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Integer Programming and Nondictatorial Arrovian Social Welfare Functions


  • Francesca Busetto
  • Giulio Codognato
  • Simone Tonin


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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    Cited by:

    1. 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).

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    JEL classification:

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

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