Set-monotonicity implies Kelly-strategyproofness
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 ClassificationD71 C70
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.
- Aizerman M, Aleskerov F (1995) Theory of choice, of studies in mathematical and managerial economics, vol 38. North-Holland, AmsterdamGoogle Scholar
- Barberà S (2010) Strategy-proof social choice. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of Social Choice and Welfare, vol. 2, Chap. 25. Elsevier, Amsterdam, pp 731–832Google Scholar
- Bordes G (1979) Some more results on consistency, rationality and collective choice. In: Laffont JJ (ed) Aggregation and Revelation of Preferences, Chap. 10. North-Holland, Amsterdam, pp 175–197Google Scholar
- Brandt F, Brill M (2011) Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions. In: Proceedings of the 13th conference on theoretical aspects of rationality and knowledge (TARK), ACM Press, pp 136–142Google Scholar
- Brandt, F. Geist C (2014) Finding strategyproof social choice functions via SAT solving. In: Proceedings of the 13th international conference on autonomous agents and multi-agent systems (AAMAS) IFAAMAS, pp 1193–1200Google Scholar
- Schwartz T (1986) The logic of collective choice. Columbia University Press, New YorkGoogle Scholar
- von Neumann J, Morgenstern O (1947) Theory of games and economic behavior, 2nd edn. Princeton University Press, PrincetonGoogle Scholar