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Unanimity in attribute-based preference domains

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  • Sidartha Gordon

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Abstract

We provide several characterizations of unanimity decision rules, in a public choice model where preferences are constrained by attributes possessed by the alternatives (Nehring and Puppe, Games Econ Behavior 59:132–153, 2007a ; Nehring and Puppe, J Econ Theory 135:269–305, 2007b ). Solidarity conditions require that when some parameters of the economy change, the agents whose parameters are kept fixed either all weakly lose or they all weakly win. Population-monotonicity (Thomson, Math Oper Res 8:319–326, 1983a ; Thomson, J Econ Theory 31:211–226, 1983b ) applies to the arrival and departure of agents, while replacement-domination (Moulin, Q J Econ 102:769–783, 1987 ) applies to changes in preferences. We show that either solidarity property is compatible with voter-sovereignty and strategy-proofness if and only if the attribute space is quasi-median (Nehring, Social aggregation without veto, Mimeo, 2004 ), and with Pareto-efficiency if and only if the attribute space is a tree. Each of these combinations characterizes unanimity. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:44:y:2015:i:1:p:13-29
    DOI: 10.1007/s00355-014-0809-8
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    References listed on IDEAS

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    1. 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.
    2. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 2005. "Voting by committees under constraints," Journal of Economic Theory, Elsevier, vol. 122(2), pages 185-205, June.
    3. Vohra, Rakesh V., 1999. "The replacement principle and tree structured preferences," Economics Letters, Elsevier, vol. 63(2), pages 175-180, May.
    4. Hervé Moulin, 1987. "The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 769-783.
    5. 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.
    6. 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.
    7. Gordon, Sidartha, 2007. "Public decisions: Solidarity and the status quo," Games and Economic Behavior, Elsevier, vol. 61(2), pages 225-241, November.
    8. Bu, Nanyang, 2013. "Unfolding the mystery of false-name-proofness," Economics Letters, Elsevier, vol. 120(3), pages 559-561.
    9. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    10. Dolors Berga & Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2004. "Stability and voting by committees with exit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 229-247, October.
    11. 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.
    12. Ehlers, Lars, 2002. "Multiple public goods and lexicographic preferences: replacement principle," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 1-15, February.
    13. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    14. Thomson, William, 1993. "The replacement principle in public good economies with single-peaked preferences," Economics Letters, Elsevier, vol. 42(1), pages 31-36.
    15. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    16. 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.
    17. Danilov, Vladimir I., 1994. "The structure of non-manipulable social choice rules on a tree," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 123-131, April.
    18. 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.
    19. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
    20. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    21. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    22. 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.
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    Cited by:

    1. 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.
    2. Bettina Klaus & Panos Protopapas, 2017. "Solidarity for public goods under single-peaked preferences: Characterizing target set correspondences," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 17.13, Université de Lausanne, Faculté des HEC, DEEP.
    3. Gordon, Sidartha, 2007. "Public decisions: Solidarity and the status quo," Games and Economic Behavior, Elsevier, vol. 61(2), pages 225-241, November.
    4. Harless, Patrick, 2016. "Solidarity in preference aggregation: Improving on a status quo," Games and Economic Behavior, Elsevier, vol. 95(C), pages 73-87.

    More about this item

    Keywords

    Solidarity; Population-monotonicity; Replacement-domination; Unanimity; Strategy-proofness; Attribute-based Domains; Generalized Single-Peaked Domains; D63; D71; H41;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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