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Nondictatorial Arrovian Social Welfare Functions, Simple Majority Rule and Integer Programming

Author

Listed:
  • Francesca Busetto

    () (Universit`a degli Studi di Udine)

  • Giulio Codognato

    () (Universit`a degli Studi di Udine)

  • Simone Tonin

    () (Durham Business School)

Abstract

In this paper, we use the linear programming approach to mechanism design, rst introduced by Sethuraman et al. (2003) and then systematized by Vohra (2011), to analyze nondictatorial Arrovian social welfare functions with and without ties. First, we provide a new and simpler proof of Theorem 2 in Kalai and Muller (1977), which characterizes the domains admitting nondictatorial Arrovian social welfare functions without ties. Then, we show that a domain containing an inseparable ordered pair admits nondictatorial Arrovian social welfare functions with ties, thereby strengthening a result previously obtained by Kalai and Ritz (1978). Finally, we propose a reformulation of the simple majority rule in the framework of integer programming with an odd or even number of agents. We use this reformulation to recast some celebrated theorems, proved by Arrow (1963), Sen (1966), and Inada (1969), which provide conditions guaranteeing that the simple majority rule is a nondictatorial Arrovian social welfare function.

Suggested Citation

  • 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.
  • Handle: RePEc:dur:durham:2017_11
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    File URL: https://www.dur.ac.uk/resources/business/working-papers/EconWP17_11.pdf
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    References listed on IDEAS

    as
    1. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    2. Kalai, Ehud & Ritz, Zvi, 1980. "Characterization of the private alternatives domains admitting arrow social welfare functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 23-36, February.
    3. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745.
    4. 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.
    5. Blair, Douglas & Muller, Eitan, 1983. "Essential aggregation procedures on restricted domains of preferences," Journal of Economic Theory, Elsevier, vol. 30(1), pages 34-53, June.
    6. Ritz, Zvi, 1985. "Restricted domains, arrow social welfare functions and noncorruptible and nonmanipulable social choice correspondences: The case of private and public alternatives," Journal of Economic Theory, Elsevier, vol. 35(1), pages 1-18, February.
    7. Kim, Ki Hang & Roush, Fred W., 1981. "Effective nondictatorial domains," Journal of Economic Theory, Elsevier, vol. 24(1), pages 40-47, February.
    8. Ritz, Zvi, 1983. "Restricted domains, arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives," Mathematical Social Sciences, Elsevier, vol. 4(2), pages 155-179, April.
    9. 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.
    10. 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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    More about this item

    Keywords

    Social Welfare Function; Simple Majority Rule; Integer Programming;

    JEL classification:

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

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