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

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 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:

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 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 — 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 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 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.