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The probability of the paradox of voting for weak preference orderings

Author

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  • Adrian Van Deemen

    (University of Nijmegen, Department of Political Science, P.O. Box 9108, 6500 HK Nijmegen, The Netherlands)

Abstract

In this paper the probability of the voting paradox for weak orderings is calculated analytically for the three-voter-three-alternative case. It appears that the probability obtained this way is considerably smaller than in the corresponding case for linear orderings. The probability of intransitive majority relations for weak orderings in the 3 þ 3 case is calculated as well, both with unconcerned and with concerned voters. Basic in the calculations are three theorems which are formulated in the field of domain conditions and restricted preferences.

Suggested Citation

  • Adrian Van Deemen, 1999. "The probability of the paradox of voting for weak preference orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 171-182.
    • Handle: RePEc:spr:sochwe:v:16:y:1999:i:2:p:171-182
    Note: Received: 18 February 1997 / Accepted: 21 October 1997
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    Citations

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    Cited by:

    1. repec:spo:wpecon:info:hdl:2441/10286 is not listed on IDEAS
    2. Regenwetter, Michel & Marley, A. A. J. & Grofman, Bernard, 2002. "A general concept of majority rule," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 405-428, July.
    3. Hervé Crès, 2001. "Aggregation of coarse preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 507-525.
    4. Hervé Crès, 2000. "Aggregation of Coarse Preferences," SciencePo Working papers hal-01064879, HAL.
    5. Hannu Nurmi, 2001. "Resolving Group Choice Paradoxes Using Probabilistic and Fuzzy Concepts," Group Decision and Negotiation, Springer, vol. 10(2), pages 177-199, March.
    6. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
    7. Mathieu Martin, 2002. "On the emptiness of the stability set of order d," Theory and Decision, Springer, vol. 52(4), pages 313-326, June.
    8. Lepelley, Dominique & Martin, Mathieu, 2001. "Condorcet's paradox for weak preference orderings," European Journal of Political Economy, Elsevier, vol. 17(1), pages 163-177, March.
    9. repec:hal:wpspec:info:hdl:2441/10286 is not listed on IDEAS
    10. repec:hal:spmain:info:hdl:2441/10286 is not listed on IDEAS
    11. Hervé Crès, 2000. "Aggregation of Coarse Preferences," SciencePo Working papers Main hal-01064879, HAL.
    12. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    13. Salvatore Barbaro & Nils D. Steiner, 2022. "Majority principle and indeterminacy in German elections," Working Papers 2202, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    14. Daniel Bochsler, 2010. "The Marquis de Condorcet goes to Bern," Public Choice, Springer, vol. 144(1), pages 119-131, July.

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