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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. Barry O'Neill & Bezalel Peleg, 2006. "Lexicographic Composition of Simple Games," Discussion Paper Series dp415, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
    Other versions:
  2. Bezalel Peleg & Ariel D Procaccia, 2007. "Mediators Enable Truthful Voting," Levine's Bibliography 843644000000000039, UCLA Department of Economics. [Downloadable!]
    Other versions:
  3. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany. [Downloadable!]
  4. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004. [Downloadable!]
    Other versions:
  5. Hans Keiding & Bezalel Peleg, 2004. "Binary Effectivity Rules," Discussion Paper Series dp378, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
    Other versions:
  6. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
    • Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May. [Downloadable!] (restricted)
  7. Otten, G.J., 1995. "Decomposable Effectivity Functions," Discussion Paper 26, Tilburg University, Center for Economic Research. [Downloadable!]
  8. Stefano Vannucci, 2004. "On Game Formats and Chu Spaces," Department of Economics University of Siena 417, Department of Economics, University of Siena. [Downloadable!]
  9. Storcken,Ton, 1995. "Strategy-proof preference rules," Research Memoranda 017, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  10. 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!]
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