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Simple majority rule and integer programming

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  • Busetto, Francesca
  • Codognato, Giulio
  • Tonin, Simone

Abstract

In this paper, we use the integer programming approach to mechanism design, first introduced by Sethuraman et al. (2003), and then systematized by Vohra (2011), to reformulate issues concerning the simple majority rule. Our main result consists in showing that, when the number of agents is even, a necessary and sufficient condition for the simple majority rule to be an Arrovian social welfare function is that it is defined on a domain which is echoic with antagonistic preferences. This result is an integer programming simplified version of Theorems 2, 3, and 4 in Inada (1969).

Suggested Citation

  • Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2021. "Simple majority rule and integer programming," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 160-163.
    • Handle: RePEc:eee:matsoc:v:113:y:2021:i:c:p:160-163
    DOI: 10.1016/j.mathsocsci.2021.07.001
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    References listed on IDEAS

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    1. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Constanze Binder & Giulio Codognato & Miriam Teschl & Yongsheng Xu (ed.), 2015. "Individual and Collective Choice and Social Welfare," Studies in Choice and Welfare, Springer, edition 127, number 978-3-662-46439-7, July.
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    Cited by:

    1. Wen Sun & Zeyang Cao & Gang Wang & Yafei Song & Xiangke Guo, 2022. "An Optimized Double-Nested Anti-Missile Force Deployment Based on the Deep Kuhn–Munkres Algorithm," Mathematics, MDPI, vol. 10(23), pages 1-17, December.

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