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Anonymous, non-manipulable binary social choice

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  • Basile, Achille
  • Rao, Surekha
  • Bhaskara Rao, K.P.S.

Abstract

Let V be a society whose members express weak preferences about two alternatives. We show simple representation formulae that are valid for all, and only, the elements of various classes of non-manipulable social choice functions on V. We represent the entire class of the non-manipulable social choice functions, and various of its subclasses corresponding to further properties. We focus mainly on anonymity. Efficiency and neutrality up to one voter are also considered. As a consequence of the representation formulae, the cardinalities of some of these classes are also established. Notably, we show that the number of anonymous and non-manipulable social choice functions on V is 2n+1 if V contains n members.

Suggested Citation

  • Basile, Achille & Rao, Surekha & Bhaskara Rao, K.P.S., 2022. "Anonymous, non-manipulable binary social choice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 138-149.
    • Handle: RePEc:eee:gamebe:v:133:y:2022:i:c:p:138-149
    DOI: 10.1016/j.geb.2022.02.007
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    1. Núñez, Matías & Sanver, M. Remzi, 2017. "Revisiting the connection between the no-show paradox and monotonicity," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 9-17.
    2. Achille Basile & Surekha Rao & K. P. S. Bhaskara Rao, 2020. "The structure of two-valued strategy-proof social choice functions with indifference," Papers 2002.06341, arXiv.org, revised Jul 2020.
    3. Abhinaba Lahiri & Anup Pramanik, 2020. "On strategy-proof social choice between two alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 581-607, April.
    4. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    5. Achille Basile & Surekha Rao & K. P. S. Bhaskara Rao, 2022. "Binary strategy-proof social choice functions with indifference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 807-826, April.
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    12. Basile, Achille & Rao, Surekha & Bhaskara Rao, K.P.S., 2021. "The structure of two-valued coalitional strategy-proof social choice functions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
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    Cited by:

    1. Achille Basile & Anna De Simone & Ciro Tarantino, 2022. "A Note on Binary Strategy-Proof Social Choice Functions," Games, MDPI, vol. 13(6), pages 1-19, November.
    2. Basile, Achille & Rao, Surekha & Bhaskara Rao, K.P.S., 2022. "Geometry of anonymous binary social choices that are strategy-proof," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 85-91.
    3. Achille Basile & K. P. S. Bhaskara Rao & Surekha Rao, 2022. "The character of non-manipulable collective choices between two alternatives," Papers 2208.01594, arXiv.org, revised Feb 2024.

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    More about this item

    Keywords

    Social choice functions; Non-manipulability; Anonymity; Veto; Quota majority; Weak preferences;
    All these keywords.

    JEL classification:

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

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