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Extending tournament solutions

Author

Listed:
  • Felix Brandt

    (Technische Universität München)

  • Markus Brill

    (Technische Universität Berlin)

  • Paul Harrenstein

    (University of Oxford)

Abstract

An important subclass of social choice functions, so-called majoritarian (or C1) functions, only take into account the pairwise majority relation between alternatives. In the absence of majority ties—e.g., when there is an odd number of agents with linear preferences—the majority relation is antisymmetric and complete and can thus conveniently be represented by a tournament. Tournaments have a rich mathematical theory and many formal results for majoritarian functions assume that the majority relation constitutes a tournament. Moreover, most majoritarian functions have only been defined for tournaments and allow for a variety of generalizations to unrestricted preference profiles, none of which can be seen as the unequivocal extension of the original function. In this paper, we argue that restricting attention to tournaments is justified by the existence of a conservative extension, which inherits most of the commonly considered properties from its underlying tournament solution.

Suggested Citation

  • Felix Brandt & Markus Brill & Paul Harrenstein, 2018. "Extending tournament solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 193-222, August.
    • Handle: RePEc:spr:sochwe:v:51:y:2018:i:2:d:10.1007_s00355-018-1112-x
    DOI: 10.1007/s00355-018-1112-x
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    References listed on IDEAS

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    1. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    2. DUGGAN, John & LE BRETON, Michel, 2001. "Mixed refinements of Shapley's saddles and weak tournaments," LIDAM Reprints CORE 1496, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    7. Duggan, John & Le Breton, Michel, 1996. "Dutta's Minimal Covering Set and Shapley's Saddles," Journal of Economic Theory, Elsevier, vol. 70(1), pages 257-265, July.
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    10. Monjardet, B., 2008. "Statement of precedence and a comment on IIA terminology," Games and Economic Behavior, Elsevier, vol. 62(2), pages 736-738, March.
    11. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2018. "On the structure of stable tournament solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 483-507, March.
    12. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
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    Cited by:

    1. Felix Brandt & Chris Dong, 2022. "On Locally Rationalizable Social Choice Functions," Papers 2204.05062, arXiv.org, revised Mar 2024.

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