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Stable Rules for Electing Committees and Divergence on Outcomes

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  • Eric Kamwa

    () (CRPLC - Centre de Recherche sur les Pouvoirs Locaux dans la Caraibe - UAG - Université des Antilles et de la Guyane - CNRS - Centre National de la Recherche Scientifique)

Abstract

Abstract For three-candidate elections, this paper focuses on the relationships that exist between three stable rules for committee elections and the classical rules from which each of these stable rules are adapted. When selecting committees, a voting rule is said to be stable if it always elects a fixed-size subset of candidates such that there is no candidate in this set that is majority dominated by a candidate outside (Barberà and Coelho in Soc Choice Welfare 31:79–96, 2008; Coelho in Understanding, evaluating and selecting voting rules through games and axioms, 2004). There are some cases where a committee selected by a stable rule may differ from the committee made by the best candidates of the corresponding classical rule from which this stable rule is adapted. We call this the divergence on outcomes. We characterize all the voting situations under which this event is likely to occur. We also evaluate the likelihood of this event using the impartial anonymous culture assumption. As a consequence of our analysis, we highlight a strong connection between three Condorcet consistent rules: the Dodgson rule, the Maximin rule and the Young rule.
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Suggested Citation

  • Eric Kamwa, 2017. "Stable Rules for Electing Committees and Divergence on Outcomes," Post-Print hal-01631174, HAL.
  • Handle: RePEc:hal:journl:hal-01631174
    DOI: 10.1007/s10726-016-9504-8
    Note: View the original document on HAL open archive server: https://hal.univ-antilles.fr/hal-01631174
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    References listed on IDEAS

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    1. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    2. repec:eee:mateco:v:70:y:2017:i:c:p:36-44 is not listed on IDEAS
    3. Eric Kamwa, 2013. "The Kemeny rule and committees elections," Economics Bulletin, AccessEcon, vol. 33(1), pages 648-654.
    4. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    5. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1079-z is not listed on IDEAS
    6. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, Oxford University Press, vol. 83(3), pages 478-490.
    7. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    8. Salvador Barberà & Danilo Coelho, 2008. "How to choose a non-controversial list with k names," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 79-96, June.
    9. Gehrlein, William V., 1985. "The Condorcet criterion and committee selection," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 199-209, December.
    10. Thomas C. Ratliff, 2003. "Some startling inconsistencies when electing committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 433-454, December.
    11. Eric Kamwa, 2015. "On the Fishburn social choice function," Post-Print hal-01702496, HAL.
    12. Eric Kamwa & Vincent Merlin, 2018. "Coincidence of Condorcet committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 171-189, January.
    13. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    14. Alexander I. Barvinok, 1994. "A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 769-779, November.
    15. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    16. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
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    1. Eric Kamwa & Vincent Merlin, 2018. "Coincidence of Condorcet committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 171-189, January.

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