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Game-theoretic analysis of voting in committees

In: Handbook of Social Choice and Welfare

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Peleg, Bezalel

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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.

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This chapter was published in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.) Handbook of Social Choice and Welfare, , chapter 08, pages 395-423, 2002.

This item is provided by Elsevier in its series Handbook of Social Choice and Welfare with number 1-08.

Handle: RePEc:eee:socchp:1-08

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This chapter was published in the following book, which is listed on IDEAS:
K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1, September. [Downloadable!] (restricted)
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I0 - Health, Education, and Welfare - - General

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  1. Bertrand Tchantcho & Lawrence Diffo Lambo, 2008. "A characterization of social choice correspondences that implement the core of simple games," Economic Theory, Springer, vol. 37(3), pages 533-542, December. [Downloadable!] (restricted)
  2. B Pezaleleleg & Hans Peters, 2006. "Consistent Voting Systems with a Continuum of Voters," Social Choice and Welfare, Springer, vol. 27(3), pages 477-492, December. [Downloadable!] (restricted)
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  3. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer, vol. 31(4), pages 621-640, December. [Downloadable!] (restricted)
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  4. Bezalel Peleg & Ariel D Procaccia, 2007. "Mediators Enable Truthful Voting," Levine's Bibliography 843644000000000039, UCLA Department of Economics. [Downloadable!]
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  5. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany. [Downloadable!]
  6. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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