Fairness and Strategy-Proofness in Automated Market Makers
2026-06-03 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors show that in automated market makers handling three or more assets, it is impossible to create a system where liquidity providers can fairly and honestly vote on how trades are executed. They prove that fairness requires combining preferences by averaging (mean), but making the system resistant to strategic manipulation requires using medians, and these two demands conflict except in the trivial case where only one provider decides. This issue disappears when there are only two assets. Their findings also connect to known challenges in combining probabilistic opinions fairly and strategically.
Automated Market MakerLiquidity ProviderWeighted-Product FamilyStrategy-ProofnessFairnessAggregation RuleAitchison CentroidLogarithmic Opinion PoolMedian vs Mean AggregationArrow's Impossibility Theorem
Authors
Frank M. V. Feys
Abstract
No deployed automated market maker lets its liquidity providers vote on the trading function. We show this is structural, not an oversight. On the weighted-product family with $n \geq 3$ assets, no aggregation rule is at once fair and strategy-proof. Arrovian fairness forces a unique form, the weighted Aitchison centroid, the weighted geometric mean of the providers' preferred pools. But fairness forces mean-type aggregation and strategy-proofness forces median-type, and the only rule that is both is a single-provider dictator. The obstruction is sharp: it vanishes at $n = 2$, where a fair strategy-proof rule exists. Under the Frongillo--Papireddygari--Waggoner equivalence, the centroid is Genest's logarithmic opinion pool, and the impossibility transfers to externally Bayesian pooling.