Theoretical Economics, Volume 19, Number 2 ( 2024)

Theoretical Economics 19 (2024), 605–634

Symmetric reduced form voting

Xu Lang, Debasis Mishra


We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probabilities can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti-majority. We also provide analogous results by requiring implementation by a unanimous voting rule. A consequence of our results is that if the prior is independent, every symmetric and ordinally Bayesian incen- tive compatible voting rule is reduced (interim) form equivalent to a symmetric and strategy-proof voting rule.

Keywords: Reduced form voting, unanimous voting, ordinal Bayesian incentive compatibility

JEL classification: D82

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