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Strategy-proof rules for two public goods: double median rules

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  • Eun Heo

Abstract

We consider the problem of selecting the locations of two (identical) public goods on an interval. Each agent has preferences over pairs of locations, which are induced from single-peaked rankings over single locations: each agent compares pairs of locations by comparing the location he ranks higher in each pair. We introduce a class of “double median rules” and characterize it by means of continuity, anonymity, strategy-proofness, and users only. To each pair of parameter sets, each set in the pair consisting of $$(n+1)$$ parameters, is associated a rule in the class. It is the rule that selects, for each preference profile, the medians of the peaks and the parameters belonging to each set in the pair. We identify the subclasses of the double median rules satisfying group strategy-proofness, weak efficiency, and double unanimity (or efficiency), respectively. We also discuss the classes of “multiple median rules” and “non-anonymous double median rules”. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:41:y:2013:i:4:p:895-922
    DOI: 10.1007/s00355-012-0713-z
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    References listed on IDEAS

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    1. Bochet, Olivier & Gordon, Sidartha, 2012. "Priorities in the location of multiple public facilities," Games and Economic Behavior, Elsevier, vol. 74(1), pages 52-67.
    2. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
    3. Ju, Biung-Ghi, 2008. "Efficiency and consistency for locating multiple public facilities," Journal of Economic Theory, Elsevier, vol. 138(1), pages 165-183, January.
    4. Olivier Bochet & Sidartha Gordon, 2012. "Priorities in the location of multiple public facilities," Post-Print hal-03417535, HAL.
    5. Olivier Bochet & Sidartha Gordon, 2012. "Priorities in the location of multiple public facilities," Post-Print hal-03417534, HAL.
    6. Ehlers, Lars, 2002. "Multiple public goods and lexicographic preferences: replacement principle," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 1-15, February.
    7. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    8. Youngsub Chun, 2006. "The Separability Principle in Economies with Single-Peaked Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 239-253, April.
    9. Masashi Umezawa, 2012. "The replacement principle for the provision of multiple public goods on tree networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 211-235, February.
    10. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    11. Eiichi Miyagawa, 2001. "Locating libraries on a street," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 527-541.
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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. Aziz, Haris & Chan, Hau & Lee, Barton E. & Parkes, David C., 2020. "The capacity constrained facility location problem," Games and Economic Behavior, Elsevier, vol. 124(C), pages 478-490.
    3. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Lars Ehlers, 2022. "Three public goods and lexicographic preferences: replacement principle," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 367-384, September.
    5. Carmelo Rodríguez-à lvarez, 2017. "On single-peakedness and strategy-proofness: ties between adjacent alternatives," Economics Bulletin, AccessEcon, vol. 37(3), pages 1966-1974.
    6. Haris Aziz & Hau Chan & Barton E. Lee & Bo Li & Toby Walsh, 2019. "Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives," Papers 1911.09813, arXiv.org.
    7. Protopapas, Panos, 2018. "On strategy-proofness and single-peakedness: median-voting over intervals," MPRA Paper 83939, University Library of Munich, Germany.
    8. 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.
    9. Bochet, Olivier & Gordon, Sidartha & Saran, Rene, 2013. "Weighted majoritarian rules for the location of multiple public facilities," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 454-459.

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