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Solidarity in choosing a location on a cycle

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  • Sidartha Gordon

Abstract

We study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Both conditions require that when circumstances change, the agents not responsible for the change should all be affected in the same direction: either they all gain or they all loose. The first condition, population-monotonicity, applies to arrival or departure of one agent. The second, replacement-domination, applies to changes in the preferences of one agent. Unfortunately, no Pareto-efficient solution satisfies any of these properties. However, if agents’ preferred points are restricted to the vertices of a small regular polygon inscribed in the circle, solutions exist. We characterize them as a class of efficient priority rules.
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  • Sidartha Gordon, 2007. "Solidarity in choosing a location on a cycle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 125-147, July.
    • Handle: RePEc:spr:sochwe:v:29:y:2007:i:1:p:125-147
    DOI: 10.1007/s00355-006-0198-8
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    1. Vohra, Rakesh V., 1999. "The replacement principle and tree structured preferences," Economics Letters, Elsevier, vol. 63(2), pages 175-180, May.
    2. Hervé Moulin, 1987. "The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 769-783.
    3. Ehlers, Lars & Klaus, Bettina, 2001. "Solidarity and Probabilistic Target Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(2), pages 167-184.
    4. 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.
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    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. Gordon, Sidartha, 2007. "Public decisions: Solidarity and the status quo," Games and Economic Behavior, Elsevier, vol. 61(2), pages 225-241, November.
    9. Lars Ehlers & Bettina Klaus, 2001. "Solidarity and Probabilistic Target Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(2), pages 167-184, April.
    10. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    11. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    12. Ching, S. & Thomson, W., 1993. "Population-Monotonic Solutions in Public Good Economies with Single- Peaked Preferences," RCER Working Papers 362, University of Rochester - Center for Economic Research (RCER).
    13. Thomson, William, 1993. "The replacement principle in public good economies with single-peaked preferences," Economics Letters, Elsevier, vol. 42(1), pages 31-36.
    14. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    15. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    16. repec:hal:spmain:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    17. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 373-394.
    18. 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.
    19. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401.
    20. Bettina Klaus, 2001. "Target Rules for Public Choice Economies on Tree Networks and in Euclidean Spaces," Theory and Decision, Springer, vol. 51(1), pages 13-29, August.
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    Cited by:

    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. Sidartha Gordon, 2015. "Unanimity in attribute-based preference domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 13-29, January.
    3. 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.
    4. Athanasoglou, Stergios, 2019. "Solidarity and efficiency in preference aggregation: A tale of two rules," Games and Economic Behavior, Elsevier, vol. 118(C), pages 126-140.
    5. Harless, Patrick, 2015. "Solidarity with respect to small changes in preferences in public good economies with single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 81-86.
    6. Gordon, Sidartha, 2007. "Public decisions: Solidarity and the status quo," Games and Economic Behavior, Elsevier, vol. 61(2), pages 225-241, November.
    7. 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.
    8. Harless, Patrick, 2016. "Solidarity in preference aggregation: Improving on a status quo," Games and Economic Behavior, Elsevier, vol. 95(C), pages 73-87.
    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. 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.
    11. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    12. Stergios, Athanasoglou, 2017. "Solidarity and efficiency in preference aggregation: a tale of two rules," Working Papers 390, University of Milano-Bicocca, Department of Economics, revised Nov 2018.
    13. repec:hal:spmain:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    14. repec:hal:wpspec:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS

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    More about this item

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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