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Voting on Multiple Issues: What to Put on the Ballot?

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  • Alex Gershkov
  • Benny Moldovanu
  • Xianwen Shi

Abstract

We study a multi-dimensional collective decision problem under incomplete information. Agents have Euclidean preferences and vote by simple majority on each issue (dimension), yielding the coordinate-wise median. Judicious rotations of the orthogonal axes -- the issues that are voted upon -- lead to welfare improvements. If the agents' types are drawn from a distribution with independent marginals then, under weak conditions, voting on the original issues is not optimal. If the marginals are identical (but not necessarily independent), then voting first on the total sum and next on the differences is often welfare superior to voting on the original issues. We also provide various lower bounds on incentive efficiency: in particular, if agents' types are drawn from a log-concave density with I.I.D. marginals, a second-best voting mechanism attains at least 88% of the first-best efficiency. Finally, we generalize our method and some of our insights to preferences derived from distance functions based on inner products.

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2018. "Voting on Multiple Issues: What to Put on the Ballot?," Working Papers tecipa-616, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-616
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    References listed on IDEAS

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    Cited by:

    1. Gregorio Curello & Ludvig Sinander, 2020. "Agenda-manipulation in ranking," Papers 2001.11341, arXiv.org, revised Sep 2022.
    2. Tobias Rachidi, 2020. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214, University of Bonn and University of Mannheim, Germany.
    3. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    4. Gershkov, Alex & Moldovanu, Benny & Shi, Xianwen, 2020. "Monotonic norms and orthogonal issues in multidimensional voting," Journal of Economic Theory, Elsevier, vol. 189(C).
    5. Sumit Goel & Wade Hann-Caruthers, 2023. "Optimality of the coordinate-wise median mechanism for strategyproof facility location in two dimensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 11-34, July.

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    More about this item

    Keywords

    Multidimensional Voting; Mechanism Design; Rotation; Strategy-Proof Mechanisms; Budgeting Procedure;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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