{"ID":3049986,"CreatedAt":"2026-06-04T02:13:16.786527022Z","UpdatedAt":"2026-06-06T14:39:32.180964103Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04959","arxiv_id":"2606.04959","title":"Fairness and Strategy-Proofness in Automated Market Makers","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.","short_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 centro...","url_abs":"https://arxiv.org/abs/2606.04959","url_pdf":"https://arxiv.org/pdf/2606.04959v1","authors":"[\"Frank M. V. Feys\"]","published":"2026-06-03T14:46:55Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"econ.TH\",\"q-fin.TR\"]","methods":"[]","has_code":false}