Combinatorial Voting


  • David S. Ahn,

    1. Dept. of Economics, University of California, 508-1 Evans Hall 3880, Berkeley, CA 94720-3880, U.S.A.;
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  • Santiago Oliveros

    1. Haas School of Business, UC Berkeley, 545 Student Services Building 1900, Berkeley, CA 94720-1900, U.S.A.;
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    • We thank a co-editor and four anonymous referees for constructive guidance; in particular, Section 5 is a direct result of their suggestions. We also thank Georgy Egorov, Nenad Kos, Cesar Martinelli, Tom Palfrey, Ken Shotts, and various seminar participants for helpful comments. We acknowledge the National Science Foundation for financial support under Grant SES-0851704.


We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is in considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probabilities that the other issues will pass should be conditioned on being pivotal. We prove that equilibrium exists when distributions over values have full support or when issues are complements. We then study large elections with two issues. There exists a nonempty open set of distributions where the probability of either issue passing fails to converge to either 1 or 0 for all limit equilibria. Thus, the outcomes of large elections are not generically predictable with independent private values, despite the fact that there is no aggregate uncertainty regarding fundamentals. While the Condorcet winner is not necessarily the outcome of a multi-issue election, we provide sufficient conditions that guarantee the implementation of the Condorcet winner.