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Coincidence of Condorcet committees

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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.

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Notes

  1. See also Black (1958) and McLean and Urken (1995).

  2. This definition of the CCG is also known in the literature as the Strong Condorcet Committee; see also Kaymak and Sanver (2003) and Ratliff (2003).

  3. A linear order is a binary relation that is transitive, complete and antisymmetric. The binary relation R on A is transitive if for \(a,b,c\in A\), if aRb and bRc then aRc. R is antisymmetric if for all for \(a\ne b\), \(aRb\Rightarrow \lnot bRa\); if we have aRb and bRa, then \(a=b\). R is complete if and only if for all \(a,b\in A\), we have aRb or bRa.

  4. Without being exhaustive, we can list Arrow and Hurwicz (1972), Packard (1979), Nitzan and Pattanaik (1984), Pattanaik and Peleg (1984), Barberà et al. (1984) and Pérez et al. (2012).

  5. As we only consider strict preferences in this paper, we will omit to present the versions of the properties that deal with weak preferences.

  6. Recall that \(aR_{i}b\) means that individual i finds a at least as good as b.

  7. We thank an anonymous referee for suggesting this profile with three voters.

  8. For more on this, the reader can refer to Benoit and Kornhauser (1991, p. 7).

  9. This also apply for the Simple voting as noticed by Benoit and Kornhauser (1991, 1994, 1999).

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Acknowledgements

We are grateful to Bernard Grofman, Hans Peters, Ashley Piggins, Claudio Zoli and to two anonymous reviewers for all their valuable comments. We would like to thank all the participants of the Voting sessions at the 2013 Annual Meeting of the Public Choice Society (New Orleans), at the 2013 Annual Meeting of the Association for Public Economic Theory (Lisbon) and at the 2013 joint 62nd AFSE Meeting-12th Journées LAGV (Aix-en-Provence). Thanks also to Reiko Gotoh and the members of the Institute of Economic Research-Hitotsubashi University (Japan) for their remarks and suggestions. Vincent Merlin acknowledges the support from the project ANR-14-CE24-0007-01 CoCoRICo-CoDec.

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Authors and Affiliations

  1. Faculté de Droit et d’Economie de la Martinique and Laboratoire Caribéen de Sciences Sociales LC2S UMR CNRS 8053, Université des Antilles, 97275, Schoelcher Cedex, France

    Eric Kamwa

  2. CNRS and Normandie Univ, Caen, France

    Vincent Merlin

  3. UNICAEN, CREM, UMR-CNRS 6211, UFR des Sciences Economiques, Gestion, Géographie et Aménagement du Territoire, Esplanade de la Paix, 14032, Caen, France

    Vincent Merlin

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Kamwa, E., Merlin, V. Coincidence of Condorcet committees. Soc Choice Welf 50, 171–189 (2018). https://doi.org/10.1007/s00355-017-1079-z

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