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Condorcet choice correspondences for weak tournaments

Author

Listed:
  • Josep Enric Peris Ferrando

    () (Universidad de Alicante)

  • Begoña Subiza Martínez

    () (Universidad de Alicante)

Abstract

Tournaments are complete and asymmetric binary relations. This type of binary relation rules out the possibility of ties or indifferences which are common in different contexts. In this work we generalize, from a normative point of view, some important tournaments solutions (top cycle, uncovered set and minimal covering) to the context where ties are possible.

Suggested Citation

  • Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1997. "Condorcet choice correspondences for weak tournaments," Working Papers. Serie AD 1997-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  • Handle: RePEc:ivi:wpasad:1997-05
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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1997-05.pdf
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    Cited by:

    1. Felix Brandt & Christian Geist & Paul Harrenstein, 2016. "A note on the McKelvey uncovered set and Pareto optimality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 81-91, January.
    2. Vincent Anesi, 2012. "A new old solution for weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 919-930, October.
    3. Martin, Mathieu & Merlin, Vincent, 2002. "The stability set as a social choice correspondence," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 91-113, September.
    4. John Duggan, 2011. "Uncovered Sets," Wallis Working Papers WP63, University of Rochester - Wallis Institute of Political Economy.
    5. John Duggan, 2013. "Uncovered sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 489-535, September.
    6. Gilbert Laffond & Jean Lainé, 2009. "Condorcet choice and the Ostrogorski paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 317-333, February.
    7. Ceyhun Coban & M. Sanver, 2014. "Social choice without the Pareto principle under weak independence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 953-961, December.
    8. repec:spr:sochwe:v:50:y:2018:i:2:d:10.1007_s00355-017-1086-0 is not listed on IDEAS
    9. repec:spr:sochwe:v:51:y:2018:i:2:d:10.1007_s00355-018-1112-x is not listed on IDEAS
    10. Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March.
    11. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
    12. Begoña Subiza & Josep Peris, 2000. "Choice Functions: Rationality re-Examined," Theory and Decision, Springer, vol. 48(3), pages 287-304, May.
    13. Monsuur, Herman, 2005. "Characterizations of the 3-cycle count and backward length of a tournament," European Journal of Operational Research, Elsevier, vol. 164(3), pages 778-784, August.
    14. 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.
    15. De Donder, Philippe & Le Breton, Michel & Truchon, Michel, 2000. "Choosing from a weighted tournament1," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 85-109, July.
    16. Felix Brandt & Christian Geist & Paul Harrenstein, 2016. "A note on the McKelvey uncovered set and Pareto optimality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 81-91, January.
    17. Marc Pauly, 2014. "Can strategizing in round-robin subtournaments be avoided?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 29-46, June.
    18. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
    19. LASLIER, Jean-François & PICARD, Nathalie, 2000. "Distributive politics: does electoral competition promote inequality ?," CORE Discussion Papers 2000022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Lainé, Jean, 2015. "Hyper-stable collective rankings," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 70-80.
    21. Begoña Subiza & Josep Peris, 2005. "Condorcet choice functions and maximal elements," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 497-508, June.
    22. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.

    More about this item

    Keywords

    Tournament; uncovered set; minimal covering;

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