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When does approval voting make the "right choices"?

Author

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  • Brams, Steven J.
  • Kilgour, D. Marc

Abstract

We assume that a voter’s judgment about a proposal depends on (i) the proposal’s probability of being right (or good or just) and (ii) the voter’s probability of making a correct judgment about its rightness (or wrongness). Initially, the state of a proposal (right or wrong), and the correctness of a voter’s judgment about it, are assumed to be independent. If the average probability that voters are correct in their judgments is greater than ½, then the proposal with the greatest probability of being right will, in expectation, receive the greatest number of approval votes. This result holds, as well, when the voters’ probabilities of being correct depend on the state of the proposal; when the average probability that voters judge a proposal correctly is functionally related to the probability that it is right, provided that the function satisfies certain conditions; and when all voters follow a leader with an above-average probability of correctly judging proposals. However, it is possible that voters may more frequently select the proposal with the greatest probability of being right by reporting their independent judgments—as assumed by the Condorcet Jury Theorem—rather than by following any leader. Applications of these results to different kinds of voting situations are discussed.

Suggested Citation

  • Brams, Steven J. & Kilgour, D. Marc, 2011. "When does approval voting make the "right choices"?," MPRA Paper 34262, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:34262
    as

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    File URL: https://mpra.ub.uni-muenchen.de/34262/1/MPRA_paper_34262.pdf
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    References listed on IDEAS

    as
    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    2. I. D. Hill, 2008. "Mathematics and Democracy: Designing Better Voting and Fair‐division Procedures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 1032-1033, October.
    3. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    4. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
    5. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Approval voting; election systems; referendums; Condorcet jury theorem;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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