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On two new social choice correspondences

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  • Borm, Peter
  • van den Brink, Rene
  • Levinsky, Rene
  • Slikker, Marco

Abstract

Preferences of a set of n individuals over a set of alternatives can be represented by a preference profile being an n-tuple of preference relations over these alternatives.A social choice correspondence assigns to every preference profile a subset of alternatives that can be viewed as the `most prefered' alternatives by the society consisting of all individuals.Two new social choice correspondences are introduced and analyzed.Both are Pareto optimal and are refinements of the well known Top cycle correspondence in case the corresponding simple majority win digraph is a tournament.One of them even is such a refinement for arbitrary preference profiles.
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Suggested Citation

  • Borm, Peter & van den Brink, Rene & Levinsky, Rene & Slikker, Marco, 2004. "On two new social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 51-68, January.
  • Handle: RePEc:eee:matsoc:v:47:y:2004:i:1:p:51-68
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    References listed on IDEAS

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    1. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    2. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771, April.
    3. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, pages 327-342.
    4. Laffond G. & Laslier, J. F. & Le Breton, M., 1996. "Condorcet choice correspondences: A set-theoretical comparison," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 59-59, February.
    5. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2001. "Measuring the Power of Nodes in Digraphs," Tinbergen Institute Discussion Papers 01-096/1, Tinbergen Institute.
    6. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    7. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
    8. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 75-93, January.
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    Cited by:

    1. Ayllon Aragon, Grisel, 2013. "On Weak Condorcet Winners: Existence and Uniqueness," MPRA Paper 53272, University Library of Munich, Germany.
    2. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, pages 327-342.
    3. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & Voorneveld, M., 2002. "Characterizations of Solutions in Digraph Competitions," Discussion Paper 2002-113, Tilburg University, Center for Economic Research.
    4. Marieke Quant & Peter Borm & Hans Reijnierse & Mark Voorneveld, 2003. "On a compromise social choice correspondence," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 311-324, December.
    5. Marco Slikker & Peter Borm & René Brink, 2012. "Internal slackening scoring methods," Theory and Decision, Springer, vol. 72(4), pages 445-462, April.
    6. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & Voorneveld, M., 2006. "On the Beta measure for digraph competitions," Other publications TiSEM 214590f7-5605-42d6-8353-6, Tilburg University, School of Economics and Management.
    7. Marieke Quant & Peter Borm & Hans Reijnierse & Mark Voorneveld, 2006. "A note on theβ-measure for digraph competitions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 167-176, June.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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