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Sets of alternatives as Condorcet winners

Author

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  • Barış Kaymak
  • M. Remzi Sanver

Abstract

We characterize sets of alternatives which are Condorcet winners according to preferences over sets of alternatives, in terms of properties defined on preferences over alternatives. We state our results under certain preference extension axioms which, at any preference profile over alternatives, give the list of admissible preference profiles over sets of alternatives. It turns out to be that requiring from a set to be a Condorcet winner at every admissible preference profile is too demanding, even when the set of admissible preference profiles is fairly narrow. However, weakening this requirement to being a Condorcet winner at some admissible preference profile opens the door to more permissive results and we characterize these sets by using various versions of an undomination condition. Although our main results are given for a world where any two sets – whether they are of the same cardinality or not – can be compared, the case for sets of equal cardinality is also considered. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Barış Kaymak & M. Remzi Sanver, 2003. "Sets of alternatives as Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 477-494, June.
  • Handle: RePEc:spr:sochwe:v:20:y:2003:i:3:p:477-494
    DOI: 10.1007/s003550200194
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    File URL: http://hdl.handle.net/10.1007/s003550200194
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    Citations

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    Cited by:

    1. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    2. 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.
    3. Barberà, Salvador & Coelho, Danilo, 2010. "On the rule of k names," Games and Economic Behavior, Elsevier, vol. 70(1), pages 44-61, September.
    4. Barberà, Salvador & Coelho, Danilo, 2017. "Balancing the power to appoint officers," Games and Economic Behavior, Elsevier, vol. 101(C), pages 189-203.
    5. Burak Can & Bora Erdamar & M. Sanver, 2009. "Expected Utility Consistent Extensions of Preferences," Theory and Decision, Springer, vol. 67(2), pages 123-144, August.
    6. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
    7. Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
    8. Edith Elkind & Jérôme Lang & Abdallah Saffidine, 2015. "Condorcet winning sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 493-517, March.
    9. Sinan Ertemel & Levent Kutlu & M. Remzi Sanver, 2015. "Voting games of resolute social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 187-201, June.
    10. repec:eee:matsoc:v:93:y:2018:i:c:p:57-66 is not listed on IDEAS
    11. İpek Özkal-Sanver & M. Sanver, 2006. "Nash implementation via hyperfunctions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 607-623, June.
    12. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers hal-01757761, HAL.
    13. 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.
    14. repec:spr:sochwe:v:48:y:2017:i:3:d:10.1007_s00355-017-1026-z is not listed on IDEAS
    15. repec:eee:mateco:v:70:y:2017:i:c:p:36-44 is not listed on IDEAS
    16. Joseph, Rémy-Robert, 2010. "Making choices with a binary relation: Relative choice axioms and transitive closures," European Journal of Operational Research, Elsevier, vol. 207(2), pages 865-877, December.
    17. Darmann, Andreas, 2013. "How hard is it to tell which is a Condorcet committee?," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 282-292.
    18. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.
    19. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    20. Andreas Darmann, 2016. "It is difficult to tell if there is a Condorcet spanning tree," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 93-104, August.

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