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Game-theoretic analysis of voting in committees

In: Handbook of Social Choice and Welfare

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  • Peleg, Bezalel

Abstract

In this chapter we adopt the axiomatic approach in order to find (new) voting procedures to committees that are immune against deviations by coalitions of voters. We shall now describe our approach. Let G be a committee and let A be a finite set of m alternatives, m [greater-or-equal, slanted] 2. Our problem is to find a social choice function F that will enable the members of G to choose one alternative out of A. We insist that F will have the following properties.(i) F should be Paretian, monotonic, and preserve the symmetries of G;(ii) the power structure induced by F should coincide with G;(iii) for each profile RN of (true) preferences of N (i.e., the set of members of G), F(RN) should be the outcome of a strong Nash equilibrium (in the strategic game specified by F and RN).Let, again, G be a committee and let A be a set of m alternatives, m [greater-or-equal, slanted] 2. The pair (G, A) is called a choice problem. A social choice function that satisfies the foregoing three criteria (i)-(iii), is called a strong representation of (G, A). If G is weak, that is, G has a vetoer, then (G, A) has a strong representation for every value of m. If G does not contain a vetoer, then there exists a natural number [mu](G) [greater-or-equal, slanted] 2 (the capacity of G), such that (G, A) has a strong representation if and only if 2 [less-than-or-equals, slant] m [less-than-or-equals, slant] [mu](G). A family of algorithms, called feasible elimination procedures, produces a strong representation to any choice problem (G, A) whenever such a representation exists. Feasible eliminations procedures produce all the strong representations of symmetric committees.

Suggested Citation

  • Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423 Elsevier.
  • Handle: RePEc:eee:socchp:1-08
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    Cited by:

    1. BHATTACHARYA, Anindya & ZIAD, Abderrahmane, 2003. "On conservative stable standard of behaviour in situations with perfect foresight," CORE Discussion Papers 2003049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. B Pezaleleleg & Hans Peters, 2006. "Consistent Voting Systems with a Continuum of Voters," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 477-492, December.
    3. Anindya Bhattacharya & Abderrahmane Ziad, 2012. "On credible coalitional deviations by prudent players," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 537-552, July.
    4. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    5. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Computability of simple games: A complete investigation of the sixty-four possibilities," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 150-158, March.
    6. Bezalel Peleg & Ariel Procaccia, 2010. "Implementation by mediated equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 191-207, March.
    7. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 621-640, December.
    8. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.
    9. Sebastian Bervoets, 2010. "An axiomatic approach to predictability of outcomes in an interactive setting," Theory and Decision, Springer, vol. 68(3), pages 311-323, March.
    10. Federico Valenciano & Annick Laruelle, 2004. "Bargaining, Voting, And Value," Working Papers. Serie AD 2004-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    11. repec:eee:matsoc:v:90:y:2017:i:c:p:2-8 is not listed on IDEAS
    12. Barberà, Salvador & Coelho, Danilo, 2010. "On the rule of k names," Games and Economic Behavior, Elsevier, vol. 70(1), pages 44-61, September.
    13. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    14. Bezalel Peleg & Ariel D Procaccia, 2007. "Mediators Enable Truthful Voting," Levine's Bibliography 843644000000000039, UCLA Department of Economics.
    15. Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
    16. Boniface Mbih & Issofa Moyouwou & Xingyu Zhao, 2010. "On the positive association of parliamentary social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 107-127, June.
    17. Masashi Umezawa, 2009. "Coalitionally strategy-proof social choice correspondences and the Pareto rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 151-158, June.
    18. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    19. Ian Ayres & Colin Rowat & Nasser Zakariya, 2011. "Optimal voting rules for two-member tenure committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 323-354, February.
    20. Ruth Ben-Yashar & Igal Milchtaich, 2003. "First and Second Best Voting Rules in Committees," Working Papers 2003-08, Bar-Ilan University, Department of Economics.
    21. Bertrand Tchantcho & Lawrence Diffo Lambo, 2008. "A characterization of social choice correspondences that implement the core of simple games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 533-542, December.
    22. Reiner Wolff & Yavuz Karagök, 2012. "Consistent allocation of cabinet seats: the Swiss Magic Formula," Public Choice, Springer, vol. 150(3), pages 547-559, March.

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    • I0 - Health, Education, and Welfare - - General

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