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Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In: Individual and Collective Choice and Social Welfare

Author

Listed:
  • Francesca Busetto

    (Università degli Studi di Udine)

  • Giulio Codognato

    (Università degli Studi di Udine
    Université de Paris Ouest Nanterre la Défense)

  • Simone Tonin

    (University of Glasgow)

Abstract

In the line opened by Kalai and Muller (J Econ Theory 16:457–469, 1977), we explore new conditions on preference domains which make it possible to avoid Arrow’s impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictatorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman et al. (Math Oper Res 28:309–326, 2003; J Econ Theory 128:232–254, 2006). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.’s work and specify integer programs in which variables are allowed to assume values in the set $$\{0, \frac{1} {2},1\}$$ : indeed, 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 all Arrovian social welfare functions—without restrictions on the range.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Simone Tonin, 2015. "Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach," Studies in Choice and Welfare, in: Constanze Binder & Giulio Codognato & Miriam Teschl & Yongsheng Xu (ed.), Individual and Collective Choice and Social Welfare, edition 127, pages 149-169, Springer.
    • Handle: RePEc:spr:stcchp:978-3-662-46439-7_10
    DOI: 10.1007/978-3-662-46439-7_10
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    Citations

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    Cited by:

    1. Francesca Busetto & Giulio Codognato & Simone Tonin, 2018. "Kalai and Muller’s possibility theorem: a simplified integer programming version," Review of Economic Design, Springer;Society for Economic Design, vol. 22(3), pages 149-157, December.
    2. Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2018. "Integer programming on domains containing inseparable ordered pairs," Research in Economics, Elsevier, vol. 72(4), pages 428-434.
    3. Francesca Busetto & Giulio Codognato & Simone Tonin, 2017. "Nondictatorial Arrovian Social Welfare Functions, Simple Majority Rule and Integer Programming," Working Papers 2017_11, Durham University Business School.
    4. Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2021. "Simple majority rule and integer programming," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 160-163.

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