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Paradox of voting under an urn model: The effect of homogeneity

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  • Sven Berg

Abstract

We propose a simple Pólya-variety urn model for calculating paradox-of-voting probabilities. The model contains a homogeneity parameter, and for specific values of this parameter the model reduces to cases previously discussed in the literature. We derive a Dirichlet family of distributions for describing the assignment of preference profiles in large committees, and we show how the homogeneity parameter relates to measures of similarity among voters, suggested in prior studies. Copyright Martinus Nijhoff Publishers 1985

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  • Sven Berg, 1985. "Paradox of voting under an urn model: The effect of homogeneity," Public Choice, Springer, vol. 47(2), pages 377-387, January.
    • Handle: RePEc:kap:pubcho:v:47:y:1985:i:2:p:377-387
    DOI: 10.1007/BF00127533
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    References listed on IDEAS

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    1. R. Abrams, 1976. "The voter's paradox and the homogeneity of individual preference orders," Public Choice, Springer, vol. 26(1), pages 19-27, June.
    2. Sven Berg & Bo Bjurulf, 1983. "A note on the paradox of voting: Anonymous preference profiles and May's formula," Public Choice, Springer, vol. 40(3), pages 307-316, January.
    3. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    4. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
    5. Jamison, Dean & Luce, Edward, 1972. "Social homogeneity and the probability of intransitive majority rule," Journal of Economic Theory, Elsevier, vol. 5(1), pages 79-87, August.
    6. repec:cup:apsrev:v:63:y:1969:i:02:p:488-497_26 is not listed on IDEAS
    7. DeMeyer, Frank & Plott, Charles R, 1970. "The Probability of a Cyclical Majority," Econometrica, Econometric Society, vol. 38(2), pages 345-354, March.
    8. Gehrlein, William V., 1981. "The expected probability of Condorcet's paradox," Economics Letters, Elsevier, vol. 7(1), pages 33-37.
    9. Peter Fishburn & William Gehrlein, 1980. "Social homogeneity and Condorcet's paradox," Public Choice, Springer, vol. 35(4), pages 403-419, January.
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    Cited by:

    1. Gehrlein, William V. & Lepelley, Dominique & Moyouwou, Issofa, 2016. "A note on Approval Voting and electing the Condorcet loser," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 115-122.
    2. Cres, Herve & Tvede, Mich, 2001. "Ordering Pareto-optima through majority voting," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 295-325, May.
    3. Yuliya Veselova, 2016. "The difference between manipulability indices in the IC and IANC models," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 609-638, March.
    4. repec:spr:grdene:v:15:y:2006:i:1:d:10.1007_s10726-005-9007-5 is not listed on IDEAS
    5. repec:spr:grdene:v:24:y:2015:i:2:d:10.1007_s10726-014-9388-4 is not listed on IDEAS
    6. Gehrlein, William V. & Lepelley, Dominique, 1997. "Condorcet's paradox under the maximal culture condition," Economics Letters, Elsevier, vol. 55(1), pages 85-89, August.
    7. William V. Gehrlein & Dominique Lepelley, 2015. "The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules," Group Decision and Negotiation, Springer, vol. 24(2), pages 243-269, March.
    8. Tataru, Maria & Merlin, Vincent, 1997. "On the relationship of the Condorcet winner and positional voting rules," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 81-90, August.
    9. James Green-Armytage & T. Nicolaus Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    10. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    11. repec:spr:sochwe:v:48:y:2017:i:4:d:10.1007_s00355-017-1033-0 is not listed on IDEAS
    12. Gehrlein, William V. & Lepelley, Dominique, 2001. "The Condorcet efficiency of Borda Rule with anonymous voters," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 39-50, January.
    13. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
    14. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.

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