For weighted-product AMMs with n≥3 assets, no aggregation rule satisfies both Arrovian fairness and strategy-proofness except single-provider dictators; the obstruction vanishes at n=2 and transfers to logarithmic opinion pools.
Manipulation of Belief Aggregation Rules
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Fairness and Strategy-Proofness in Automated Market Makers
For weighted-product AMMs with n≥3 assets, no aggregation rule satisfies both Arrovian fairness and strategy-proofness except single-provider dictators; the obstruction vanishes at n=2 and transfers to logarithmic opinion pools.