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:

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:

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:

And the protection is exact rather than statistical. P3 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 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.

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.

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 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 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 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:

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.

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.