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On strategy-proofness and single-peakedness: median-voting over intervals

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  • Protopapas, Panos

Abstract

We study solutions that choose an interval of alternatives when agents have single-peaked preferences. Similar to Klaus and Storcken (2002), we ordinally extend these preferences over intervals. Loosely speaking, we extend the results of Moulin (1980) to our setting and show that the results of Ching (1997) cannot always be similarly extended. Our main results are the following. First, strategy-proofness and peaks-onliness characterize the class of generalized median solutions. Second, although peaks-onliness cannot be replaced by the "weaker" property of continuity in our first result -as is the case in Ching (1997)- this equivalence is achieved when voter-sovereignty is also required. Finally, if preferences are symmetric and single-peaked, strategy-proofness and voter-sovereignty characterize the class of efficient generalized median solutions.

Suggested Citation

  • Protopapas, Panos, 2018. "On strategy-proofness and single-peakedness: median-voting over intervals," MPRA Paper 83939, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:83939
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    References listed on IDEAS

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    1. Bettina Klaus & Panos Protopapas, 2020. "Solidarity for public goods under single-peaked preferences: characterizing target set correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 405-430, October.
    2. Núñez, Matías & Xefteris, Dimitrios, 2017. "Implementation via approval mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 169-181.
    3. Bettina Klaus & Panos Protopapas, 2020. "On strategy-proofness and single-peakedness: median-voting over intervals," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1059-1080, December.
    4. Bettina Klaus & Ton Storcken, 2002. "Choice correspondences for public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 127-154.
    5. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    6. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
    7. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    8. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
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    13. 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.
    14. 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.
    15. Eun Heo, 2013. "Strategy-proof rules for two public goods: double median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 895-922, October.
    16. Bettina Klaus & Panos Protopapas, 2016. "Solidarity Properties of Choice Correspondences," Cahiers de Recherches Economiques du Département d'économie 16.14, Université de Lausanne, Faculté des HEC, Département d’économie.
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    Cited by:

    1. Bettina Klaus & Panos Protopapas, 2020. "On strategy-proofness and single-peakedness: median-voting over intervals," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1059-1080, December.
    2. Carmelo Rodríguez-à lvarez, 2024. "Strategy-Proof Social Choice Correspondences and Single Peaked Preferences," Documentos de Trabajo del ICAE 2024-02, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Hans Gersbach & Kremena Valkanova, 2024. "Voting with Random Proposers: Two Rounds Suffice," Papers 2410.20476, arXiv.org, revised Mar 2025.

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    More about this item

    Keywords

    Social choice; strategy proofness; single peaked preferences; choice correspondences; voting; median solutions;
    All these keywords.

    JEL classification:

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

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