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Binary strategy-proof social choice functions with indifference

Author

Listed:
  • Achille Basile

    (Università di Napoli “Federico II”)

  • Surekha Rao

    (Indiana University Northwest)

  • K. P. S. Bhaskara Rao

    (Indiana University Northwest)

Abstract

We prove a representation formula that gives a new characterization of the coalitionally strategy-proof binary social choice functions. We give this characterization in the case of social choice functions selecting one of two alternatives (i.e., binary social choice). The domain of the functions we consider consists of profiles of preferences over a society of arbitrary cardinality and indifference is admitted. Strategy proofness is meant to be coalitional: No group of agents has incentives to form a coalition that can manipulate the social choice for their own advantage with false reporting.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:73:y:2022:i:2:d:10.1007_s00199-020-01273-1
    DOI: 10.1007/s00199-020-01273-1
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    References listed on IDEAS

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    1. 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.
    2. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 227-245, August.
    3. 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.
    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. Surekha Rao & Achille Basile & K. P. S. Bhaskara Rao, 2018. "On the ultrafilter representation of coalitionally strategy-proof social choice functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 1-13, April.
    6. Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
    7. Jerry S. Kelly & Donald E. Campbell, 1997. "Relaxing Pareto optimality in economic environments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 115-130.
    8. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    9. 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.
    10. Biung-Ghi Ju, 2003. "A characterization of strategy-proof voting rules for separable weak orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 469-499, December.
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    Citations

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    Cited by:

    1. 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.
    2. Stergios Athanasoglou & Somouaoga Bonkoungou, 2024. "Sequential unanimity voting rules for binary social choice," Papers 2402.13009, arXiv.org, revised Apr 2024.
    3. Rabah Amir & Bernard Cornet & M. Ali Khan & David Levine & Edward C. Prescott, 2022. "Special Issue in honor of Nicholas C. Yannelis – Part II," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 377-385, April.
    4. Anna De Simone & Ciro Tarantino, 2021. "Functional Form of Nonmanipulable Social Choice Functions with Two Alternatives," Mathematics, MDPI, vol. 9(21), pages 1-14, November.
    5. 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

    Keywords

    Social choice functions; Strategy proofness; Coalitions; Weak orderings;
    All these keywords.

    JEL classification:

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

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