Set-Monotonicity Implies Kelly-Strategyproofness

TL;DR

This paper introduces set-monotonicity as a new property of social choice functions, demonstrating it guarantees Kelly-strategyproofness and applies to several well-known Condorcet extensions.

Contribution

It establishes set-monotonicity as a sufficient condition for Kelly-strategyproofness and shows that key Condorcet extensions satisfy this property even in unrestricted domains.

Findings

Set-monotonicity implies Kelly-strategyproofness.

Several Condorcet extensions satisfy set-monotonicity in unrestricted domains.

Answers longstanding questions about strategyproofness of Condorcet extensions.

Abstract

This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred to all elements of the latter. It is shown that set-monotonicity---a new variant of Maskin-monotonicity---implies Kelly-strategyproofness in comprehensive subdomains of the linear domain. Interestingly, there are a handful of appealing Condorcet extensions---such as the top cycle, the minimal covering set, and the bipartisan set---that satisfy set-monotonicity even in the unrestricted linear domain, thereby answering questions raised independently by Barber\`a (1977) and Kelly (1977).