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Integer Programming and Nondictatorial Arrovian Social Welfare Functions

Author

Listed:
  • Francesca Busetto
  • Giulio Codognato

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • 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," Working Papers hal-04141048, HAL.
    • Handle: RePEc:hal:wpaper:hal-04141048
    Note: View the original document on HAL open archive server: https://hal.science/hal-04141048
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    References listed on IDEAS

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    1. Jay Sethuraman & Teo Chung Piaw & Rakesh V. Vohra, 2003. "Integer Programming and Arrovian Social Welfare Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 309-326, 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.
    3. 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.
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