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Anonymous, non-manipulable, binary social choice

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

Abstract

Let V be a finite society whose members express weak orderings (hence also indifference, possibly) about two alternatives. We show a simple representation formula that is valid for all, and only, anonymous, non-manipulable, binary social choice functions on V . The number of such functions is $2^{n+1}$ if V contains $n$ agents.

Suggested Citation

  • Achille Basile & Surekha Rao & K. P. S. Bhaskara Rao, 2020. "Anonymous, non-manipulable, binary social choice," Papers 2007.01552, arXiv.org.
    • Handle: RePEc:arx:papers:2007.01552
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    References listed on IDEAS

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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. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 791-808, November.
    5. 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.
    6. 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.
    7. Larsson, Bo & Svensson, Lars-Gunnar, 2006. "Strategy-proof voting on the full preference domain," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 272-287, December.
    8. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    9. 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).
    10. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    11. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    12. Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
    13. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    14. Antonio Quesada, 2005. "Abstention as an escape from Arrow's theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 221-226, October.
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    Cited by:

    1. 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.
    2. Stergios Athanasoglou & Somouaoga Bonkoungou, 2024. "Sequential unanimity voting rules for binary social choice," Papers 2402.13009, arXiv.org, revised Apr 2024.
    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.
    4. 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.

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    More about this item

    JEL classification:

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

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