Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/314982 
Year of Publication: 
2024
Citation: 
[Journal:] Social Choice and Welfare [ISSN:] 1432-217X [Volume:] 63 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2024 [Pages:] 19-55
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
Social decision schemes (SDSs) map the preferences of a group of voters over some set of m alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard (Econometrica 45(3):665–681, 1977) implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem . We relax Condorcet-consistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Pareto-dominated alternatives, respectively. We then show that the randomized Copeland rule is the only anonymous, neutral, and strategyproof SDS that guarantees the Condorcet winner a probability of at least 2/ m . Secondly, we prove a continuous strengthening of Gibbard’s random dictatorship theorem: the less probability we put on Pareto-dominated alternatives, the closer to a random dictatorship is the resulting SDS. Finally, we show that the only anonymous, neutral, and strategyproof SDSs that maximize the probability of Condorcet winners while minimizing the probability of Pareto-dominated alternatives are mixtures of the uniform random dictatorship and the randomized Copeland rule.
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Published Version

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