TY - GEN

T1 - Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes

AU - Brandt, Felix

AU - Lederer, Patrick

AU - Romen, René

N1 - Publisher Copyright:
© 2022 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved

PY - 2022

Y1 - 2022

N2 - 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 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 SDS that assigns probabilities proportional to Copeland scores is the only anonymous, neutral, and strategyproof SDS that can guarantee the Condorcet winner a probability of at least 2/m. Moreover, no strategyproof SDS can exceed this bound, even when dropping anonymity and neutrality. 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.

AB - 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 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 SDS that assigns probabilities proportional to Copeland scores is the only anonymous, neutral, and strategyproof SDS that can guarantee the Condorcet winner a probability of at least 2/m. Moreover, no strategyproof SDS can exceed this bound, even when dropping anonymity and neutrality. 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.

KW - Condorcet-consistency

KW - Randomized Social Choice

KW - Social Decision Schemes

KW - Strategyproofness

KW - ex post efficiency

UR - http://www.scopus.com/inward/record.url?scp=85134317925&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85134317925

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 181

EP - 189

BT - International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

T2 - 21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022

Y2 - 9 May 2022 through 13 May 2022

ER -