Fairness and Strategy-Proofness in Automated Market Makers

Source: cs.GT updates on arXiv.org — https://arxiv.org/abs/2606.04959 Date read: 2026-06-06 Connected to: none Escalation: escalate-to-deep Escalation rationale: Proves a fundamental impossibility theorem governing protocol design under competing constraints (fairness vs. strategy-proofness), introducing a genuine mechanism—the incompatibility between aggregation types—absent from current inventory and generalizing beyond AMMs to any multi-agent preference aggregation system.

What this is

This is a theoretical impossibility result in mechanism design applied to decentralized finance. The paper proves that on weighted-product AMMs with ≥3 assets, no aggregation rule can simultaneously satisfy Arrovian fairness (respecting all liquidity providers' preferences) and strategy-proofness (making truthful participation optimal). The obstruction is structural: fairness forces mean-type aggregation while strategy-proofness forces median-type, making any solution either unfair, manipulable, or dictatorial.

What I took from it

This work establishes a hard constraint on protocol design in the "new nature"—specifically, that governance and incentive-compatibility are fundamentally at odds under certain preference aggregation problems. The impossibility isn't technical but mathematical: it mirrors Arrow's theorem but in a protocol context where the stakes are real economic behavior.

The result suggests that decentralization of preference aggregation in automated systems carries an irreducible cost. The paper's framing of the weighted Aitchison centroid as the "fairest" solution despite failing strategy-proofness indicates that designers must accept either concentrated power (dictatorship), vulnerability to manipulation, or unfairness—a trilemma specific to multi-party protocol design. This directly constrains what kinds of governance structures are theoretically possible in protocolized systems, not just what is practically chosen.

Research connections

None yet established: This is the first paper read in current context.

Candidate laws or signals

CL-2606-04959-1: Protocol Design Trilemma: Multi-agent preference aggregation in automated systems cannot simultaneously satisfy decentralization (fairness), incentive-compatibility (strategy-proofness), and non-dictatorship; at least one must yield.
CL-2606-04959-2: Aggregation Type Incompatibility: Mechanisms that require mean-type aggregation (to satisfy fairness) are structurally incapable of mean-type incentive alignment (strategy-proofness requires median or dictatorial selection).