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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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    1. Marco Battaglini, 2002. "Multiple Referrals and Multidimensional Cheap Talk," Econometrica, Econometric Society, vol. 70(4), pages 1379-1401, July.
    2. Yannis Bakos & Erik Brynjolfsson, 1999. "Bundling Information Goods: Pricing, Profits, and Efficiency," Management Science, INFORMS, vol. 45(12), pages 1613-1630, December.
    3. Scott Feld & Bernard Grofman, 1988. "Majority rule outcomes and the structure of debate in one-issue-at-a-time decision-making," Public Choice, Springer, vol. 59(3), pages 239-252, December.
    4. Palfrey, Thomas R, 1983. "Bundling Decisions by a Multiproduct Monopolist with Incomplete Information," Econometrica, Econometric Society, vol. 51(2), pages 463-483, March.
    5. Kaas, R. & Dhaene, J. & Vyncke, D. & Goovaerts, M.J. & Denuit, M., 2002. "A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(01), pages 71-80, May.
    6. repec:cup:apsrev:v:63:y:1969:i:01:p:40-56_26 is not listed on IDEAS
    7. repec:aea:aecrev:v:107:y:2017:i:6:p:1477-1506 is not listed on IDEAS
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    More about this item

    Keywords

    Multidimensional Voting; Mechanism Design; Rotation; Strategy-Proof Mechanisms; Budgeting Procedure;

    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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