuous trading
- **R2** first-dollar cold start
- **R3** no subsidy
- **R4** entry-time price integrity
- **R5** profitable passive bootstrapping

The paper adds two:

**R6. Verifiability.** A permissionless market whose pricing rule cannot be inspected has reintroduced the trusted operator through the back door. A mechanism asking participants to accept its solvency on the strength of the designer's own testing is offering a promise rather than a guarantee, however carefully that testing was done.

This is a pointed requirement and the paper is precise about its target. The Melee litepaper states of its own design that "the PMM's production curve family, parameter schedule, and rebalancing implementation are proprietary and are not disclosed." The disagreement is *only* with that — a non-public curve is not necessarily an unsound one, and the paper makes no claim that it is. The objection is that a permissionless venue's soundness should not require taking the venue's word for it.

**R7. A structural origin for the first dollar.** Floors make early capital safer; they do not summon it. A venue hosting millions of markets needs a participant class for which discovering, pricing, and seeding a brand-new market is cheap and systematic. [That is the agent argument.](/vpm-whitepaper/articles/agents-as-market-makers)

---

*Next: [Against the classic parimutuel](/vpm-whitepaper/articles/vpm-vs-classic-parimutuel) — the comparison where the case is strongest.*


---

# Against the classic parimutuel

This is the comparison where the case is strongest, and it is strongest for an unglamorous reason: **there is almost nothing to change.**

Same pot. Same conservation. Same first-dollar cold start. Same absence of a market maker. Same integer accounting, same fee schedule, same custody, same resolution problem. One moment moves — the losing money is assigned when it arrives rather than at resolution — and a matching constraint arrives with it.

For a venue already running pools, this is a **settlement-rule change, not a venue rebuild**. Everything below follows from that.

## The four things you gain

### 1. The lock window disappears

Your pools close before the event because under the flat-multiple rule, late money free-rides on early money. It is not a policy choice you made badly; it is forced.

The paper measures the strategy you are defending against, on the same triggers under both rules, across 20 seeds × 2,000 markets:

| | your current rule | vested rule |
|---|---|---|
| buzzer snipe, unconditional EV pre-fee | **+25.27% ± 0.33** | **−1.05% ± 0.13** |
| post-fee | +22.76% | −3.03% |
| sniper's multiple when the leader wins | 1.273× | 1.005× |

Under the vested rule the strategy has no target, so the door does not need to be closed. Every minute you currently shut is handle you can take — and it is the *peak-interest* minute, which is the expensive one to be dark for.

The paper's behavioural study puts a number on where the volume goes when the lock comes off. Late pool volume falls from 5.1% to 1.7% of total **without prohibiting anything**, and first-third volume rises from 32.9% to 43.9%.

### 2. Dilution stops, exactly

The lock only ever addressed the buzzer. It did nothing about ordinary late money, which is quietly transferring value inside every one of your markets right now.

Median winning multiple by entry-time decile, same experiment:

| decile | 1st | 3rd | 5th | 8th | 10th |
|---|---|---|---|---|---|
| **classic** | 1.40 | 1.36 | 1.36 | 1.39 | **1.42** |
| **vested, κ = 9** | **2.54** | 1.45 | 1.20 | 1.06 | **1.004** |

The classic row is flat and *rising at the end*. Your earliest and most committed participants — the ones who took the risk when it was real — are paid slightly *less* than the ones who showed up last.

Under a 50%-of-pool late entry:

| | early winners' payouts fall by |
|---|---|
| classic | **13.64% average, 64.4% worst case** |
| vested | **0.19% average, 4.9% worst case** |

And the protection is exact rather than statistical. [P3](/vpm-whitepaper#5-properties) says appending *any* stake to the log leaves every previously accrued claim unchanged. Nothing anyone does after you can reduce what you have already accrued. The residual 0.19% is early winners sharing the flow that arrives *after* the newcomer, which is P3 working as stated.

### 3. Your first dollar gets a floor

You already pay for cold start — pools work from the first dollar — so this reads as a nicety rather than a fix. It is not.

If your venue **guarantees or tops up thin pools** today, you are bearing an expected cost for that guarantee, and it is uncapped in the direction that hurts. The same commitment, made as a vintage-0 seed, is **floored**: [P6](/vpm-whitepaper#5-properties) says a party seeding every outcome recovers at least the total seeded, in every branch, under every continuation.

Verified over 8,910 branches at n = 2 to 4 with random later flow: zero violations, worst case exactly break-even. Over the 40,000-market study, worst case **+10.9% pre-fee, +8.6% after a 2% fee**, and 0 markets of 40,000 settling negative.

Compare the classic column of the same table, where the *same* seeding straddle has a worst case of **−46.8%** and settles negative in **83.4%** of markets. That is what an unfloored guarantee looks like when you measure it.

### 4. Your seeding capital becomes a float

A guarantee budget is consumed. A floored seed is parked and recovered. $50 a side at κ = 9 admits a $400 first entry; ten thousand binary markets at $5 a side is $100,000 of total float against zero mechanism-level expected loss. [The economics are here.](/vpm-whitepaper/articles/venue-economics)

## The three things you give up

An article that stopped there would be a brochure.

### 1. Your late price gets worse

This is the real cost, and it is measured in the direction that hurts.

| Brier score, final 5% of market life | |
|---|---|
| classic, unlocked | 0.148 |
| **classic + lock — what you deploy today** | **0.150** |
| **vested** | **0.174** |

Lower is better. Compare against the row you actually run, not the theoretical ideal. You are paying 0.024 Brier in the last act of every market to buy dilution protection for everyone before it.

The mean absolute gap to the true probability, `|q − p|`, is weakly worse **in every phase**, not just the last: 0.102 / 0.173 / 0.277 / 0.353 against classic's 0.101 / 0.164 / 0.244 / 0.321. If your product surface displays "the market says 68%", you need to know that under this rule that number is a pool composition, not a probability, and [§7's two-sided band](/vpm-whitepaper/articles/the-vesting-yield) proves it can fail to sum to one in a fast-growing market.

A fixed-clock control (one snapshot per market at identical instants across arms) confirms this is not a sampling artifact: 0.167 versus 0.145 unlocked and 0.152 locked.

### 2. You now owe your users a secondary layer

Late information has to go *somewhere*. Under your current rule it goes into the pool, at everyone else's expense. Under this one it has nowhere to go unless you build somewhere.

The paper measures what that layer would deliver: a stylized dealer where each late informed arrival prints at its belief shaded by half a spread produces a composite final-phase Brier of **0.054–0.057 at every spread from 2% to 20%** — better than any pool arm. But the model is deliberately generous (no inventory risk, no quote withdrawal, every informed arrival prints), so it is an **upper bound on what the layer can deliver**, and it says nothing about who quotes it or at what adverse-selection cost.

For short recurring rounds no position market can form inside the round at all, and [§15](/vpm-whitepaper#15-deployment) is explicit that those markets need a **venue-side RFQ cash-out at a published spread** as the degenerate secondary layer. That is a thing you have to build and price, and its quote must never be a mechanical function of the pool ratio or you reintroduce the manipulation you just removed.

### 3. Total volume falls

In the behavioural study: **$2,254 a market against classic's $2,845**, about 21% lower. You are trading volume for time-placement, and if your business model is a percentage of handle, that is the line to model first.

There is a real counterweight — you recover the lock window's handle, which the study's artificial 5% understates badly for real venues that close for hours — but do not assume the two cancel. Model both.

## Nothing at all changes here

Worth listing, because migration risk lives in what people *think* changes:

- **Conservation.** Payouts sum to the accepted pool exactly, in integer units, per branch. Same property you have now, proved the same way.
- **No operator position.** You still take no side and carry no market risk.
- **Fees.** Same schedule, same base, your choice. The reference convention charges on the accepted stake at entry.
- **Custody, KYC, settlement asset.** Untouched.
- **Resolution.** Mechanically unchanged — though the *incentives* around it change in three specific ways, two of them for the worse. [That has its own article](/vpm-whitepaper/articles/resolution-under-vested-claims) and you should read it before shipping.
- **Settlement cost.** O(1) per entry and per claim, so on-chain deployment is no harder than a classic pool's.

## λ = 0 is the rule you already run

This is the migration property, and it is what makes the whole thing tractable.

The paper defines a family: vest a fraction λ of each stake by Rule 1 and settle the remaining `1 − λ` as a classic terminal pool. **λ = 0 is the classic parimutuel** — your current rule, up to Rule 2's 0.10% refusal. λ = 1 is the pure mechanism.

You do not flip a switch. You turn a dial, per market class, at your own pace, and the paper publishes what every point costs:

| λ | last-decile multiple | early-winner dilution | seed straddle: mean / worst / % positive |
|---|---|---|---|
| 0 | 1.416× | 13.5% | −18.0% / −44.4% / 16.6% |
| 0.25 | 1.315× | 9.0% | +27.7% / −30.6% / 70.8% |
| 0.5 | 1.213× | 5.5% | +73.4% / −16.8% / 97.0% |
| 0.75 | 1.112× | 2.6% | +119.0% / −3.0% / >99.9% |
| **1** | **1.004×** | **0.2%** | +164.7% / **+10.9%** / **100%** |

Two warnings on that table. **The creation floor is void at every interior λ** — at λ = 0.5 the seed's measured worst case is −16.8%, and even λ = 0.75 dips to −3.0%. And the lock-window incentive comes back in proportion to `1 − λ`, so a market at interior λ still needs a lock. [Choosing λ has its own article.](/vpm-whitepaper/articles/choosing-lambda)

## Where the comparison goes the other way

Be fair to Pennock. The Dynamic Pari-Mutuel Market (2004) already delivers a monotone floor, protection from same-side dilution, an *approximate* late-entry neutrality, and — crucially — **native exit**. The paper is explicit that its P2 and P3 "should be understood as re-derivations of Pennock's insight under a different rule, not as new results."

What differs here is that the assignment is to identified counterparties at a moment rather than to a share price, so the payout is a pure accounting identity with no price function to choose; the late-entry neutrality is *exact* rather than approximate; and the capacity rule has no DPM analogue.

And the exactness cuts both ways. Because P3 makes accrued claims irrevocable, the last entrant must be paid exactly 1× at λ = 1. So no member of this family with λ > 0 can reproduce the DPM's near-fair current-ratio pricing for late entrants.

**If you need a live late price and native exit more than you need exact claim invariance, prefer the DPM's point in the design space.** The paper says so directly, and so should anyone recommending this.

---

*Next: [Against AMMs and scoring rules](/vpm-whitepaper/articles/vpm-vs-amms).*


---

# Against AMMs and scoring rules

The lazy version of this comparison is "AMMs need a subsidy and we don't." That version is wrong, and the paper says so in as many words:

> The one-line dismissal ("a bounded per-market subsidy is still a per-market subsidy") is too quick.

It is too quick because the subsidy does not have to come from the venue. **Manifold runs creator-funded AMM liquidity at scale** — thousands of user-created markets, each capitalized by the person who wanted it to exist, no professional market makers anywhere. That puts the whole scoring-rule and CPMM family in exactly the same funding position as the vested seed: per-market capital at risk, supplied by whoever wants the market.

So the comparison is not about whether capital is required. It is about **what happens to it**.

## The incidence comparison

| | funded LMSR / CPMM | vested seed |
|---|---|---|
| who commits capital | creator or LP, per market | seeder, per market |
| **expected outcome** | **a loss, chosen deliberately** | **floored at nominal, every branch** |
| worst case | `−b · ln n` (LMSR); rebalance-into-loser (CFMM) | nominal recovery (P6) |
| real costs | that expected loss, plus carry | fees, carry, resolution risk |
| what it buys | continuous quotes, native exit, hedging | none of those three |

The paper's own summary of its claim is narrower than a slogan, and worth quoting because it is the honest form:

> The VPM converts an *expected loss* into a *floored position compensated by later entrants*, which we argue is the allocation that scales to the long tail, not that the per-market cost disappears.

## The apples-to-apples case

Take a Manifold-style creator. They want a market to exist. They post it and fund the CPMM out of their own balance. Informed traders arrive, the curve rebalances into the losing side, and the creator eats it. That is not a bug — it is the LP's job, and the creator accepted it in exchange for the market existing.

Now run the identical person through the vested rule. They post the same capital as a vintage-0 seed across all outcomes. They own every position in the market for one instant, which is what [P6](/vpm-whitepaper#5-properties) needs: every branch pays the whole pool to its owners, and later flow only adds.

Measured over 40,000 settled markets in the paper's crowd model:

| | worst case | markets settling negative | mean |
|---|---|---|---|
| vested seed | **+10.9% pre-fee, +8.6% post-fee** | **0 of 40,000** (95% upper bound 0.0075%) | +164.7% ± 1.3 |
| λ = 0.5 blend | −16.8% | 3.0% | +73.4% |
| classic pool | −46.8% | 83.4% | −18.0% |

**Same person, same slot, same capital, floor instead of a loss.**

Two immediate caveats, both the paper's own. The **mean** is a property of the crowd model and would differ under yours — it is not a yield, and quoting it as an APY misquotes the paper explicitly. The **floor** is a property of the mechanism, and P6's unconditional form is exact: a market with zero subsequent flow returns the seed to the cent, minus fees. That is the number to plan against.

## What the AMM keeps that you are giving up

The three things in that last table row are not decorations.

**A live price at every moment.** An AMM always has a quote, and that quote is a probability. A vested pool's ratio is a *composition*, and [§7's two-sided band](/vpm-whitepaper/articles/the-vesting-yield) proves it need not even sum to one in a fast-growing market. If your product shows a percentage, the AMM's number means what users think it means and yours does not.

**Native exit.** An AMM lets you sell back into the curve. A vested position is transferable in principle, but the mechanism itself provides no exit, and [§8](/vpm-whitepaper#8-the-separation-principle) — the layer that is supposed to supply one — is the paper's own weakest section, currently a measured bound rather than a design.

**Hedging.** A party with real exposure wanting protection late faces **+0% on a win and −100% on a loss** under λ = 1. In an LMSR they buy at 0.93 and are covered. The paper calls this "a genuine loss of function," and notes a second-order problem: hedging demand is a principal *source* of the uninformed flow that the secondary layer needs in order to exist at all.

The prescription for hedging-relevant markets is λ well below 1 — which voids the creation floor and partially re-opens the lock window. There is no setting that gives you all of it.

## Two mechanical advantages worth naming

Beyond the funding argument, two things are simply better and should be claimed as such.

**No curve to choose.** An AMM's behaviour depends on a parameterization someone picked. Payouts here are an accounting identity: your payout is `s · (1 + A_ω(T) − A_ω(τ))` — your outcome's accumulator at resolution minus at entry — and **no participant's payout depends on any other participant's record**. Anyone can recompute it from the public log.

This matters most where the curve is not published. The paper's disagreement with the Melee PMM is precisely and only this: their litepaper states that "the PMM's production curve family, parameter schedule, and rebalancing implementation are proprietary and are not disclosed." A non-public curve is not necessarily unsound, and the paper makes no claim that it is. The objection is that a permissionless venue's soundness should not require the participant to take the venue's word for it.

**O(1) settlement that is actually O(1).** Both structures are constant-time, so this is a tie in principle. It is worth stating anyway because the naive reading of the vested rule is O(m²) — a loop over every standing opposing position on every stake, which at ~5,000 gas per position touched puts a single entry in the tens of millions of gas on a book of a few thousand. The [accumulator form](/vpm-whitepaper/articles/implementing-vpm) collapses that to one scalar update per outcome. The paper verifies exact agreement with the naive reference across 26,458 positions in 800 random markets, in rational arithmetic, including cases where the capacity cap binds.

## pm-AMM, Azuro, Overtime

Paradigm's **pm-AMM** is the closest thing to a direct answer to the CFMM problem: a curve designed specifically for expiring claims, which reshapes the LP's loss profile rather than pretending it away. The paper's response is not that the curve is wrong. It is that pm-AMM "still requires a funded liquidity provider per market, which is the constraint that binds here." If your bottleneck is LP loss *shape*, pm-AMM is the better answer. If your bottleneck is LP *existence* at market ten thousand, it is not.

**Azuro** and **Overtime** are deployed on-chain pooled designs whose liquidity providers likewise fund the quote. The paper's summary of the whole landscape is one sentence, and it is the empirical shape of the problem rather than an argument: *none of these deployed answers is subsidy-free.*

## Who should switch, and who should not

**Strong fit: creator-funded market venues.** If your creators already pay per market and absorb the loss, you are offering them the same slot with a floor instead. The funding argument is unambiguous, the audience already accepts per-market capital as normal, and the migration is a settlement change rather than a business-model change.

**Weak fit: anything where users trade in and out.** If your product is people scalping positions and taking profit before resolution, you are removing the core interaction. This is not a tuning problem; the mechanism has no exit, and [§8](/vpm-whitepaper/articles/where-the-late-price-comes-from) is a bound rather than a shipped layer.

**Weak fit: hedging venues.** See above. λ < 1 is the prescription, and at interior λ you have given up the floor that made the comparison favourable in the first place.

**No fit at all: markets where the displayed price is the product.** If people come to you *for the number*, the mechanism degrades exactly that number, by a measured 0.174 against 0.150.

## The honest bottom line

Against AMMs and scoring rules, the vested rule wins on one axis and loses on three:

- **Wins:** the per-market capital stops being an expected loss. Nothing else in the space does that.
- **Loses:** no live price, no exit, no hedge.

Which is why the venues it fits are the ones where all three of those were already unavailable — the long tail, where no LP was going to fund a curve anyway, and where the actual alternative is not an AMM but *no market at all*.

---

*Next: [Against order books](/vpm-whitepaper/articles/vpm-vs-order-books).*


---

# Against order books

Order books are the best market structure ever invented, and this mechanism is not trying to replace them.

That should be the opening line of any honest comparison, because the alternative — a pooled settlement rule arguing that it beats a deep CLOB on the CLOB's own ground — is not a serious position. Where books work, they work better than anything else, and the paper says so: Polymarket's order books are "the deployed existence proof of how far books do reach."

The argument is about where they stop.

## What a book gives you that this cannot

Four things, and all four are load-bearing for a real trading product.

**A price.** Not a composition, not a ratio — an actual, continuously updated price, produced by two people willing to transact at it. It is a probability in the sense users assume it is. A vested pool's ratio is a pool composition, and [§7's two-sided band](/vpm-whitepaper/articles/the-vesting-yield) proves it need not sum to one.

**Exit.** You can sell. At any moment, at some price. Under the vested rule you are in until resolution unless a secondary layer exists, and the paper's own section on that layer is a measured bound rather than a design.

**Hedging.** A party with exposure can buy protection at 0.93 and be covered. Under λ = 1 they face +0% on a win and −100% on a loss. The paper calls this a genuine loss of function.

**Scalping.** The entire day-trading interaction. Take a view, be right in twenty minutes, book the profit. There is nothing here for that trader at all — [P4](/vpm-whitepaper#5-properties) is specifically the rule that makes late pool entry pointless.

If your users come for those, this is a downgrade. Not a trade-off with compensations; a downgrade.

## Where books stop

The failure is not gradual and it is not about quality. It is about *existence*.

An empty book has **no price**. Not a bad price — none. And a professional market maker will not quote regional, niche, or machine-generated claims, because the expected spread income does not cover the attention it costs to price them.

So a book venue's reach is bounded by how many markets are worth a market maker's time, and the venue can extend that boundary by paying for it. Liquidity incentives are the standard tool, and they are **spent money**. The long tail's empty books are what unspent looks like.

The paper's framing of this is the whole reason the mechanism exists ([§1](/vpm-whitepaper#1-introduction)):

> The problem this paper addresses is narrower and it is a problem of the long tail: in the ten-thousandth market there is no book to sell into, no market maker willing to quote, and no operator able to subsidize.

Note the concession embedded in that sentence: *in a deep market, being early already pays.* You buy at 20¢ and sell at 80¢. That is what a price is for. The mechanism's entire reward gradient is solving a problem that a working book does not have.

## Polymarket

Polymarket runs a CLOB with off-chain matching and on-chain settlement. Its head markets are deep, tightly quoted, and staffed by real market makers. There is no version of this comparison where swapping that for a pool is an improvement for those markets.

The narrower pitch is about the other end of the catalogue: **the tail is thin, and a pooled surface is the only structure that makes a market nobody will quote actually tradeable.** That is a complement to a book, not a replacement for one — a second surface for markets that fail the market-maker-attention test, sitting alongside the book rather than instead of it.

There is one secondary point worth making without overselling it. Off-chain matching is a trust surface: you take the venue's word that the match happened as reported. The vested rule's payout is recomputable by anyone from the public log, because each position's payout is a function of two scalars — its outcome's accumulator at entry and at resolution — and **no participant's payout depends on any other participant's record**. That is [R6](/vpm-whitepaper/articles/four-ways-to-make-a-market) in its sharpest form.

Whether a venue's users care about that is a separate question, and mostly they do not. It is a real property, not a compelling sales argument.

## Kalshi

*The whitepaper does not discuss Kalshi; what follows is the general shape of the comparison rather than anything the paper measures.*

Kalshi is a CFTC-regulated exchange running an order book with a designated market-maker structure, real-money contracts, and a filed rulebook. Every part of that sentence is an obstacle to adopting a novel settlement rule:

- **The head, not the tail.** Its markets are the ones books serve well. The cold-start problem is not its binding constraint.
- **Market makers exist and are structural.** The participant class this mechanism exists to replace is already there, by design.
- **The product is continuous two-sided quotes with exit.** That is the exact list of things λ = 1 gives up.
- **The settlement rule is regulated.** Changing how contracts settle at a designated contract market is a rulebook matter with a regulator attached, not an engineering decision.

The realistic answer for a venue of that shape is **no**, and it is no for reasons that have nothing to do with whether the mechanism is sound.

## Where the pooled rule actually competes

Not against a working book. Against **the absence of a market**.

The comparison that matters is not "vested pool versus Polymarket's BTC market." It is "vested pool versus this market does not exist, because no market maker will quote a 15-minute round on a mid-cap token's price direction, and no LP will fund a curve for it."

In that comparison the book is not an option that was rejected. It was never on the table.

This is also why the two structures do not really compete for the same venue. A book venue's growth problem is *reach*: how far down the catalogue can I extend before the economics break? A pooled venue's growth problem is *depth*: my markets all exist, and most of them are thin. Those are different businesses with different bottlenecks.

## A summary that does not flatter either side

| | order book | vested pool |
|---|---|---|
| live price that is a probability | **yes** | no — a composition |
| exit before resolution | **yes** | no (needs a layer above) |
| hedging | **yes** | no at λ = 1 |
| scalping | **yes** | none by design |
| works at market #10 | **yes, well** | yes |
| works at market #10,000 | **no** | **yes** |
| per-market capital | recruited MM, often paid | seeder, floored |
| price when nobody quotes | none | a pool ratio, degrading late |
| payout recomputable by anyone | depends on the venue | **yes, from two scalars** |
| rewards early risk-bearing | via price movement | **as an identity** |

Read the two middle rows together. Everything a book does better, it does better *where a book exists*. The mechanism's whole claim is about the rows below that line.

## The honest verdict

Against order books, this loses on every axis a trader cares about and wins on exactly one: it produces a functioning market where a book produces nothing at all.

A venue running deep books should not adopt it for those books. A venue running deep books and staring at a dead tail might run it *beside* them.

And a venue that has no books because it never had market makers — which is most venues, and every venue with more markets than staff — is not choosing between these two structures at all.

---

*Next: [Should your venue adopt this?](/vpm-whitepaper/articles/should-you-adopt-vpm) — the decision, with the disqualifications first.*


---

# Should your venue adopt this?

Most venues should not, and it is more useful to start there.

This mechanism buys one thing — a settlement rule that pays for early risk-bearing and needs no market maker — and pays for it with three: no exit, no live late price, no hedging. If you need any of those three, no amount of tuning gets them back, because they are not missing features. They are the consideration.

So: the disqualifications first.

## Do not adopt it if…

### 1. Your users trade in and out

Scalping, taking profit early, cutting a loser, rolling a position — all of it is gone. There is no exit in the mechanism. Positions are transferable in principle, but nothing in the rule provides a buyer, and the layer that would ([§8](/vpm-whitepaper#8-the-separation-principle)) is a measured bound rather than a shipped design even in the paper's own account of it.

This is the single most common disqualification and the one most often rationalized away. Do not.

### 2. The displayed price is your product

If people come to you for the number — if your market page's headline is "73%" and that number is the thing being consumed, syndicated, or cited — this mechanism degrades exactly that number, on purpose, and the degradation is measured:

| Brier score, final 5% | |
|---|---|
| classic + lock (deployed baseline) | 0.150 |
| **vested** | **0.174** |

The mean absolute gap to true probability, `|q − p|`, is weakly worse in **every** phase, not just the last. And [§7's two-sided band](/vpm-whitepaper/articles/the-vesting-yield) shows the ratio is not a probability at all in a fast-growing market — the two implied prices need not sum to one.

### 3. You serve hedgers

A party with real exposure wanting protection late faces +0% on a win and −100% on a loss. In a book or an LMSR they buy at 0.93 and are covered. The paper's prescription for hedging-relevant markets is λ well below 1 — but interior λ **voids the creation floor** (measured worst case −16.8% at λ = 0.5) and re-opens the lock window in proportion to `1 − λ`. A hedging market under this family is an operator-seeded or floor-waived market, and the reason to adopt has evaporated.

### 4. Your markets are long-dated

Capital is locked from entry to resolution. At 4% and six months, the 2% carry hurdle is **the same order as the entire observed late-tercile win-conditional yield** (median 2.7%) and exceeds the median final-decile winner's post-fee return. It applies to the seed too, which turns the nominal floor into a *real* loss on slow markets.

The paper's own summary: **λ = 1 is a short-horizon mechanism.**

### 5. Your markets are mostly n-way, and you want a finite κ

With three or more outcomes, one stake of `S(κ − n + 1)` renders the market **permanently un-enterable on every outcome** — an absorbing state with no in-mechanism recovery, reachable at any point in the market's life. At the reference parameters (κ = 9, n = 3, $50 seed) the trigger is **$350**.

This one is survivable: run n-way markets at large or unbounded κ, where soundness rests on the seed and scale-invariance instead. But if you had a specific reason to want a tight leverage cap on multi-outcome markets, you cannot have it. [Details.](/vpm-whitepaper/articles/capacity-and-kappa)

### 6. You are a regulated exchange with a filed rulebook

Changing how contracts settle is a regulatory matter, and the venues in that position generally run books at the head of the market, where the cold-start problem they would be solving does not exist.

## Adopt it if…

### 1. You already run classic parimutuel pools

The strongest case in the paper, and it is strong because there is almost nothing to change. Same pot, same conservation, same cold start, same lack of a market maker. **λ = 0 is the rule you already run**, so the dial is a migration path rather than a rebuild, and κ is published policy like a fee table.

You have already paid for cold start. You are paying instead at the other end, through the lock window, where the free-ride you are defending against measures **+25.27% pre-fee**. That window deletes as an identity. [The full case.](/vpm-whitepaper/articles/vpm-vs-classic-parimutuel)

### 2. Your creators fund per-market liquidity today

If you are Manifold-shaped — creators capitalize their own markets and absorb the loss — you are offering the same person the same slot with a **floor** instead of an expected loss. Worst case over 40,000 markets: +10.9% pre-fee, +8.6% after a 2% fee, 0 markets settling negative. Against a classic straddle's −46.8% worst case and 83.4% negative.

Your users already accept per-market capital as normal, which is the hard part of the sell, and you skip it.

### 3. Your bottleneck is market count, not market depth

If the reason you have 400 markets instead of 40,000 is that each one needs someone's attention, this is the mechanism aimed at your problem. Seeding is a **legible job**: a floor, a closed-form position value, and economics that depend on forecastable quantities (flow volume and balance) rather than on out-quoting a professional. [The long-tail argument.](/vpm-whitepaper/articles/the-long-tail-ceiling)

### 4. You run short recurring rounds

Fifteen-minute price-direction rounds, hourly settlements, that shape. No book can form, no LP will fund a curve, and no position market can form inside the round either — so you were never getting exit anyway, and the mechanism's biggest cost is one you had already paid.

The paper puts these markets third in its adoption order, with one requirement attached: a **venue-side RFQ cash-out at a published spread** as the degenerate secondary layer, whose quote must never be a mechanical function of the pool ratio.

## The three questions that decide it

If you want to skip the lists:

**1. Can your users currently sell before resolution, and would they mind stopping?**
If yes and yes — stop here.

**2. Is your displayed probability consumed as a probability by anyone outside your product?**
If yes — you are paying 0.174 against 0.150 for something you sell. Probably stop.

**3. Is your binding constraint "we can't make enough markets" or "our markets aren't deep enough"?**
Only the first one is the problem this solves.

## Partial adoption is the normal answer

Nobody has to flip a venue. The dial exists precisely so this can be done per market class:

| your market class | setting | rationale |
|---|---|---|
| short recurring rounds | **λ = 1**, κ = 9 | no exit was available anyway; lock window deleted |
| binary event markets, days-to-weeks | λ = 1 or 0.75 | check carry against duration |
| hedging-relevant markets | λ well below 1 | accept the floor is void |
| n-way ladders | λ = 1, **κ unbounded** | P9c is absorbing |
| long-dated markets | leave as they are | carry eats the yield |
| your deep flagship markets | leave as they are | they already work |

[Choosing λ in detail.](/vpm-whitepaper/articles/choosing-lambda)

## The order of adoption

If you decide yes, the paper prescribes an order, least-recoverable risk last ([§15](/vpm-whitepaper#15-deployment)):

1. **Paper first.** Flow-vesting settlement in a paper-money twin, behind your existing payout authority.
2. **The secondary layer, where it can exist.** For markets long enough for a position market to form, ship transferable positions and the cash-out affordance **before real money** — §8 is a precondition, not a follow-up.
3. **Real money where P4 bites**, with the degenerate secondary layer built in: short recurring markets at λ = 1 plus the RFQ cash-out.
4. **Creator-seeded permissionless creation**, with vintage 0 as the first rung of the resolution bond and [§12's timeout-forfeiture and scaling-bond rules](/vpm-whitepaper/articles/resolution-under-vested-claims) in place from day one.

Step 2 is the one people skip, and it is the one the paper is most insistent about.

## What you owe your users if you do it

Three disclosures, none optional:

- **The displayed ratio is not a probability.** Say so on the surface, not in a FAQ.
- **There is no exit unless you built one.** If you built an RFQ vault, publish its spread; if you did not, say there is no exit.
- **The published parameters.** κ, λ, the fee schedule and its base, the minimum stake, and the residue owner are all venue policy, and the paper says they should be committed on-chain per market, before it opens.

And one more, from [§14](/vpm-whitepaper#14-limitations), which venues will not enjoy: **featuring a market transfers expected value toward its earliest vintages.** If you promote markets, you are moving value to whoever seeded them, and that should be disclosed rather than discovered.

---

*Next: [Migrating a pool venue, step by step](/vpm-whitepaper/articles/migrating-a-parimutuel-venue).*


---

# Migrating a pool venue, step by step

You run parimutuel pools. You have decided the [lock window](/vpm-whitepaper/articles/the-lock-window) and the [flat multiple](/vpm-whitepaper/articles/vpm-vs-classic-parimutuel) are costing you more than they save. This is the path from here to there.

The good news is structural: **λ = 0 is the rule you already run.** You are not replacing a settlement engine, you are moving a parameter that currently sits pinned at one end of its range. The bad news is that two things must be built before real money touches the far end, and skipping either is how this goes wrong.

## Stage 0 — Decide the four published parameters

Before any code, decide what you will publish per market, because these are venue policy rather than mechanism and they belong in your rulebook next to the fee table:

| parameter | what it is | sane default |
|---|---|---|
| **κ** | capacity coefficient — a maximum-odds cap | 9 for binary; **unbounded for n ≥ 3** |
| **λ** | vesting fraction | start at 0, end at 1 for the classes that want it |
| **fee base** | the reference convention charges on the *accepted* stake at entry | your current base, unchanged |
| **residue owner** | who claims the fixed-point rounding residue | your fee sink |

Two hard constraints. **κ ≥ 1 is a domain requirement** — below it no symmetric seed passes the clamp and creation voids. And the residue **must have a named owner fixed before the market opens**; an unassigned residue is funds nobody can withdraw.

The paper's recommendation is that all of these be committed on-chain per market, because [§14](/vpm-whitepaper#14-limitations) is explicit that verifiability of the settlement rule does not extend to trusting that you applied the parameters you said you would.

## Stage 1 — Paper money, behind your existing payout authority

Run flow-vesting settlement in a paper twin. Not a testnet fork, not a staging environment — a live paper surface with real users making real decisions, settling behind whatever your production payout authority is today.

**What you are checking.** Not correctness; the [conformance suite](/vpm-whitepaper/articles/implementing-vpm) does that. You are checking behaviour: does volume actually migrate early, do your users understand a partial fill, does anyone complain that they cannot sell, and does your support load change shape.

**What to instrument from day one:**

- Volume share by phase of market life. The study's shift is 32.9% → **43.9%** into the first third, with late pool volume collapsing 5.1% → 1.7%. If yours does not move, the incentive is not reaching your users and something in the surface is wrong.
- Refusal rate. At κ = 9 the study refuses **0.10% ± 0.02** of gross stake. If yours is materially higher, your markets are thinner or more skewed than the study's and κ needs raising.
- Realized growth curves per market class. You will need these in Stage 3 and they take time to accumulate. `L̂ = ln(T/t)` is the naive estimator, and in thin markets it is catastrophically optimistic — agents using it realize **−11.5% per entry** in the sparse arm.

## Stage 2 — Build the exit before you need it

This is the stage that gets skipped, and the paper is blunt that it is a **precondition, not a follow-up.**

Your current pools have no exit either, so it is tempting to treat this as no regression. It is not, and the reason is the late price. Under your current rule, late information enters the pool — badly, at everyone else's expense, but it enters, and your displayed ratio updates. Under λ = 1, informed late money has no reason to enter at all, so **the ratio goes stale exactly when it matters most.**

Two shapes, depending on market duration.

**Markets long enough for a position market to form.** Ship transferable positions and a cash-out affordance. A position is four numbers — outcome, principal, entry accumulator, vintage — so it trades cleanly, and its win-case payout splits into a *floor tranche* (principal plus accrued claims: a digital option with a known payout) and a *flow tranche* (whatever vests later). A holder can keep conviction and sell activity, or the reverse.

**Short recurring rounds.** No position market can form inside a fifteen-minute round, so the paper specifies the degenerate form: a **venue-side RFQ cash-out at a published spread**, and it attaches one structural requirement that is easy to get wrong —

> The vault's quote must never be a mechanical function of the current pool ratio.

If it is, the manipulation the mechanism disarms comes straight back through the vault, at near-zero cost for a party that dominates both books. The quote must price from your own model over wash-excluded flow and off-market inputs.

The honest framing: this vault is a **designated adverse-selection sink**. It will widen or decline exactly when information is most valuable. The paper does not pretend to have solved its pricing, and lists it as an open problem. It is the acknowledged cost of this stage, and you should staff it accordingly.

What you get for building it is measurable. A stylized dealer where every late informed arrival prints at its belief shaded by half a spread produces a composite final-phase Brier of **0.054–0.057 at every spread from 2% to 20%** — better than any pool arm, locked or not. That is an upper bound on what the layer can deliver, not a forecast of your vault's performance, but it establishes that the information is there and a thin layer is enough to surface it.

## Stage 3 — Real money, where P4 bites hardest

Start where the mechanism's cost is lowest and its benefit highest: **short-duration recurring markets at λ = 1**, with the RFQ cash-out from Stage 2 built in.

Why these first:

- Carry is negligible over fifteen minutes, so [the carry limitation](/vpm-whitepaper#14-limitations) does not bite.
- No exit existed anyway, so you are not taking anything away.
- The lock window on these markets is proportionally enormous — a 60-second close on a 15-minute round is 6.7% of the market's life.
- Binary, so finite κ is safe.

**Turn the dial rather than flipping it** if you want a gentler path. The λ table, from 20 seeds × 2,000 markets:

| λ | last-decile multiple | early-winner dilution | seed straddle: mean / worst / % positive |
|---|---|---|---|
| 0 | 1.416× | 13.5% | −18.0% / −44.4% / 16.6% |
| 0.25 | 1.315× | 9.0% | +27.7% / −30.6% / 70.8% |
| 0.5 | 1.213× | 5.5% | +73.4% / −16.8% / 97.0% |
| 0.75 | 1.112× | 2.6% | +119.0% / −3.0% / >99.9% |
| **1** | **1.004×** | **0.2%** | +164.7% / **+10.9%** / **100%** |

**Two things to know before you park at an interior value.**

The creation floor is **void** at every λ < 1. Not weakened — void. At λ = 0.5 the seed's measured worst case is −16.8%, and even λ = 0.75 dips to −3.0%. If your seeding programme depends on the floor, interior λ is not a halfway house, it is a different deal.

The lock-window incentive returns in proportion to `1 − λ`. A buzzer snipe at interior λ pays `λ + (1−λ)·M`. So a market at λ = 0.5 still needs a lock, and you have given up the floor without having bought the deleted window.

There is one pleasant surprise in the table: degradation is **monotone but not uniform**. The late entrant's reward is exactly linear in λ, while measured mean dilution sits *strictly below* the linear reading at every interior λ. The dial protects early capital better than a naive reading suggests.

## Stage 4 — Permissionless creation

Open vintage 0 to whoever wants to take it, with the resolution rules in place **from day one** rather than added later. [§12's requirements](/vpm-whitepaper/articles/resolution-under-vested-claims) are not optional hardening:

- **Freeze the accumulator at a resolution timestamp fixed at creation** (or, for event-driven markets, at the earlier of a fixed outside date and the first bonded attestation). Without this, a resolver holding a winning position has a weakly dominant incentive to *delay*, because every extra opposing dollar vests to them at no risk. That incentive is new relative to your classic pools, where delay dilutes the winner.
- **Timeout forfeits the resolver's seed.** A resolver on the losing side of a large vested payout has a strictly profitable strategy of never resolving. Forfeiture makes the stall cost 2× seed.
- **Fallback resolution is permissionless**, with a **bonded void declaration** through the same escalation path so an honest creator of a genuinely unresolvable market is not punished for ambiguity.
- **Escalation bonds scale with the disputed payout.** The seed is fixed at creation while what it secures grows: the study's $100 seed against a $2,254 mean pool is 4.4%, and the ratio only falls as a market succeeds.
- **Display the resolution premium live.** Because the winning seed leg farms the *losing* flow, the seed always pays more in the branch with more opposing volume. The gap is two accumulator reads and it is a publicly computable bribe. Displaying it converts it into a bond at risk.

## Two things that will surprise your team

**Volume falls.** In the behavioural study, **$2,254 a market against classic's $2,845** — about 21% lower. You are trading volume for time-placement. You recover some of it from the deleted lock window, and for a real venue that closes for hours rather than 5% of a market's life that recovery is much larger than the study shows. Model both; do not assume they cancel.

**Your trust metrics stop working.** [P5](/vpm-whitepaper#5-properties) shows that a party dominating both books of a market can print wash volume at near-zero mechanism cost — the donation is `(1−f)`-scaled in the washer's own share of the opposing book, so for a book-dominant participant the mechanism-level cost falls toward zero and the binding cost is your fee. In exactly the whale-seeded regime that [§9](/vpm-whitepaper#9-incentives) flags as the most likely real-world drift, **headline volume stops being evidence of anything.**

The paper's consequence: creator track-record metrics must **exclude self-vested flow** — flow whose vesting lands on positions of the same funding cluster, which is identifiable from the public log — and weight bonded, aged, distinct counterparties instead. Distinct-counterparty counting alone is sybil-purchasable, and volume alone is worse.

## What does not change

- Conservation, per branch, in integer units.
- Your operator position: none, same as now.
- Fees, custody, KYC, settlement asset.
- Resolution mechanics (the *incentives* change; the oracle does not).
- Settlement cost: O(1) per entry and per claim.

---

*Next: [What it saves, what it costs](/vpm-whitepaper/articles/venue-economics) — the numbers to put in the model.*


---

# What it saves, what it costs

Every article in this library that says "the seed is floored" is making an accounting claim, and accounting claims should be written out as line items. This one does that.

Two warnings before the numbers. Every figure below is from the paper's own simulations, and every simulated return is **a property of the stated crowd model, not a projection**. And the paper is explicit on one point in particular: the seeding return is payment for cold-start risk-bearing, **not a yield**, and quoting it as an APY misquotes the paper.

What survives model choice is the **floor rows** and the identity-based claims. Those are mechanism properties. Everything else is a measurement of one simulated crowd.

## The saving that is actually structural

### Per-market capital moves from *spent* to *parked*

This is the whole economic argument, and it is one line:

> A subsidy budget is consumed. A floored seed is a revolving float.

Compare the two balance sheets for a venue that wants ten thousand markets to exist.

**Subsidy model** (LMSR, CPMM, market-maker incentives): you allocate `X` per market, expect to lose some fraction of it to informed flow, and that fraction is gone. Ten thousand markets means ten thousand times the expected loss. The number scales with your catalogue and never comes back.

**Float model** (vested seed): you allocate `S` per leg, park it for the market's life, recover it in every branch, and redeploy. The number scales with your *concurrent* market count and your average market duration, not with your lifetime market count.

The arithmetic is small enough to be uncomfortable:

| | |
|---|---|
| symmetric seed per leg | `S` |
| first-vintage headroom opened per book | `S(κ − n + 1)` |
| at S = $50, κ = 9, binary | **$400 of first-entry capacity** |
| 10,000 binary markets at $5 a side | **$100,000 total float** |
| mechanism-level expected loss | **zero** |

Against that, the real costs of the seed are three, and none of them is an expected loss to informed flow: **fees**, **carry on locked capital**, and **resolution risk**.

### Small seeds are correct, not just cheap

The instinct is to seed heavily so markets look liquid. [§9](/vpm-whitepaper#9-incentives) measures what that does:

| seed per leg | ordinary early winners' multiple |
|---|---|
| $50 | **1.70×** |
| $5,000 (≈3× the organic pool) | **1.09×** |

The seeder sits at its floor either way. So over-seeding crowds out exactly the participants you were trying to attract, and the policy that costs least is the policy the mechanism prefers. That is an unusual alignment and worth taking advantage of.

### The seed is also your resolution bond

Not a separate line item. Vintage 0 doubles as the first rung of the escalation path in [§12](/vpm-whitepaper#12-resolution), which means the capital is doing two jobs. It also means it is **slashable** on adverse escalation rulings, which is what converts the direction premium from a bribe into a bond at risk.

### Measured seeding outcomes

Creator seed, matched vintage 0, 20 seeds × 2,000 markets:

| | vested | λ = 0.5 blend | classic |
|---|---|---|---|
| **worst case, 40,000 markets, pre-fee** | **+10.9%** | −16.8% | −46.8% |
| **worst case, post-2%-fee** | **+8.6%** | n/a | n/a |
| **markets settling negative** | **0 of 40,000** (95% UB 0.0075%) | 3.0% | 83.4% |
| mean | +164.7% ± 1.3 | +73.4% | −18.0% |

Read the floor rows, not the mean. The mean is crowd-model-dependent; the floor is the mechanism. And P6's unconditional form is exact: **a market with zero subsequent flow returns the seed to the cent, minus fees** — so in a market that attracts nothing at all, the seed returns −2% at a 2% fee.

## The saving that depends on your current lock

Every minute your pools are closed is handle you do not take, at the peak-interest minute. Deleting the lock recovers it.

The study's number understates this badly for a real venue. Its lock arm closes only the final 5% of a market's life and loses **5.0% of total volume** relative to unlocked. Real venues close for minutes or hours before an event, in a period where arrival rates are at their highest, so your recovery is your own number and you should compute it from your own closed-window traffic rather than from 5%.

Set against it: total volume in the study is **$2,254 a market under the mechanism against classic's $2,845**, about 21% lower, because rational late entry stops.

| | classic (no lock) | classic + lock | vested |
|---|---|---|---|
| first third | 32.9% | 34.6% | **43.9%** |
| middle third | 33.3% | 35.1% | 34.7% |
| 67–95% | 28.7% | 30.2% | 19.7% |
| final 5% | 5.1% | 0.1% | **1.7%** |
| **total $/market** | **2,845** | **2,702** | **2,254** |

If you charge on handle, model both directions. Volume falls; the window you recover is real; whether they net positive depends on how long you currently close for and how much of your traffic sits inside that window.

## The costs, priced

### Carry, which is a real loss on slow markets

Capital is locked from entry to resolution, and this applies to the seed as well as to entrants.

At 4% and six months, the 2% hurdle is **the same order as the entire observed late-tercile win-conditional yield** (median 2.7%) and **exceeds the median final-decile winner's post-fee return**. On the seed side, carry turns the nominal floor into a real loss.

The paper's conclusion is unhedged: **λ = 1 is a short-horizon mechanism.** If your markets run for months, the floor is nominal only, and you should price accordingly.

### The late price, which you are selling if you display it

0.174 final-phase Brier against the deployed lock baseline's 0.150. If your product surfaces a probability that anyone consumes as a probability — syndicated, cited, used by another product — you are degrading a thing you distribute. See [the disqualification list](/vpm-whitepaper/articles/should-you-adopt-vpm).

### The secondary layer, which is a build and a book

For long-enough markets this is transferable positions plus a cash-out affordance. For short recurring rounds it is a **venue-side RFQ vault at a published spread**, and that vault is a book you are running:

- It is a designated adverse-selection sink. It will be picked off precisely when information is most valuable.
- Its quote must **not** be a function of the pool ratio, or the manipulation the mechanism disarms returns through the vault at near-zero cost for a book-dominant party.
- So it must price from your own model over wash-excluded flow and off-market inputs.

The paper lists the vault's adverse-selection pricing as an open problem and calls it "the acknowledged cost of this step." Budget engineering and risk staff, not just a feature.

### Resolution risk, now with sharper edges

The mechanism does not create resolution risk, but it changes its shape in ways that cost money to defend against ([full article](/vpm-whitepaper/articles/resolution-under-vested-claims)):

- **Delay farming** — a resolver holding a winning position profits from delay. Fixed by freezing the accumulator at a timestamp set at creation.
- **Stall-into-void** — a resolver on the losing side of a large vested payout profits from never resolving, and because accrued claims are public they know exactly what it saves them. Fixed by seed forfeiture plus permissionless fallback plus a bonded void declaration.
- **The direction premium** — the seed always pays more in the branch with more opposing volume, and the gap is publicly computable. Mitigated by displaying it live and making vintage 0 slashable.

None of these is free to implement, and all three are required before permissionless creation.

### Your volume metric stops meaning anything

Not a cost in dollars, a cost in decision quality. A participant who dominates both books of a market can print wash volume at near-zero mechanism cost — the donation is `(1−f)`-scaled in their own share of the opposing book — so in exactly the whale-seeded regime [§9](/vpm-whitepaper#9-incentives) flags as the most likely drift, headline volume is manufacturable.

Consequence: track records must exclude **self-vested flow** (identifiable from the public log) and weight bonded, aged, distinct counterparties. If your growth reporting or your creator ranking runs on volume, both need rebuilding.

## The one-page summary

| | direction | size | certainty |
|---|---|---|---|
| per-market capital: spent → parked | **save** | scales with catalogue | **mechanism property** |
| lock-window handle recovered | **save** | your own number | depends on your current window |
| seed doubles as resolution bond | **save** | one capital line, two jobs | structural |
| over-seeding no longer tempting | **save** | 1.70× vs 1.09× | measured |
| total volume | **cost** | ≈ −21% | crowd-model measured |
| carry on locked capital | **cost** | 2% at 4%/6mo — exceeds late-decile return | arithmetic |
| late forecast quality | **cost** | 0.174 vs 0.150 Brier | measured |
| secondary layer / RFQ vault | **cost** | a build plus a risk book | open problem in the paper |
| resolution hardening | **cost** | three specific defences | required, not optional |
| volume as a trust metric | **cost** | rebuild it | P5 |

The shape of the trade: **you stop spending per-market capital and start spending on a layer above the pool.** Whether that is a good deal depends entirely on how many markets you want to run — because the first cost scales with your catalogue and the second one does not.

---

*Next: [Choosing λ, market class by market class](/vpm-whitepaper/articles/choosing-lambda).*


---

# Choosing λ, market class by market class

λ is the vesting fraction — the share of each stake that vests to the opposing book on arrival. λ = 0 is the classic parimutuel. λ = 1 is the pure mechanism. Everything in between is a blend, and the blend is a real setting rather than a hedge: the venue picks it per market class and publishes it like a fee.

The reason this article exists is that the interior is not a compromise between two good things. It is a specific trade with a specific casualty, and the casualty is not obvious until you look at the table.

## How the blend works

Vest a fraction λ of each stake by Rule 1; settle the remaining `1 − λ` as a classic terminal pool. The composition with the capacity rule is part of the specification and is easy to get wrong:

> **Acceptance, capacity, and the seed clamp operate on the full stake exactly as at λ = 1. Only the settlement of the accepted amount splits.**

Because vesting is linear and every stake vests the same fraction, a winner's blended payout collapses to a closed form from a single λ = 1 settlement:

```
Π_i(λ)  =  λ · (s_i + v_i)  +  (1 − λ) · s_i · M
```

with `M` the classic multiple of the accepted pool. That is how the reference implements it, and how the table below is generated — one settlement, then a blend, not two settlements.

## The trilemma

Four properties. No point on the dial delivers all four.

| | no-lock corollary (P4) | creation floor (P6) | dilution protection | late hedging |
|---|---|---|---|---|
| **λ = 1** | exact: buzzer entry pays 1× | **unconditional** | maximal | **none** |
| **interior λ** | void: buzzer pays `λ + (1−λ)·M` | **void** | ≈ `(1−λ)` of classic, on average | partial |
| **λ = 0** | void | void | none | **full (classic)** |

The word doing the work is **void** in the middle row's second column. Not "reduced." Not "weaker." The creation floor does not exist at any interior λ, because the classic component pays the seeder less than its stake whenever its realized-side share falls below its pool share.

Measured, across 40,000 markets:

| λ | seed straddle: mean / **worst** / % positive |
|---|---|
| 0 | −18.0% / **−44.4%** / 16.6% |
| 0.25 | +27.7% / **−30.6%** / 70.8% |
| 0.5 | +73.4% / **−16.8%** / 97.0% |
| 0.75 | +119.0% / **−3.0%** / >99.9% |
| **1** | +164.7% / **+10.9%** / **100%** |

Even λ = 0.75 — which sounds like "almost all the way there" — dips to −3.0%. The floor is a knife edge at λ = 1, not a gradient.

## The rest of the dial

| λ | last-decile multiple | early-winner dilution (mean) |
|---|---|---|
| 0 | 1.416× | 13.5% |
| 0.25 | 1.315× | 9.0% |
| 0.5 | 1.213× | 5.5% |
| 0.75 | 1.112× | 2.6% |
| **1** | **1.004×** | **0.2%** |

Two structural facts about how this degrades.

**The late entrant's reward is exactly linear in λ.** That is [P7](/vpm-whitepaper#5-properties): a late entrant's multiple is exactly `λ·1 + (1−λ)·M`. The sniper's own multiple runs 1.273× to 1.005× linearly across those same rows, by the composition identity.

**Dilution degrades better than linearly.** The measured mean sits *strictly below* the linear reading at every interior λ. So the dial protects early capital better than a naive reading suggests — a pleasant surprise, with a caveat.

The caveat is that the per-position dilution law is **signed**, not one-sided. Position `i`'s dilution satisfies `D_i(λ) ⋚ (1−λ)·D_i(classic)` according as the position's pure multiple `1 + v_i/s_i` is above or below the classic multiple `M`. An individual early position on the wrong side of that crossover can exceed the naive per-position bound, and the suite pins a log where exactly that happens. So "dilution is about `(1−λ)` of classic" is true in aggregate and false for some positions, and a venue should not promise it per position.

## The market-class table

| market class | λ | κ | why |
|---|---|---|---|
| **short recurring rounds** (5–60 min) | **1** | 9 | No exit was ever available; carry is negligible; the lock window is proportionally enormous. The paper's first real-money class. |
| **binary event markets, days** | **1** | 9 | Check carry against duration first. |
| **binary event markets, weeks–months** | 1, with eyes open | 9 | Carry at 4%/6mo ≈ 2% hurdle, which **exceeds the median final-decile winner's post-fee return**. The floor goes nominal-only. |
| **hedging-relevant markets** | **well below 1** | 9 | Hedgers need to buy protection late. Accept that the floor is void and the market is operator-seeded or floor-waived. |
| **n-way ladders, OTM bands** | 1 | **unbounded** | The [P9c freeze is absorbing](/vpm-whitepaper/articles/capacity-and-kappa); finite κ refuses 97.5% of gross volume on skewed books. |
| **n-way, balanced, 3–5 outcomes** | 1 | **unbounded** | The balanced arm's 1.03% refusal is *not representative*; skew arrives on its own. |
| **long-dated (6mo+)** | 0 — leave them | — | Carry eats the entire yield. |
| **your deep flagship markets** | 0 — leave them | — | They already work. |

## Reading the interior honestly

The interior of the dial is not "most of the benefits, some of the safety." It is:

- **You still need a lock window**, because the buzzer snipe pays `λ + (1−λ)·M` and that is positive at every λ < 1. The reason to adopt has partly evaporated.
- **You have no creation floor**, so the whole seeding-as-a-float argument does not apply, and your seeders are back to bearing a real expected loss.
- **You get partial hedging and partial dilution protection**, which is genuinely useful if hedging is what you needed.

So the interior is the right answer for exactly one situation: **markets where hedging demand is the point.** [§14](/vpm-whitepaper#14-limitations) states this as its own conclusion — "a hedging market is an operator-seeded or floor-waived market" — and calls it "the honest reason λ exists."

There is a second-order reason to care about hedgers beyond serving them: **hedging demand is a principal source of the uninformed flow that the secondary layer needs in order to exist.** Push all of it out with λ = 1 and you have made the [late-price problem](/vpm-whitepaper/articles/where-the-late-price-comes-from) harder for yourself.

## Using λ as a migration path rather than a destination

The most useful thing about the dial is that it lets you move without a cutover. You are at λ = 0 today. You can run a class at 0.25, watch what your users do, and move again — and the paper publishes what every stop costs, so nothing about the trip is a surprise.

But do not *park* in the interior thinking it is a safe middle. The two ends are the coherent positions:

- **λ = 0**: full late trading, full hedging, no early reward, needs a lock. Your current venue.
- **λ = 1**: no late free-ride, exact dilution protection, unconditional floor, no exit and no hedge, needs a secondary layer.

The interior has the lock *and* no floor. It is a waypoint, or it is a deliberate choice made for hedgers. It is not a default.

## What λ does not touch

Worth stating because it removes a class of worry:

- **Acceptance and capacity** operate on the full stake at every λ. A partial fill at λ = 0.5 is the same partial fill it would be at λ = 1.
- **Conservation** holds at every λ, for every log and outcome, exactly, in integer units.
- **The seed clamp** — the joint vintage-0 acceptance condition `a_o ≤ κ · min_{w≠o} a_w` — is λ-independent.
- **Settlement cost** stays O(1); the blend is one closed-form combination applied to a single λ = 1 settlement.

And one implementation note: **λ = 0 under this mechanism is not quite the classic parimutuel.** It differs by Rule 2's refusal, measured at 0.10% of gross in the study. If you are running an A/B against your existing pools, that is the discrepancy you will see, and it is expected.

---

*Next: [Implementing it](/vpm-whitepaper/articles/implementing-vpm) — the settler, the arithmetic, and the suite.*


---

# Implementing it

The settlement rule reads as a loop. Implemented as a loop, it is unshippable. This article is about the form that is shippable, the arithmetic decision that will silently strand funds if you get it wrong, the four rules a JavaScript test suite cannot check for you, and the suite that checks everything else.

License first, because it determines whether the rest is relevant: **CC BY 4.0 on the text, MIT on the code, any chain, no permission.**

## Why the naive form does not ship

Rule 1 says: when a stake arrives, assign it pro-rata to every position standing on every opposing outcome. Read literally, that is a loop over the opposing book on every stake — O(m²) per market in the log length.

On-chain that is fatal. At roughly 5,000 gas per position touched, a book of a few thousand positions puts a **single entry in the tens of millions of gas** — beyond any per-transaction budget a user or an RPC will carry — and it grows linearly with the book, forever.

The paper is pointed about this because the mistake is attractive:

> It is tempting to describe the settlement identity as one loop over a public trade log, cheap to compute on-chain. That is exactly backwards.

## The constant-time form

The rule is linear in principal, so it collapses to a reward-per-share accumulator. Maintain, per outcome, the principal `P_w` and one scalar `A_w`.

On a stake of `c` on outcome `o`:

```
for each w ≠ o:   A_w += c / P_w          (O(1))
record position:  (o, s, A_o at entry, vintage)
P_o += c
```

At resolution, position `i` on the realized outcome is paid:

```
Π_i = s_i · (1 + A_ω(T) − A_ω(τ_i))
```

which telescopes to exactly the sum in [§4.1](/vpm-whitepaper#41-the-two-rules).

**Rule 2 costs nothing here.** Acceptance is `min over w ≠ o of (C_w − V_w)`, with `C_w` (granted capacity, `κ·P_w`) and `V_w` (total vested-in) two more running scalars per outcome. So the *entire* mechanism — matching and batching included — is **O(1) per outcome per entry and O(1) per claim**.

State is a few words per outcome and **four per position**: outcome, principal, entry accumulator, vintage. Those four numbers are the complete transferable state of a position, which is what makes transfer, split, merge, and the whole positions-as-primitives idea possible.

**Verified** across 26,458 positions in 800 random markets at κ = 3 and κ = 9: the accumulator and the naive reference agree **exactly, in rational arithmetic**, including settlements where the capacity cap binds, partial fills occur, and multi-entry block vintages ration. The same equivalence in integer-cent arithmetic holds to within rounding, bounded by one cent per opposing event. One claim, two arithmetics — the rational form is the proof, the cent form is what you actually run.

## The sharper statement of verifiability

Conservation is a weak property. It holds for the classic parimutuel too. The distinctive one is this:

> **Each position's payout is a function of two scalars — its outcome's accumulator at entry and at resolution — so no participant's payout depends on any other participant's record.**

That is what makes third-party recomputation cheap and what removes pricing trust. It does not remove trust in the completeness and ordering of the trade log, in resolution, or in the venue having applied the parameters it published. [§14](/vpm-whitepaper#14-limitations) is explicit about all three.

## Block vintages, and why they are normative

All entries in one block share a **vintage**, and the batching rule is specification, not an implementation choice:

1. **Every entry in a vintage vests to the books as they stood at the start of the vintage**, so same-vintage entries never vest to each other.
2. **Capacity granted by a vintage's entries becomes usable only from the next vintage.**
3. **When joint same-vintage demand `D_w` against an opposing book exceeds its headroom `H_w = C_w − V_w`, every entry is filled at the same book fraction**, `⌊c_e · H_w / D_w⌋`, and an entry's accepted amount is the minimum of its rationed caps over the books it opposes.

Rule (iii) is the one that completes the claim. Without it, acceptance under a binding κ would fill in intra-block order, and the priority race the vintage removes from *vesting* would reappear exactly where priority is most valuable. With it, settlement is invariant under permutation within a vintage in **both** vesting and acceptance (conformance cases V1–V3).

Batching stays O(1): per vintage, snapshot each `A_w` and `P_w` at the vintage start, accept and record every entry against the snapshot with one scale factor per book per vintage, then apply the summed increments and principals.

Two honesty notes. **Order-free is not size-strategyproof** — an entry's rationed share rises with its offered size while the refused remainder costs nothing, so under a binding κ the within-block contest becomes an oversizing game. That is the standard property of pro-rata matching everywhere it is used; the mitigations are to fee or bond the *offered* amount rather than the accepted one, cap per-account offers, or run κ large. And **inter-block priority is a real game**, treated as [a limitation with its own article](/vpm-whitepaper/articles/mev-vintages-and-block-time).

## The arithmetic decision that strands funds

With fixed-point floor division the conservation identity becomes an inequality that can never break in the dangerous direction: payouts plus refused stake plus a residue equal the pool, with residue `≥ 0`. **The safe half is unconditional**, because every floor under-pays — across 27,150 settlements at scales 10¹², 10¹⁸ and 10²⁷, and 800 more with stakes to 4×10¹⁵ units, the accepted pool was never overpaid.

But the residue bound is **not one unit per winner at all scales**, and this is where implementations go wrong. The analytic bound is:

```
residue  ≤  W  +  Σ_i s_i · m_i / S
```

with `W` the number of winning positions, `m_i` the opposing vesting events after position `i`'s entry, and `S` the fixed-point scale. The comfortable "one unit per winner" reading holds exactly when `max s_i · m_i ≪ S`.

**So: choose `S ≳ s_max · m_max`, or store the accumulator as a rational.**

Concretely:

| scale | behaviour |
|---|---|
| `S = 10¹⁸` | holds the one-unit reading for 6-decimal USDC up to ~10⁹-unit positions and hundreds of events, and comfortably beyond |
| `S = 10¹²` at adversarial sizes (stakes to 4×10¹⁵) | **strands tens of thousands of units per winner** (measured: 68,000) |

Never insolvent in either case — only stranded. But stranded funds are a support ticket per market, forever.

One attack that does not work, worth knowing so you do not defend against it: **dust-position spam cannot farm the residue.** The truncation is global rather than per-position-per-event, so 300 one-unit positions against a whale extract at most 3 units.

And the residue is a single computable claim — `accepted pool − Σ payouts` — which **must have a named owner fixed before the market opens** (your fee sink, the resolver, or the last claimant, as policy). An unassigned residue is funds nobody can withdraw.

## Four MUSTs a test suite cannot check for you

These are specification for any on-chain deployment, stated in [§6](/vpm-whitepaper#6-settlement-in-constant-time) because the arithmetic suite cannot execute them:

**(a) The settlement asset must be transfer-exact.** No fee-on-transfer, no rebasing — or all accounting must use measured balance deltas.

**(b) Payouts and the residue claim must be pull-based.** One blocked or blacklisted recipient must not be able to delay any other claim. The per-claim O(1) form exists precisely so claims are independent; paying winners in a resolution-time loop hands one blacklisted address a lever over every claim behind it.

**(c) All state updates must complete before any external transfer** in an entry (`P`, `A`, `C`, `V`, the position record), and the same-transaction refund of a partial fill must **revert the entry atomically** if it cannot be delivered.

**(d) Batched or relayed entry paths must isolate per-stake failure.**

## The other four pitfalls

From [Appendix A.6](/vpm-whitepaper#appendix-a-design-alternatives-and-how-they-fail), each caught by the suite or stated as a MUST:

- **Floating point.** Compute capacity or the accumulator in floats and your settlement disagrees with the published integer rule on grid points — the float form disagrees on **438 of 2,700 grid points** in the pinned test. The reference computes `κ·s`, headroom, and rationing in integers.
- **Hard-coding two outcomes.** Every `n ≥ 2` claim in the specification then goes untested, and the n-way coupling is where the interesting failures are.
- **Accepting an invalid seed.** A seed leaving any outcome unbacked — *including a dust leg floored to zero by integer allocation* — makes the market silently un-enterable forever, because every book's capacity is zero. It must **void at creation** (P11).
- **Admitting a third party into vintage 0.** The creation floor is a theorem about atomicity: it needs the creator to be first on every outcome. An implementation that lets someone else in takes the floor to **−50% in half of all branches** (A.3). The conformant entrypoint assigns a same-block stake to vintage 1, and the floor holds.

## Claiming conformance

The suite for the mechanism the paper specifies is **version 1.1.1**:

| file | covers |
|---|---|
| `vpm-capacity.mjs` | properties P1–P7 with asymmetric-seed variants, cases P8–P11, V1–V4, P7a–P7c′, P9b, P10b, P5w, A4 |
| `vpm-accumulator.mjs` | exact O(1) equivalence including block vintages, residue bounds, seed-validity voiding |
| `vpm-vectors.json` | **106 fixture vectors**, sha256 prefix `52b0fcdea345` |
| `vpm-conformance.mjs` | the settler-injection harness |

Every file is served verbatim at `playhunch.xyz/vpm-whitepaper/sim/<file>`, including the `LICENSE` and the `README.md` documenting the settler interface.

The harness accepts any implementation exporting a `settle(vector)` interface. **An implementation claims conformance by passing the property suite and reproducing the 106 fixture vectors exactly on acceptance and to one unit per position on payouts**, and should state the suite version and vectors hash it passed.

Two scoping notes the paper insists on. Passing the suite verifies **one thing**: that entry-and-settlement arithmetic matches §4. The exit semantics of §4.4 (transfer, split, merge) and §12's freeze rule are specified but not exercised by the executable suite. And conformance is not an endorsement of any venue — it says nothing about resolution integrity, custody, or solvency.

Two files are **not** conformance: `vpm-edge-tests.mjs` and `vpm-sim.mjs` preserve the *deleted* v2 mechanism (the ρ-decay bounty) and its failing cases as a labelled historical record.

## A build order

1. Naive reference settler first, in rational arithmetic. It is slow and it is your oracle.
2. Accumulator settler second. Assert exact agreement with the reference on random logs — that is conformance case P8 and it will catch most mistakes.
3. Capacity and the joint vintage-0 clamp. The clamp is a fixed point (the reference iterates it); an asymmetric seed is *partially refused*, never allowed to violate the leverage bound.
4. Block vintages with pro-rata rationing. Test permutation invariance explicitly (V1–V3).
5. Integer-cent arithmetic and the residue owner. Pick `S` against your real `s_max · m_max`.
6. The four MUSTs, which are contract-level and need contract-level tests.
7. Run `vpm-conformance.mjs` against your `settle(vector)` and publish the version and hash you passed.

If you find a case the suite does not cover, that is the interesting one. The paper's canonical page is where to report it.

---

*Next: [Resolution when the claims are already accrued](/vpm-whitepaper/articles/resolution-under-vested-claims).*


---

# Resolution when the claims are already accrued

Liquidity is half of permissionless. The other half is who says what happened.

The mechanism proposes nothing new here — staked resolution bonds with slashing, escalation games, and dispute juries are the deployed designs of Augur, UMA and Kleros, and have been in production for years. But **vesting changes the resolver's incentive landscape in three specific ways, two of them for the worse**, and a venue that ships the settlement rule without shipping the three defences has built something more attackable than the classic pool it replaced.

Naming those three is the point of this article.

## 1. Delay farming

**The incentive.** Accrued claims are monotone — nothing ever decrements them. So a resolver who holds a winning position has a **weakly dominant incentive to delay**: every extra dollar of opposing flow vests to them, at no risk, for as long as the market stays open.

**Why it is new.** In a classic parimutuel, delay *dilutes* the winner — more money joins the winning book and everyone's multiple falls. The incentive points the other way. Here it points at the resolver, and it points hard.

**The fix, for known-schedule markets.** Mechanical and complete:

> Fix the resolution timestamp **at creation**, freeze the accumulator there, and let the resolution transaction land whenever it lands.

Entries with a vintage after the freeze are refused in full. That is not a lock window — it is the market ending at its declared time, and P4's no-lock corollary is about markets *before* their declared end. Once the accumulator is frozen, **latency has zero payoff impact**, and the incentive is gone rather than policed.

**The scope is real, and the paper says so.** This fix is exact only for markets whose resolution time is knowable at creation. For **event-driven** markets it is not, and the freeze must trigger at:

> the earliest of a fixed outside date and the first bonded resolution attestation

so the resolver can *accelerate* the freeze but never extend it. Between attestation and finality the accumulator is frozen and post-freeze entries are refused.

**An implementation that instead accepts post-freeze entries has broken P1**, because a frozen accumulator orphans their vesting. This is not a policy preference; it is a conservation violation.

**And the attestation trigger is itself a lever that must be priced.** Any bonded party can halt entry by attesting. So a defeated attestation must **un-freeze the market and slash the attestor's bond**, sized at least to the blocking value of the halt.

The residual honesty note, which the paper states rather than buries: event-driven markets *do* close entry for the length of a challenge window. That is a bounded reintroduction of the lock, and P4's corollary should be read as excluding it.

## 2. Stall-into-void

The auto-refund safety net is itself an attack surface, and the two must be designed together.

**The incentive.** A resolver on the losing side of a large vested payout has a **strictly profitable strategy of never resolving.** At the refund deadline they recover their full losing principal, and every counterparty's accrued claim evaporates.

**Why vesting makes it sharper.** Accrued claims are *public*. So the staller knows exactly what refusing to resolve saves them, down to the cent, and can attempt to extort large vested winners inside the refund window with a precise number in hand. In a classic pool the equivalent figure does not exist until settlement.

**Three rules close it**, and they compose without contradiction.

**First — a timeout forfeits the resolver's seed.** The seed legs' principal is a branch-independent amount, so forfeiting it funds the dispute layer and makes the stall cost 2× the seed, rising with whatever escalation has attached. The legs are extinguished as positions, and anything they would have collected beyond principal in a later resolution redistributes pro-rata to that branch's other winners — so the direction premium below never accrues to the seed or to the dispute layer as such.

(A fallback resolver who happens to hold positions in the declared branch still inherits a pro-rata slice like any other branch winner. That is the generic resolver-conflict the escalation game has to price, and it does not go away.)

**Second — fallback resolution is permissionless**, so anyone may post a bond to resolve after the timeout, with the standard escalation game. A void becomes the outcome of genuine ambiguity rather than a strategy.

But a timeout alone cannot distinguish a stall from honest ambiguity. So the venue must also provide a **bonded void declaration** through the same escalation path, letting an honest creator of a genuinely unresolvable market resolve to void *without* forfeiture. That is what makes the forfeiture price **silence** specifically, rather than punishing bad luck.

**Third — "irrevocable" is conditional on the market resolving.** In the void branch, every non-seed position refunds at its accepted principal, exactly. That conserves the pool and is pinned in the suite as case V4. The resolver-seed's refund is what the timeout redirects.

## 3. The direction premium

This is the subtle one, and the only one of the three that is unfixable in the mechanism and must be handled at the venue.

**The incentive.** A creator-resolver holds the seed on *every* outcome. So whichever way they resolve, they hold the winning leg. But **the legs do not pay alike**: the winning seed leg farms the *losing* flow, so the seed always pays more in the branch with **more opposing volume** — typically the minority outcome.

The gap across the two declarations is:

```
seed · ( A_w(T) − A_w'(T) )
```

a **closed-form, publicly computable premium that the mechanism itself attaches to resolving toward one side.** It is steeper here than in a classic pool because vintage 0 captures an outsized share of losing flow.

That is an uncomfortable property, and it is worth being clear about what it is: the mechanism computes, and publishes, a number that quantifies the bribe for resolving dishonestly in a particular direction.

**Three mitigations**, none of which removes it:

- **Display the market's resolution premium live.** It is two accumulator reads. A visible bribe is a priced bribe.
- **Score creators on resolution direction against the pool-implied favourite** over their history. A creator who repeatedly resolves toward the premium is legible.
- **Make vintage 0 slashable on adverse escalation rulings.** This is the one that changes the sign: it converts the premium from a bribe into a bond at risk.

A creator's seed is a better starting rung for the escalation path than reputation alone. It is only a rung.

## The bond-scaling problem

One structural issue applies to all three, and it is the kind of thing that is fine in month one and dangerous in month twelve.

**The bond is fixed at creation. What it secures grows with the market.** The behavioural study's $100 seed against its $2,254 mean accepted pool is 4.4% — and the ratio *only falls as a market succeeds*. Your most valuable markets are your least-bonded markets.

The requirement:

> **Escalation bonds must scale with the disputed declared-branch payout.**

And here the mechanism actually helps, which is worth claiming: [§6](/vpm-whitepaper#6-settlement-in-constant-time) makes that payout **O(1)-computable per position**. The dispute layer can price exactly what is at stake, rather than guessing from volume. That is a concrete advantage over classic pools, where the equivalent figure requires a settlement pass.

## What the venue owes, operationally

None of this is mechanism. All of it is required before permissionless creation:

- **A public creator history** — markets resolved, volume settled, disputes, time-to-resolution — surfaced via API so agents can price resolution risk *before* staking. Agents cannot inspect a reputation they cannot fetch.
- **Auto-refund for unresolved markets**, with the stall defences above attached.
- **A winning outcome with no backers voids.**
- **Track-record metrics that exclude self-vested flow.**

That last one is not optional hygiene, and the reason is [P5](/vpm-whitepaper#5-properties). A participant who dominates both books of a market can print wash volume at near-zero mechanism cost — the donation is `(1−f)`-scaled in their own share of the opposing book, so for a book-dominant party the mechanism-level cost falls toward zero and only your fee binds.

So:

> Track-record metrics must exclude **self-vested flow** — flow whose vesting lands on positions of the same funding cluster, which is identifiable from the public log — and weight **bonded, aged, distinct counterparties** instead.

Distinct-counterparty counting alone is sybil-purchasable. Volume alone is worse. If your creator ranking runs on handle, it can be bought.

## The summary

| | classic pool | vested pool | fix |
|---|---|---|---|
| delay | dilutes the winner | **farms the winner** | freeze the accumulator at a creation-set timestamp |
| stalling | loses the pool | **saves a known, public sum** | seed forfeiture + permissionless fallback + bonded void |
| resolving toward a side | small edge | **closed-form public premium** | display it, score it, make vintage 0 slashable |
| bond adequacy | fixed vs fixed | **fixed vs growing** | scale bonds with the O(1)-computable disputed payout |
| volume as a trust signal | weak | **manufacturable** | exclude self-vested flow; weight bonded distinct counterparties |

A perfect settlement identity resolved by a liar pays the liar's friends exactly. That is the whole reason this article is longer than it looks like it should be.

---

*Next: [MEV, vintages, and the price of one block](/vpm-whitepaper/articles/mev-vintages-and-block-time).*


---

# MEV, vintages, and the price of one block

In a classic parimutuel, delaying someone's transaction by one block is **economically inert**. Everyone in the pool is paid the same multiple regardless of when they arrived, so ordering does not matter and there is nothing to extract from seeing flow early.

Under the vested rule, ordering *is* payout. That makes advance sight of order flow **directly monetizable**, and the paper is explicit that this is a **new risk class relative to a classic parimutuel** — not a pre-existing problem the mechanism inherits.

This article is about what the mechanism removes, what it prices, and what it can only mitigate.

## What is removed: the intra-block game

All entries in one block share a **vintage**, and the batching rule is normative:

1. **Every entry in a vintage vests to the books as they stood at the start of the vintage** — so same-vintage entries never vest to each other.
2. **Capacity granted by a vintage's entries becomes usable only from the next vintage.**
3. **When joint same-vintage demand `D_w` exceeds a book's headroom `H_w`, every entry is filled at the same book fraction** `⌊c_e · H_w / D_w⌋`.

Rules (i) and (ii) remove the ordering game from *vesting*. Rule (iii) removes it from *acceptance*, and it is the one that completes the claim — without it, acceptance under a binding κ would fill in intra-block order, and the priority race that vesting no longer has would reappear exactly where priority is most valuable.

With all three, **settlement is invariant under permutation within a vintage in both vesting and acceptance** (conformance cases V1–V3). The paper's claim is narrow and, after the rationing rule, actually true:

> No intra-block ordering game.

**But order-free is not size-strategyproof.** An entry's rationed share rises with its offered size while the refused remainder costs nothing, so under a binding κ the within-block contest becomes an **oversizing game** — offer more than you want, take your pro-rata slice.

This is the standard property of pro-rata matching everywhere it is used, and it is disclosed rather than solved. The mitigations, at their stated costs:

- Fee or bond the **offered** amount rather than the accepted one.
- Cap per-account offers (costs sybil pressure).
- Run κ large enough that headroom rarely binds.

## What is priced: the inter-block game

Between blocks, the game is real, and the paper gives the capture formula rather than gesturing at it.

A party who sees a stake before inclusion — a sequencer, an RPC or API operator, a peered searcher — can take the **opposing vintage one block earlier** and capture that stake's vesting with little principal and little uncertainty.

Front-running a victim stake `c` into an opposing book of principal `P` with a stake of `f` captures:

```
c · f / (P + f)
```

of contingent claim. So the marginal value of one block of foresight on one stake is `≈ c·f/(P+f)` — **increasing in the victim's size and in the thinness of the book** — and the front-runner's optimum trades that against `(1−p)·f` of event risk.

Three things to read off that formula.

**Thin books are the target.** As `P → 0`, the capture approaches the whole of `c`. New markets and unloved outcomes are where this is worth doing, which is exactly the long tail the mechanism is for.

**The victim is indifferent.** Their stake is accepted at the same size and vests to the opposing book either way. **The loss falls on the honest early holders** who would otherwise have shared that flow. That makes it a hard attack to complain about, because the party who notices is not the party who is hurt.

**Under a binding κ there is a second surface, and there the victim is not indifferent.** The same foresight steals *acceptance headroom* — the front-runner consumes the capacity, and the victim is **refused**. That one has a visible victim and a visible complaint.

## The mitigations, each with its cost

The paper lists mechanical mitigations that compose, and prices each:

| mitigation | what it does | cost |
|---|---|---|
| **commit–reveal entry** | removes flow visibility entirely | a round trip of latency, plus a griefing-bond design for unrevealed commits |
| **threshold-encrypted mempool** | same, at the chain level | only available where the chain offers it |
| **k-block epoch vintages** | widens the batch, so foresight buys less | trades time resolution against ordering value |
| **non-extraction commitment** | a venue promise covering ordering and flow visibility | **weaker than any of the above** — it is a promise, not a property |

The epoch dial is the natural extension of what [§4.4](/vpm-whitepaper#44-creation-entry-exit) already specifies: if a one-block vintage removes the game inside one block, a k-block vintage removes it inside k. What you lose is granularity — a market whose vintage is 12 blocks wide has a coarser notion of "when you arrived", which is the thing the mechanism pays for.

For a venue on a **centralized sequencer**, the paper's instruction is direct: treat **flow confidentiality as a mechanism parameter**, publish a non-extraction commitment covering ordering and flow visibility, and understand that a commitment is weaker than any of the mechanical options. Saying "we don't front-run" is not the same kind of object as "we cannot see the flow."

## Block time is the mechanism's time resolution

This is the mechanism's one genuine chain sensitivity, and it is worth stating plainly because everything else about it is chain-agnostic. The settlement identity is one accumulator update per outcome and nothing in it prefers an execution environment.

But **vintages batch per block, so block time is the mechanism's time resolution.** The ordering games removed at the intra-block level reappear between blocks, and their value scales with how long a block is.

The paper's summary: **"At two seconds they are small; at twelve they are not."**

A practical reading:

| block time | inter-block MEV surface | posture |
|---|---|---|
| ~1–2s | small | ordinary mitigations suffice |
| ~12s | material | commit–reveal or encrypted mempool worth the cost |
| centralized sequencer, any speed | operator-controlled | flow confidentiality is a parameter you must publish |

The rest of the deployment requirements are about rails rather than consensus: settlement in a native stablecoin, per-transaction attribution, a machine-payable request standard, and agent-readable market discovery. **Any chain that offers short blocks and those rails will carry this.**

## Why this is worse than in a classic pool, stated plainly

It would be easy to file MEV under "a general blockchain problem." The paper refuses that framing, and it is right to:

> Delaying someone by one block is economically inert in a classic parimutuel and a direct transfer here.

That is the honest comparison. A venue migrating from classic pools is acquiring an extraction surface it did not previously have, and the acquisition is a direct consequence of the property that makes the mechanism worth adopting — **if when you arrived determines what you are paid, then whoever controls when you arrive has something to sell.**

There is no version of this design where that is not true. The mechanism's contribution is to remove the sub-block portion of it as an identity, publish the formula for the rest, and list the mitigations with their prices — rather than to claim the problem away.

---

*Next: [Where the late price comes from](/vpm-whitepaper/articles/where-the-late-price-comes-from).*


---

# Where the late price comes from

The mechanism kills late pool entry on purpose. A stake arriving after the last opposing dollar is paid exactly 1×, so a rational trader with any belief short of certainty will not make it, and the measured unconditional EV of the buzzer strategy is **−1.05% here against +25.27% under classic rules**.

That is the design working. It also creates a hole, and the hole is the most serious open problem in the paper.

**If informed money stops entering the pool late, the pool's ratio stops updating late.** And the last hour of a prediction market is when its forecast matters most.

## The hole, measured

Brier score of the pool ratio against the realized outcome, by phase of market life, agents responding to whichever rule they face (lower is better):

| arm | first third | middle | 67–95% | **final 5%** |
|---|---|---|---|---|
| classic, unlocked | 0.239 | 0.202 | 0.168 | **0.148** |
| classic + lock | 0.239 | 0.202 | 0.168 | **0.150** |
| **this mechanism** | 0.239 | 0.201 | 0.171 | **0.174** |

And the harsher metric, mean absolute gap to the generator's true probability:

| arm | first third | middle | 67–95% | final 5% |
|---|---|---|---|---|
| classic | 0.101 | 0.164 | 0.244 | 0.321 |
| **this mechanism** | 0.102 | 0.173 | 0.277 | **0.353** |

Three readings the paper insists on, all of them uncomfortable:

**The volume migration buys no measurable early forecast gain.** First-third Brier is identical across arms — 0.239 everywhere — and `|q − p|` is weakly worse under the mechanism in *every* phase. Within this crowd model, paying for time-priority does not improve the price. It protects the payout. The paper's own conclusion is that "the instrument case for the mechanism is dilution protection, the deleted lock, and the seeding economics, not forecast quality, and this paper stops implying otherwise."

**The fair headline is against the deployed baseline, not the ideal.** 0.174 against the lock arm's 0.150. The unlocked classic's 0.148 is a bound, not a practice — no venue runs it, because [+25% buzzer EV](/vpm-whitepaper/articles/the-lock-window) is not survivable.

**It is not a sampling artifact.** A fixed-clock control — one end-of-phase snapshot per market at identical instants across arms — agrees: 0.167 for the mechanism against 0.145 unlocked and 0.152 locked.

## The separation principle

The paper's answer is a division of labour, stated as two claims.

**The primary layer settles.** No payout depends on the final pool ratio, so end-of-life manipulation of that ratio has nothing to grab: **you cannot expropriate settled claims by trading against them.** And manipulating the displayed ratio late is *strictly more expensive* here than in a classic pool or a book, because the manipulator's stake earns nothing even when it is correct.

That is a real security property and it is the reason the hole exists in the first place. The pool is a bad late forecaster precisely because it is an unprofitable place to express a late view — which is the same fact as being an expensive place to lie.

**The secondary layer prices.** A position is four numbers (outcome, principal, entry accumulator, vintage), so it trades cleanly. An informed trader late in a market does not inject into the pool — P4 makes that pointless — but **buys positions from holders**. That reroutes late information through prices paid *to* risk-bearers rather than taken *from* them.

## What is established, and what is not

The paper used to concede this section as a weakness. It now has a number, and the number is better than expected — with a very specific scope.

Adding a **stylized dealer** to the behavioural study, where every late-arriving informed agent prints a transaction at their belief shaded by half the spread:

| composite forecast, final phase | Brier |
|---|---|
| **dealer composite, spreads 2%–20%** | **0.054–0.057** |
| dealer composite, sparse arm | 0.075–0.077 |
| this mechanism's own pool ratio | 0.174 |
| classic + lock | 0.150 |
| classic, unlocked | 0.148 |

Better than every pool arm, by a lot, and **flat across a ten-fold range of spreads** — which is the surprising part. The layer does not need to be tight to work; it needs to exist.

Now the scope, which the paper states before anyone else can:

> The model is deliberately generous (no inventory risk, no quote withdrawal, every informed arrival prints), so read it as an **upper bound on what the layer can deliver and a lower bound on nothing.**

What it establishes is narrow and useful: **the late information exists, and a thin transaction layer suffices to surface it.** So the open question is not *whether a quote would help*. It is the **adverse-selection economics of who quotes.**

## The structural worry that stands

There is no guaranteed source of uninformed selling late in a market.

A standing cash-out vault is a **designated adverse-selection sink**: it will widen or decline exactly when information is most valuable, because that is when it is most likely to be picked off. That is not a bug to be engineered around; it is the job description.

This is also where λ bites in an unexpected direction. **Hedging demand is a principal source of the uninformed flow the layer needs**, and λ = 1 removes hedging entirely. Setting the dial to maximize the mechanism's own properties makes the layer that repairs its biggest weakness harder to run. The paper flags this as one of the reasons λ exists at all.

## The cheaper repair does not exist

Before accepting that the late price must come from a position market, the paper tested whether it can be recovered from **primary-layer state alone** — which would be free, since every position's vintage and stake are stored anyway.

Three candidate estimators, against the classic arm as a control under identical treatment (`vpm-estimators.mjs`, 20 seeds × 2,000 markets):

**Recency-weight the pool by vintage.** It works — final-phase Brier improves from 0.1736 to 0.1395 at weight `(t/T)⁴`. But it improves the **classic** arm more (0.1478 → 0.0942), so the vpm-minus-classic gap *widens* from 0.0258 ± 0.0007 to 0.0453 ± 0.0014. It is a generic recency result owned by neither mechanism.

**Weight toward early vintages.** Halves the gap to 0.0126 ± 0.0006, but degrades both arms absolutely (vpm to 0.1948). That is convergence, not repair.

**Invert the entry rule into a revealed-belief bound.** Destroyed by noise entries, which reveal no bound and are indistinguishable from those that do: final-phase Brier **0.4700**, far worse than doing nothing.

Against the dealer arm's 0.054 on the same instants, no primary-layer construction the paper found is competitive.

> **The negative result is the point: §8 is not a convenience.**

That is the strongest statement in the paper about its own weakest section, and it is worth reading as an instruction to implementers. You do not get to skip the layer and post-process your way to a late price.

## What to build

Two shapes, by duration.

**Markets long enough for a position market to form.** Ship transferable positions and a cash-out affordance **before real money** — [§15](/vpm-whitepaper#15-deployment) makes this a precondition, not a follow-up. The position's payout splits usefully: a **floor tranche** (principal plus accrued claims — a digital option with a known payout) and a **flow tranche** (whatever vests later), so a holder can keep conviction and sell activity, or the reverse.

**Short recurring rounds.** No position market can form inside a fifteen-minute round, so the paper specifies the degenerate form: a **venue-side RFQ cash-out at a published spread**, and its quotes *are* the composite's late price.

One structural requirement on that vault, which is easy to miss and expensive to get wrong:

> The vault's quote must **never** be a mechanical function of the current pool ratio.

If it is, the manipulation the separation principle disarms comes straight back through the vault — at [P5](/vpm-whitepaper#5-properties)'s near-zero printing cost for a book-dominant party. The quote must price from the venue's own model over **wash-excluded flow** and off-market inputs. Manipulation-robustness is the second half of the vault's pricing problem, and the paper lists both halves as open.

A venue unwilling to run the vault should run those markets at λ < 1 and accept [the other trade](/vpm-whitepaper/articles/choosing-lambda) instead.

## The most valuable missing experiment

The paper names it explicitly in [§13.3](/vpm-whitepaper#133-threats-to-validity):

> Backtesting the composite estimator against recorded live tapes remains the most valuable missing experiment.

Everything above is simulation. The dealer arm shows a thin layer *would* carry the late forecast; it does not show who quotes it, at what cost, or how the composite behaves on real order flow with real withdrawal behaviour. Until that exists, **the live late price is simply worse here**, and any venue adopting the mechanism is accepting that on the paper's own evidence.

Which is the correct place for a whitepaper to leave its weakest claim: with a bound, a negative result ruling out the cheap alternative, a named experiment, and no pretence that the design is finished.

---

*Next: [Why there are only a few thousand prediction markets](/vpm-whitepaper/articles/the-long-tail-ceiling).*


---

# Why there are only a few thousand prediction markets

There are more questions worth pricing than there are prediction markets, by several orders of magnitude. Every sports fixture in every league, every token's weekly range, every product launch date, every local election, every earnings print, every "will this ship by Q3" inside every company. Millions of them, easily.

The actual count is in the low thousands.

That gap is usually explained as a demand problem — people do not want to bet on obscure things, the audience is small, regulation is hard. Those are all real and none of them is the binding constraint. The binding constraint is on the **supply** side, and it is precise:

> Prediction markets number in the low thousands because **each one must be worth a market maker's attention or an operator's subsidy.**

## The per-market cost, in every structure

Go through them. Each one has a per-market cost with a name.

**Order book.** The cost is a professional's attention. A market maker must decide this market is worth pricing, monitor it, and quote both sides. There is a floor on how much attention costs, and it does not fall with the market's size — pricing a niche market takes *more* effort than pricing a liquid one, for less spread income. Venues extend their reach by paying liquidity incentives, which is the same cost paid in cash instead of attention.

**CFMM.** The cost is an LP's expected loss. On an expiring event contract the pool mechanically rebalances into the losing side as information arrives, and the LP absorbs it. That is a real, funded, negative-expectation position, per market.

**Scoring rule.** The cost is the liquidity subsidy, bounded at `b · ln n`. Elegant, known in advance, and still `b · ln n` times your market count.

**Classic parimutuel.** The cost looks like zero, and this is the interesting case. Pools genuinely work from the first dollar. But the venue pays at the *other* end of the market's life: it must close entry before the event, because late money free-rides at a measured **+25.27% expected value**. And it pays continuously through dilution — the last decile of entrants captures **13.20%** of the losing pool, transferred from the people who were early.

So four structures, four per-market costs, and every one of them scales linearly with catalogue size. That is a ceiling, and it is roughly where the industry sits.

## What "the ten-thousandth market" actually means

The paper's framing is worth quoting because it locates the problem precisely:

> In a deep market, being early already pays: you buy at 20¢ and sell at 80¢, and that is what a price is for. The problem this paper addresses is narrower and it is a problem of the long tail: **in the ten-thousandth market there is no book to sell into, no market maker willing to quote, and no operator able to subsidize.**

Note the concession in the first clause. Where a book works, the mechanism is solving a problem that does not exist. Nobody needs an engineered early-entry gradient in a market that already has a price you can trade against.

The failure at the tail is not gradual. Market ten works. Market ten thousand has a thirty-point spread or does not exist. **There is no partial version of "a market maker will quote this."**

## What removing the constraint would look like

The claim is not that the vested rule creates demand. It is that it removes *one specific gate*, and that gate is currently binding.

The per-market capital does not disappear — the paper is careful about this and repeats it in three places. It **stops being spent**:

| | subsidy model | float model |
|---|---|---|
| what you allocate per market | `X` | `S` per leg |
| what happens to it | expected loss to informed flow | recovered in every branch (P6) |
| how it scales | **your lifetime market count** | your **concurrent** market count |
| 10,000 binary markets | 10,000 × expected loss | **$100,000 float at $5 a side** |

That is the arithmetic difference between a ceiling and a working capital line.

And the mechanism's own crowding measurement pushes in the same direction: growing the seed from $50 to $5,000 a leg — about three times the organic pool — compresses ordinary early winners from **1.70× to 1.09×**. So the venue that seeds thinly across many markets does better by the mechanism's own lights than the venue that seeds heavily across few. **The policy that scales is the policy the mechanism prefers.**

## Who arrives at market ten thousand

Removing the capital gate is necessary and not sufficient. Someone still has to *find* the market, price it, and post the seed. That is [R7](/vpm-whitepaper/articles/four-ways-to-make-a-market) — the requirement the paper adds to Melee's five:

> Floors make early capital safer; they do not summon it. A venue hosting millions of markets needs a participant class for which discovering, pricing, and seeding a brand-new market is cheap and systematic.

Humans are not that class. Nobody is going to manually evaluate the ten-thousandth market, and the reason has nothing to do with capital — it is attention again, in a different costume.

The paper's answer is that seeding is the first market-making job that is **legible to software**: a creation floor, a closed-form position value from two scalars, and economics that depend on forecastable quantities — flow volume and balance — rather than on out-quoting a professional. [That argument, with its limits, is here.](/vpm-whitepaper/articles/agents-as-market-makers)

## Three honest limits on the claim

**Nothing here creates demand.** A market nobody wants to trade is a market nobody wants to trade, seeded or not. What changes is that its non-existence stops being a *supply* decision. The paper's version: a market nobody will seed at any tilt "has no believer willing to stand on any side of it, and the mechanism declines to pretend otherwise."

**The mechanism trades volume for placement.** In the behavioural study, total volume falls from $2,845 to $2,254 a market — about 21%. A venue with ten times as many markets at 79% of the volume each is ahead; a venue with the same markets is not.

**Thin markets are where the entry rule is hardest to use.** In the sparse arm — arrival rate 0.03, roughly 27 stakes a market, exactly the long-tail regime — agents using the naive growth estimate realize **−11.5% per entry post-fee** while the same beliefs under classic rules earn **+11.2%**. The naive estimator wildly overstates growth precisely where flow is thin. The gate is removed; the pricing problem behind it is not.

## The claim, stated at its actual size

The paper's closing paragraph is unusually restrained for a whitepaper, and the restraint is the point:

> A market settled by arithmetic and seeded by its own creator carries no such per-market cost. **We do not know what the ceiling is. We know it stops being the number of market makers.**

That is the whole argument. Not that a million markets will exist. Not that demand is waiting. Only that the count is currently a function of how many markets are worth a professional's attention or an operator's budget — and that a settlement rule with a floored seed makes it a function of something else.

What the new ceiling is, nobody knows. Finding out requires someone to build the thing and count.

---

*Next: [Agents as market makers](/vpm-whitepaper/articles/agents-as-market-makers).*


---

# Agents as market makers

Market making has never been a job software could do end to end. Not because the arithmetic is hard, but because the job is *out-quoting other professionals* — a competitive, adversarial, latency-sensitive contest where the edge is in reading flow better than the person on the other side.

Seeding a vested market is a different job, and the difference is the whole argument of [§10](/vpm-whitepaper#10-agents).

## What makes the job legible

Three properties, and they compose:

**A floor.** [P6](/vpm-whitepaper#5-properties): a party seeding every outcome recovers at least the total seeded, in every branch, under every continuation. Worst case over 40,000 simulated markets: **+10.9% pre-fee, +8.6% after a 2% fee, 0 of 40,000 settling negative.** An automated strategy whose worst case is nominal recovery is a fundamentally different object from one whose worst case is `−b · ln n`.

**A closed-form position value.** A position is four numbers — outcome, principal, entry accumulator, vintage — and its payout is `s · (1 + A_ω(T) − A_ω(τ))`. Two scalar reads. No curve to model, no book to reconstruct, and **no dependence on any other participant's record**. An agent can value its entire portfolio from public state in O(positions).

**Economics that depend on forecastable quantities.** The entry rule needs `q` (observable now) and `L̂`, the pool's remaining log growth. That is a *volume* forecast, not a *price* forecast. You are not being asked to know whether the token goes up. You are being asked to know how much money will show up.

Add machine-payable rails and the marginal cost of discovering and reaching a new market goes to near zero. What remains is the cost of *seeding* it: the opportunity cost of floored capital plus resolution risk — which is exactly what the position is compensated for.

## The three limits, stated before the pitch

The paper puts these immediately after the claim, and an article that buried them would be doing the opposite of what the paper does.

**The competition for vintage 0 is a conjecture about behaviour, not a mechanism property.** Nothing guarantees agents will race for seeds.

**Whether the race clears at agent speed is empirical**, and simulation cannot answer it.

**The entry rule's profitability is exactly as good as its flow forecast — with teeth.** This one has a number, and it is brutal.

## The −11.5%

In the sparse long-tail arm — arrival rate 0.03, roughly 27 stakes a market, which is precisely the regime this whole argument is about:

| | this mechanism | classic |
|---|---|---|
| agents using `L̂ = ln(T/t)`, realized per-entry PnL post-fee | **−11.5%** | **+11.2%** |

Same beliefs. Same opportunities. The naive growth estimator **wildly overstates growth precisely where flow is thin**, and thin flow is the long tail's defining feature.

Read that as the central warning of the agent argument, not a footnote to it. The mechanism hands software a job with a floor and a closed-form value, and then makes the one input it needs hardest to estimate exactly where the job is most worth doing.

The same effect shows up in the dense arm more mildly: agents trusting the naive optimistic estimator overtrade their informed edge down to **+1.4%**, against classic's +5.9%, while the conservative-estimator arm using `L̂/2` recovers to +5.7%. Being wrong about growth is expensive in both directions and the naive estimator is wrong in the expensive one.

## Building an estimator that works

The paper's operational prescription, from [§10](/vpm-whitepaper#10-agents) and [§7.1](/vpm-whitepaper#71-what-the-formula-does-not-price):

**Form `L̂` from realized per-class growth curves.** Not `ln(T/t)`. Not the market's observed early growth. Historical growth curves for *this class of market*, measured.

**Never from promotional volume.** [P5](/vpm-whitepaper#5-properties)'s wash analysis shows a book-dominant party can manufacture volume at near-zero mechanism cost — the donation is `(1−f)`-scaled in their own share of the opposing book — so observed early growth is a manipulable input. An agent conditioning `L̂` on it can be fed.

**Apply the winner's-curse correction as a floor on required edge, not a refinement.** Your yield and your win event are negatively correlated by construction: vesting comes from opposing inflow, opposing inflow is disproportionately informed, and informed opposing flow concentrates in the histories where your side loses. In the paper's crowd model `E[y|win]/E[y] = 0.48` overall — **roughly half** — degrading from 0.57 for first-tercile entries to 0.40 late. For a first-tercile entrant the naive break-even belief of 0.337 corrects to **0.473**.

**Expect composition drift to break the closed form pointwise.** It is roughly unbiased in aggregate (mean signed error −0.03 in yield units) but the median absolute gap between realized and predicted yield is **55% of the prediction**, with a mass point at 100% from positions whose side receives no further opposing flow at all.

There is one encouraging result. Iterating `L̂` to self-consistency — replacing it with the realized growth curve of the previous round and repeating — **converges in four iterations under a 0.3pp criterion** rather than unravelling. Volume contracts about 20%, first-third share rises to 50.4%, informed PnL improves from +1.3% to +4.6%, and the fixed-point growth curve sits well below the naive one (at `t = 0.1T`: 1.61 against 2.30). That is simulation evidence on an open question, not a theorem, and the paper labels it so.

## What the rails have to provide

The paper's chain requirements are mostly about rails rather than consensus:

- **Settlement in a native stablecoin.**
- **Per-transaction attribution**, so an agent's positions are its own.
- **A machine-payable request standard** — x402 is the deployed one.
- **Agent-readable market discovery**, so finding market ten thousand is an API call.
- **Short block times**, because [vintages batch per block and block time is the mechanism's time resolution](/vpm-whitepaper/articles/mev-vintages-and-block-time). "At two seconds they are small; at twelve they are not."

And one thing the *venue* has to provide, from [§12](/vpm-whitepaper#12-resolution): **a public creator history surfaced via API** — markets resolved, volume settled, disputes, time-to-resolution — so agents can price resolution risk before staking. An agent cannot inspect a reputation it cannot fetch, and resolution risk is one of the two real costs of the seeding position.

With the caveat that those metrics must **exclude self-vested flow**, or the reputation an agent is pricing off is purchasable.

## What happens to the returns

The mean seeding return in the study is +164.7%, and the paper spends a paragraph telling you not to quote it:

> **This is payment for cold-start risk-bearing, concentrated in whoever bears it first. It is not a yield, and quoting it as an APY misquotes us.**

The mean is a property of the crowd model. The floor is a property of the mechanism. And the expected trajectory under competition is stated plainly:

> Under free entry the seeding rent should compete away toward the cost of floored capital, which is the design working as intended: **the profit competes away, the seeded market remains.**

That is the right thing to want. A mechanism whose seeding returns stayed at +164% forever would be one where the seeding job was not actually contestable.

## The drift to watch for

[§9](/vpm-whitepaper#9-incentives) names the most likely real-world outcome, and it is not the ideal one.

Vesting is pro-rata by principal, so a large enough first vintage absorbs most future flow. A seed three times the organic pool takes ordinary early winners from **1.70× to 1.09×**, while the seeder sits at its floor. Under a binding κ the same concentration appears within a side as a race for headroom.

Three forces push back — vintage 0 is contestable in principle, crowded-out traders can buy the seeder's positions rather than disappearing, and λ < 1 keeps small entrants' returns alive — and **none is an identity**.

So a venue whose creators seed heavily will look like a market-maker venue with floors. The paper calls that "an acceptable degenerate case": the market maker is permissionless, floored, and earns no information rent. But it is not the time-priced ideal, and it is the mechanism's most likely drift.

It has a second cost worth naming, because it compounds: in exactly that regime, a participant dominating both books can print wash volume at near-zero cost, so **headline volume stops being evidence of anything.** An agent ecosystem that ranks markets or creators by volume is, in the regime it is most likely to produce, ranking by a manufactured number.

## The honest summary

Seeding a vested market is the first market-making job with a floor, a closed-form value, and public state. That is genuinely new and it is why software can do it.

It is also a job whose single required input — future flow — is hardest to estimate in exactly the markets where the job matters, with a measured **−11.5% per entry** for getting it wrong the obvious way.

The mechanism makes the position *legible*. It does not make it *easy*.

---

*Next: [The objections, answered honestly](/vpm-whitepaper/articles/honest-objections).*


---

# The objections, answered honestly

Some of these have answers. Some of them land, and this article says so where they do. The paper's own posture is that "a case the suite does not cover is the interesting one," and an objections article that only contained rebuttals would not be following it.

## "Isn't this a Ponzi? Early people get paid by later people."

**No, and the distinction is structural rather than rhetorical.** But the objection deserves the full ledger rather than a denial, because the surface pattern genuinely rhymes.

The funding ledger, stated exactly ([§9](/vpm-whitepaper#9-incentives)):

> A position's return above principal is funded **exclusively by subsequent opposing stakes** — event-contingent counterparties who, in the other branch, collect the position's own principal.

Read that clause twice. The people funding your upside are the people who *take your money if you are wrong*. That is what a counterparty is, and it is the opposite of the pyramid structure, where later entrants on *your own side* fund you.

Five specifics:

- **Later same-side entrants fund earlier ones with nothing.** Their entry cannot touch your accrued claims (P3), and the last same-side cohort is paid **exactly its principal** (P4) — disclosed as the design goal up front, not discovered at the exit.
- **Payment is contingent on an exogenous, verifiable event.** Not on recruitment, not on inflow, not on anything anyone in the market controls.
- **Conservation is exact**, with no operator skim: payouts sum to the accepted pool, per branch, in integer units.
- **No return is promised anywhere.** The marketing surface is a *conditional* floor: your outcome has to realize, or you get zero.
- **No participant's payout improves by recruiting anyone.** Self-referral is measured strictly costly outside the book-dominance regime that P5 discloses.

The paper's own analogy: **a bookmaker's book that pays its counterparties by arrival time.**

What *is* true, and disclosed: expected seeding returns are a claim on future two-sided flow arriving. Seed a market nobody trades and you get your money back, minus fees. That is a real dependency, and it is why the venue's marketing incentive is to recruit counterparties for standing positions — which the next objection is about.

## "A whale can seed everything and take the whole venue."

**Nothing stops them.** This one lands, and the paper's answer is a measurement rather than a defence.

Vesting is pro-rata by principal, so a large enough first vintage absorbs most future flow:

| seed per leg | ordinary early winners' multiple |
|---|---|
| $50 | **1.70×** |
| $5,000 (≈3× the organic pool) | **1.09×** |

The seeder sits at its floor either way.

Three forces push back, and the paper is explicit that **none is an identity**: vintage 0 is contestable in principle; crowded-out traders can buy the seeder's positions rather than disappearing; and λ < 1 keeps small entrants' returns alive.

The conclusion is a concession: a venue whose creators seed heavily "will look like a market-maker venue with floors." The paper calls that an acceptable degenerate case — the market maker is permissionless, floored, and earns no information rent — while calling it **"the mechanism's most likely real-world drift."**

The mitigation available to a venue is not mechanism, it is policy: per-account seeding caps, contested vintage 0 (at the cost of the unconditional floor, which [Appendix B.3](/vpm-whitepaper#appendix-b-toward-an-equilibrium-analysis) proves is a strict trade-off), or λ < 1 for the classes where it matters.

## "So you can wash-trade it."

**In one specific regime, yes, and cheaply.** This is the drift's second cost and it is the one with the widest blast radius.

The baseline is reassuring: a trader staking `x` on each side into books owned by strangers vests to those strangers on both sides and receives nothing from their own opposing leg, because same-vintage entries do not vest to each other. Pinned as conformance case P5w: **a $100/$100 wash into an existing $100/$100 market returns −50% in both branches** when the legs share a vintage, and −25%/−50% by branch when sequential, before fees.

But the donation is `(1−f)`-scaled, where `f` is the washer's share of the opposing book. Across vintages, a wash leg vests pro-rata into a book that may include the washer's *own* earlier positions. So:

> For a participant who dominates both books, the **mechanism-level cost of wash volume falls toward zero** and the binding cost is the fee.

And Rule 2 does not impede sustained alternating self-play, because each leg grants κ times the headroom the next consumes.

The consequence the paper draws is not a defence, it is an instruction: **track-record metrics must exclude self-vested flow** — flow whose vesting lands on positions of the same funding cluster, identifiable from the public log — and weight bonded, aged, distinct counterparties instead. Distinct-counterparty counting alone is sybil-purchasable; volume alone is worse.

If your venue ranks anything by handle, it can be bought in the regime the mechanism is most likely to produce.

## "Can I just split my stake across wallets and win more?"

**No.** Vesting is linear in principal, so splitting across wallets at one vintage changes nothing, and return on capital is **scale-invariant**: every position on a book earns the same accumulator increment per unit of principal.

A dust position earns exactly what honest capital entering at the same moment earns. Verified: an ε-position probing a seeded market returns **9.0–9.7× at κ = 9** across stakes from 1 to 10,000 units — against **200,001×** for the same 1-unit probe under Rule 1 without the capacity rule.

The paper is careful to say this is **not a general sybil-resistance claim**. It closes the dominance channel specifically. Venue-level sybil pressure exists wherever per-account caps do.

## "Doesn't the mechanism make the favourite-longshot bias worse?"

**Partly, and the shape of the answer is not what you would guess.**

Since `y ∝ (1−q)/q`, the mechanism pays more per winning dollar for backing the minority side. That payment is information-blind, so in any crowd where contrarians skew noisy, the minority premium pays noise more per winning dollar than information. Measured: early **noise** winners at **2.22×** against early **informed** winners at **2.10×**. If the bias is driven by probability misperception, the misperception is untouched and a mechanical inducement is added pointing the same way.

But the corrected calibration shows this is **not a realized-frequency tilt.** Snapshotted at 0.95T: in the 0.2–0.3 pool-implied bin, outcomes realize at 0.02 under classic rules and 0.03 here (binomial SE ±0.002–0.003); in the 0.7–0.8 bin, 0.99 against 0.97. Within one to two points.

The visible effect is **compression** — thinner tail bins, and a displayed ratio dragged toward the seed's uninformative 50/50 prior as rational late flow stays out. The measured price anomaly is the widening `|q − p|` gap in every phase, not a longshot subsidy.

## "The price signal is worse. Isn't that fatal for a prediction market?"

**It is the strongest objection in the list, and the paper concedes the measurement rather than arguing with it.**

Final-phase Brier: **0.174** for the mechanism against **0.150** for the deployed lock baseline. And the mean absolute gap to true probability is weakly worse in *every* phase, not just the last.

Worse still for the sales pitch: **the volume migration buys no measurable early forecast gain.** First-third Brier is 0.239 across every arm. Paying for time-priority does not improve the price; it protects the payout. The paper says so in its own voice and removes the claim it used to imply.

What survives is a narrower case, stated as such: "the instrument case for the mechanism is dilution protection, the deleted lock, and the seeding economics, not forecast quality."

The partial answer is that the late information still exists and is recoverable off-pool — a stylized dealer layer produces a composite Brier of **0.054–0.057** — but that is an upper bound from a deliberately generous model, and building the venue that recovers it is [an open design problem](/vpm-whitepaper/articles/where-the-late-price-comes-from).

## "It can be MEV'd."

**Yes, and this is a new risk class relative to a classic parimutuel** — not an inherited blockchain problem.

Inside a block, no: the vintage rule makes settlement permutation-invariant in both vesting and acceptance. Between blocks, yes, with a published capture formula: front-running a victim stake `c` into an opposing book of principal `P` with a stake `f` captures `c·f/(P+f)` of contingent claim — increasing in the victim's size and the thinness of the book.

The paper's own comparison is the honest one: "delaying someone by one block is economically inert in a classic parimutuel and a **direct transfer** here." [Mitigations and their costs.](/vpm-whitepaper/articles/mev-vintages-and-block-time)

## "Doesn't everyone just wait, so the market never fills?"

**Open question. Simulation says no; there is no theorem.**

The unravelling worry is that if no rational flow arrives after some `t*`, then `L` just before `t*` is generated by noise alone, shrinking the yield and pushing the horizon earlier, recursively.

Two things temper it. The horizon is **side-dependent**: `y` is `((1−q)/q)·L` on one side and `(q/(1−q))·L` on the other — an **81-fold gap at q = 0.9** — so favourite-side rational flow dies far earlier than longshot-side flow, and the object of study is a pair of cutoffs, not a scalar. And **abstention is self-limiting**: while rational flow stays out, arriving information accumulates as a widening `|p − q|` edge that eventually clears any entry threshold.

The fixed-point iteration is consistent with both: volume thins about 20% and shifts earlier but **stabilizes interior** rather than collapsing to vintage 0. That is simulation evidence in one crowd model. The paper calls the theorem "the sharpest question we can hand a theorist" and leaves it open.

## "Is early entry just obviously optimal, then?"

**No, and the paper does not claim it.**

For a trader committed to a side *and a size*, entering earlier captures every intervening allocation, all non-negative. The paper labels that as close to tautological.

It is **not** a claim that waiting is irrational. Waiting buys information, and a trader with market impact facing a concave `V(s)` will generally split and delay — so **strategic withholding is generically profitable** relative to immediate full entry, not a knife-edge case. Withholding cannot revise any accrued claim (P3) and forfeits the withholder's own vesting, so its direct cost is real; its unmodelled harm is informational, because a metering whale shapes the public `q`-path every other entrant conditions on.

The dynamic-execution equilibrium with that signalling channel is open.

## "Can a market get stuck?"

**Yes, permanently, with three or more outcomes at finite κ.** One stake of `S(κ − n + 1)` renders the market un-enterable on every outcome forever — **$350 at the reference parameters**, and reachable at any point in the market's life. Binary markets are the sole exception and self-heal.

The venue-level answer is complete but inelegant: **run n-way markets at large or unbounded κ**, where soundness rests on the mandatory seed and scale-invariance instead. The elegant repair — a matched all-outcome top-up — is stated in [Appendix B.5](/vpm-whitepaper#appendix-b-toward-an-equilibrium-analysis) with three unresolved questions and explicitly declined. [Full treatment.](/vpm-whitepaper/articles/capacity-and-kappa)

## "How do I break it?"

The paper's answer, verbatim in spirit: **please do.**

Appendix A is the set of attacks that already killed earlier candidate designs, each pinned in shipped code. Structured adversarial review has already broken two of the paper's *own* formal claims, both restated with their counterexamples pinned in the suite. A case the conformance suite does not cover is the interesting one, and the paper's canonical page is where to send it.

That is the appropriate closing posture for a mechanism that asks to be adopted: a published rule, 106 fixture vectors with a content hash, every failing variant preserved as a labelled historical record, and an open invitation to find the next one.

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