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A Computer Simulation of the Paradox of Voting*

Published online by Cambridge University Press:  01 August 2014

David Klahr
David Klahr*
Affiliation:
Carnegie Institute of Technology
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Extract

This paper presents estimates of the probability that the occurrence of the Paradox of Voting, commonly known as Arrow's Paradox, will prevent the selection of a majority issue when odd-sized committees of m judges vote upon n issues. The estimates, obtained through computer simulation of the voting process, indicate that the probability of such an intransitive social ordering is lower than the ratio of intransitive outcomes to all outcomes.

Many of the arguments in political theory and welfare economics dealing with the paradox (e.g., Downs, 1957; Black, 1958; Schubert, 1960) seem to have implicitly assumed that since the paradox exists, its likelihood of occurrence is very close to 1. The results in this paper may call for a re-examination of these positions.

Type
Research Notes
Information
American Political Science Review , Volume 60 , Issue 2 , June 1966 , pp. 384 - 390
Copyright
Copyright © American Political Science Association 1966

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References

1. Black, Duncan. The Theory of Committees and Elections. Cambridge: Cambridge University Press, 1958.Google Scholar
2. Downs, Anthony. An Economic Theory of Democracy. New York: Harper & Brothers, 1957.Google Scholar
3. Edwards, Ward. “Probability Preferences in Gambling” American Journal of Psychology, 66 (1953), 349–364.CrossRefGoogle ScholarPubMed
4. May, Kenneth O. “Intransitivity, Utility, and the Aggregation of Preference Patterns,” Econometrica, 22 (1954), 1–13.CrossRefGoogle Scholar
5. Morrison, H. W. “Intransitivity of Paired Comparisons.” Unpublished Doctoral Dissertation, University of Michigan, 1962.Google Scholar
6. Naur, Peter (ed.). “Revised Report on the Algorithmic Language ALGOL-60.” Communications of the ACM, 6 (1963), 1–17.Google Scholar
7. Nicholson, Michael. “Conditions for the ‘Voting Paradox’ in Committee Decisions.” Metroeconomica, 42 (1965), 29–44.CrossRefGoogle Scholar
8. Riker, William H. “Voting and the Summation of Preferences: An Interpretive Bibliographical Review of Selected Developments During the Last Decade,” American Political Science Review, 40 (1961), 900–911.CrossRefGoogle Scholar
9. Riker, William H. “Arrow's Theorem and Some Examples of the Paradox of Voting”: Mathematical Applications in Political Science, Claunch, Q. M. (ed.). Dallas: The Arnold Foundation, Southern Methodist University, 1965.Google Scholar
10. Rose, Arnold M. “A Study of Irrational Judgments.” Journal of Political Economy, 65 (1957), 394–402.CrossRefGoogle Scholar
11. Schubert, Glendon. The Public Interest. Glencoe: The Free Press, 1960.Google Scholar
12. Quandt, R. E. “A Probabilistic Theory of Consumer Behavior.” Quarterly Journal of Economics, 70 (1956), 507–536.CrossRefGoogle Scholar
13. Campbell, Colin D. and Tullock, Gordon, “A Measure of the Importance of Cyclical Majorities,” The Economic Journal, 75 (1965), 853–856.CrossRefGoogle Scholar