Brams, Steven J. and Kilgour, D. Marc (2011): When does approval voting make the "right choices"?
Download (602kB) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||When does approval voting make the "right choices"?|
|Keywords:||Approval voting; election systems; referendums; Condorcet jury theorem|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice; Clubs; Committees; Associations
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||Steven J. Brams|
|Date Deposited:||22. Oct 2011 15:46|
|Last Modified:||16. Feb 2013 05:25|
Brams, Steven J. (2008). Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Princeton, NJ: Princeton University Press.
Brams, Steven J., and Peter C. Fishburn (1978), “Approval Voting.” American Political Science Review 72, no. 3 (September): 831-847.
Brams, Steven J., and Peter C. Fishburn (1983/2007), Approval Voting. New York: Springer.
Brams, Steven J., and R. Remzi Sanver (2009). “Voting Systems That Combine Approval and Preference.” In Steven J. Brams, William V. Gehrlein, and Fred S. Roberts (eds.), The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn. Berlin: Springer, pp. 215-237.
“Condorcet Jury Theorem,” Wikipedia (2011). http://en.wikipedia.org/wiki/Condorcet's_jury_theorem
Davis, Morton D. (2001). The Math of Money: Making Mathematical Sense of Your Personal Finances. New York: Springer.
Epstein, Richard A. (1977). The Theory of Gambling and Statistical Logic, rev. ed. Waltham, MA: Academic Press.
Feddersen, Timothy, and Wolfgang Pesendorfer (1999), “Elections, Information Aggregation, and Strategic Voting,” PNAS 96, no. 19 (September 14): 10572- 10574.
Grofman, Bernard, and Guillermo Owen (1986). “Review Essay: Condorcet Models, Avenues for Future Research.” In Bernard Grofman and Guillermo Owen (eds.), Information Pooling and Group Decision Making: Proceedings of the Second University of California, Irvine, Conference on Political Economy. Greenwich, CT: JAI Press, pp. 93-1922.
Hannaford-Agor, Paula L., Valerie P. Hans, Nicole L. Mott, and G. Thomas Munsterman (2002). “Are Hung Juries a Problem?” Washington, DC: National Institute of Justice.
Janis, Irving L. (1972). Victims of Groupthink: A Psychological Study of Foreign-Policy Decisions and Fiascoes. Boston: Houghton-Mifflin.
Miller, Nicholas R. (1986). “Information, Electorates, and Democracy: Some Extensions and Interpretations of the Condorcet Jury Theorem.” In Bernard Grofman and Guillermo Owen (eds.), Information Pooling and Group Decision Making: Proceedings of the Second University of California, Irvine, Conference on Political Economy. Greenwich, CT: JAI Press, pp. 173-192.
Nitzan, Schmuel (2010). Collective Preference and Choice. Cambridge, UK: Cambridge University Press.
Prasad, Mahendra (2011). “A Multiple Alternatives Extension of Condorcet Jury Theorem Using Approval Voting.” Department of Political Science, University of California, Berkeley.