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Upper set rules with binary ranges

Author

Listed:
  • Makoto Hagiwara

    (Tokyo Institute of Technology)

  • Hirofumi Yamamura

    (Komazawa University)

Abstract

We investigate the social choice problem in which the range of a rule consists of only two alternatives. While Barberà et al. (Int J Game Theory 41:791–808, 2012a) capture the feature of “strategy-proof” rules based on the monotonicity condition of winning coalitions, we newly consider the “monotonicity condition with respect to the direction of preference changes.” We show that a rule is strategy-proof if and only if it satisfies the monotonicity condition of preference changes. In addition, we define the class of “upper set rules,” and show that these rules are characterized by strategy-proofness.

Suggested Citation

  • Makoto Hagiwara & Hirofumi Yamamura, 2020. "Upper set rules with binary ranges," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 657-666, April.
    • Handle: RePEc:spr:sochwe:v:54:y:2020:i:4:d:10.1007_s00355-019-01225-2
    DOI: 10.1007/s00355-019-01225-2
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    References listed on IDEAS

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    1. 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.
    2. Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
    3. Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
    4. Stefano Vannucci, 2013. "On two-valued nonsovereign strategy-proof voting rules," Department of Economics University of Siena 672, Department of Economics, University of Siena.
    5. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    6. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    7. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    8. Patrick Harless, 2015. "Reaching consensus: solidarity and strategic properties in binary social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 97-121, June.
    9. Thierry Marchant & Debasis Mishra, 2015. "Mechanism design with two alternatives in quasi-linear environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 433-455, February.
    10. Vikram Manjunath, 2014. "Efficient and strategy-proof social choice when preferences are single-dipped," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 579-597, August.
    11. 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.
    12. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    13. 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.
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    Cited by:

    1. Achille Basile & K. P. S. Bhaskara Rao & Anna De Simone & Ciro Tarantino, 2024. "Isotone Classes of Social Choice Functions with Binary Range," Games, MDPI, vol. 15(6), pages 1-18, December.
    2. Anna De Simone & K. P. S. Bhaskara Rao, 2024. "Two-Valued Strongly Group Strategy-Proof Social Choice Functions," Games, MDPI, vol. 15(6), pages 1-9, December.
    3. 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.

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