When does approval voting make the "right choices"?
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 34262.
Date of creation: 22 Oct 2011
Date of revision:
Approval voting; election systems; referendums; Condorcet jury theorem;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-22 (All new papers)
- NEP-CDM-2011-10-22 (Collective Decision-Making)
- NEP-CIS-2011-10-22 (Confederation of Independent States)
- NEP-POL-2011-10-22 (Positive Political Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
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