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Coincidence of Condorcet committees

Author

Listed:
  • Eric Kamwa

    () (Université des Antilles)

  • Vincent Merlin

    () (CNRS and Normandie Univ
    UFR des Sciences Economiques, Gestion, Géographie et Aménagement du Territoire)

Abstract

The Condorcet Committee à la Gehrlein (CCG) is a fixed-size subset of candidates such that each of its members defeats in a pairwise contest any candidate outside. The Condorcet Committee à la Fishburn (CCF) is a fixed-size subset of candidates that is preferred to all other subsets of the same size by a majority of voters. In general, these two types of Condorcet committees may not always exist. Kaymak and Sanver (Soc Choice Welf 20:477–494, 2003) studied the conditions under which the CCF exists under a large class of extensions of preferences. We focus here on the most important members of their class, the lexicographic extension of preferences, and we define more precisely, the conditions under which these committees coincide when they exist. Our results depart from the rather optimistic conclusions of Kaymak and Sanver (Soc Choice Welf 20:477–494, 2003) on the coincidence between the CCG and the CCF. We exhibit profiles for which the CCF is empty while the CCG exists and the preferences are all of lexicographic type. Furthermore, we obtain the same conclusion when we derive preferences on candidates from those on sets of candidates using the separability assumption.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1079-z
    DOI: 10.1007/s00355-017-1079-z
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    References listed on IDEAS

    as
    1. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
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    5. Darmann, Andreas, 2013. "How hard is it to tell which is a Condorcet committee?," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 282-292.
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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. Eric Kamwa, 2017. "Stable Rules for Electing Committees and Divergence on Outcomes," Group Decision and Negotiation, Springer, vol. 26(3), pages 547-564, May.
    3. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    4. Eric Kamwa, 2017. "Stable Rules for Electing Committees and Divergence on Outcomes," Group Decision and Negotiation, Springer, vol. 26(3), pages 547-564, May.

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