When Does Approval Voting Make the 'Right Choices'?

33 Pages Posted: 21 Oct 2011

See all articles by Steven J. Brams

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

D. Marc Kilgour

Wilfrid Laurier University - Department of Mathematics

Date Written: October 20, 2011

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.

Keywords: approval voting, Condorcet jury theorem, groupthink, referendums

JEL Classification: C61, D63, D71, D72

Suggested Citation

Brams, Steven and Kilgour, D. Marc, When Does Approval Voting Make the 'Right Choices'? (October 20, 2011). Available at SSRN: https://ssrn.com/abstract=1946886 or http://dx.doi.org/10.2139/ssrn.1946886

Steven Brams (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

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D. Marc Kilgour

Wilfrid Laurier University - Department of Mathematics ( email )

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