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Integer Programming and Nondictatorial Arrovian Social Welfare Functions

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  • Francesca Busetto
  • Giulio Codognato
  • Simone Tonin

Abstract

Following Sethuraman, Teo and Vohra ((2003), (2006)), we apply integer programming tools to the analysis of fundamental issues in social choice theory. We generalize Sethuraman et al.'s approach specifying integer programs in which variables are allowed to assume values in the set {0; 1/2 ; 1}. We show that there exists a one-to-one correspondence between the solutions of an integer program defined on this set and the set of the Arrovian social welfare functions with ties (i.e. admitting indifference in the range). We use our generalized integer programs to analyze nondictatorial Arrovian social welfare functions, in the line opened by Kalai and Muller (1977). Our main theorem provides a complete characterization of the domains admitting non- dictatorial Arrovian social welfare functions with ties by introducing a notion of strict decomposability.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Simone Tonin, 2012. "Integer Programming and Nondictatorial Arrovian Social Welfare Functions," EconomiX Working Papers 2012-36, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2012-36
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    References listed on IDEAS

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    1. Sethuraman, Jay & Teo, Chung-Piaw & Vohra, Rakesh V., 2006. "Anonymous monotonic social welfare functions," Journal of Economic Theory, Elsevier, vol. 128(1), pages 232-254, May.
    2. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
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    Cited by:

    1. Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2014. "Integer Programming on Domains Containing Inseparable Ordered Paris," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-22, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2014. "Integer Programming on Domains Containing Inseparable Ordered Paris," SIRE Discussion Papers 2015-22, Scottish Institute for Research in Economics (SIRE).
    3. Francesca Busetto & Giulio Codognato & Simone Tonin, 2014. "Integer Programming on Domains Containg Inseparable Ordered Pairs," Working Papers 2014_14, Business School - Economics, University of Glasgow.

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    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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