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Strategy-proofness with single-peaked and single-dipped preferences

Author

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  • Alcalde-Unzu, Jorge
  • Gallo, Oihane
  • Vorsatz, Marc

Abstract

We analyze the problem of locating a public facility in a domain of single-peaked and single-dipped preferences when the social planner knows the type of preference (single-peaked or single-dipped) of each agent. Our main result characterizes all strategy-proof rules and shows that they can be decomposed into two steps. In the first step, the agents with single-peaked preferences are asked about their peaks and, for each profile of reported peaks, at most two alternatives are preselected. In the second step, the agents with single-dipped preferences are asked to reveal their dips to complete the decision between the preselected alternatives. Our result generalizes the findings of Moulin (1980) and Barberà and Jackson (1994) for single-peaked and of Manjunath (2014) for single-dipped preferences. Finally, we show that all strategy-proof rules are also group strategy-proof and analyze the implications of Pareto efficiency.

Suggested Citation

  • Alcalde-Unzu, Jorge & Gallo, Oihane & Vorsatz, Marc, 2024. "Strategy-proofness with single-peaked and single-dipped preferences," Games and Economic Behavior, Elsevier, vol. 147(C), pages 107-127.
    • Handle: RePEc:eee:gamebe:v:147:y:2024:i:c:p:107-127
    DOI: 10.1016/j.geb.2024.05.011
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    References listed on IDEAS

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    1. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 335-352, July.
    2. 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.
    3. 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.
    4. Berga, Dolors & Serizawa, Shigehiro, 2000. "Maximal Domain for Strategy-Proof Rules with One Public Good," Journal of Economic Theory, Elsevier, vol. 90(1), pages 39-61, January.
    5. 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.
    6. Gopakumar Achuthankutty & Souvik Roy, 2018. "Dictatorship on top-circular domains," Theory and Decision, Springer, vol. 85(3), pages 479-493, October.
    7. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2022. "Restricted environments and incentive compatibility in interdependent values models," Games and Economic Behavior, Elsevier, vol. 131(C), pages 1-28.
    8. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    9. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    10. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    12. Andrew Jennings & Rida Laraki & Clemens Puppe & Estelle Varloot, 2021. "New Characterizations of Strategy-Proofness under Single-Peakedness," Papers 2102.11686, arXiv.org, revised Jun 2022.
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    Cited by:

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    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other

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