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A Computer Simulation of the Paradox of Voting

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  • Klahr, David

Abstract

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.

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  • Klahr, David, 1966. "A Computer Simulation of the Paradox of Voting," American Political Science Review, Cambridge University Press, vol. 60(2), pages 384-390, June.
    • Handle: RePEc:cup:apsrev:v:60:y:1966:i:02:p:384-390_12
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    Cited by:

    1. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    2. Robi Ragan, 2015. "Computational social choice," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 5, pages 67-80, Edward Elgar Publishing.
    3. Roger Marz & Thomas Casstevens & Harold Casstevens, 1973. "The hunting of the paradox," Public Choice, Springer, vol. 15(1), pages 97-102, June.
    4. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    5. Kurrild-Klitgaard, Peter, 2001. "An Empirical Example of the Condorcet Paradox of Voting in a Large Electorate," Public Choice, Springer, vol. 107(1-2), pages 135-145, April.
    6. Leon Gleser, 1969. "The paradox of voting: Some probabilistic results," Public Choice, Springer, vol. 7(1), pages 47-63, September.
    7. R. Abrams, 1976. "The voter's paradox and the homogeneity of individual preference orders," Public Choice, Springer, vol. 26(1), pages 19-27, June.
    8. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support," Group Decision and Negotiation, Springer, vol. 25(5), pages 967-994, September.
    9. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    10. Thomas Hansen & Barry Prince, 1973. "The paradox of voting," Public Choice, Springer, vol. 15(1), pages 103-117, June.
    11. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

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