# Set-monotonicity implies Kelly-strategyproofness

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## 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 Barberà (J Econ Theory 15(2):266–278(1977a)) and Kelly (Econometrica 45(2):439–446 (1977)).

## JEL Classification

D71 C70## Notes

### Acknowledgments

I am grateful to Florian Brandl, Markus Brill, and Paul Harrenstein for helpful discussions and comments. This material is based on work supported by the Deutsche Forschungsgemeinschaft under Grants BR 2312/3-3, BR 2312/7-1, and BR 2312/7-2. Early results of this paper were presented at the 22nd International Joint Conference on Artificial Intelligence (Barcelona, July 2011). A previous version of this paper, titled “Group-Strategyproof Irresolute Social Choice Functions,” circulated since 2010.

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