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Voting by committees under constraints


  • Barbera, Salvador
  • Masso, Jordi
  • Neme, Alejandro


Many problems of social choice take the following form. There are n voters and a set of k objects. These objects may be bills considered by a legislature, candidates to some set of positions, or the collection of characteristics which distinguish a social alternative from another. The voters must choose a subset of the set of objects. Sometimes, any combination of objects is feasible: for example, if we consider the election of candidates to join a club which is ready to admit as many of them as the voters choose. It is for these cases that Barbera, Sonnenschein, and Zhou (1991) provided characterizations of all voting procedures which are strategy-proof and respect voter's sovereignty when voters' preferences are additively representable, and also when these are separable. For both of these restricted domains, voting by committees turns out to be the family of all rules satisfying the above requirements. Most often, though, some combinations of objects are not feasible, while others are: if there are more candidates than positions to be filled, only sets of size less than or equal to the available number of slots are feasible. Our purpose in this paper is to characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters' preferences are separable or additively representable. Our main conclusions are the following. First: all rules that satisfy strategy-proofness must still be voting by committees. Second: the committees for different objects must be interrelated, in precise ways which depend on what families of sets of objects are feasible. Third: unlike in Barbera, Sonnenschein, and Zhou (1991), the class of strategy- proof rules when preferences are additively representable can be substantially larger that the set of rules satisfying the same requirement when voter' preferences are separable.
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  • Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 2005. "Voting by committees under constraints," Journal of Economic Theory, Elsevier, vol. 122(2), pages 185-205, June.
  • Handle: RePEc:eee:jetheo:v:122:y:2005:i:2:p:185-205

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    References listed on IDEAS

    1. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    2. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    3. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    4. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
    5. Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 45-62, August.
    6. 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.
    7. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 153-170.
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    Cited by:

    1. Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
    2. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.
    3. Klamler, Christian & Pferschy, Ulrich & Ruzika, Stefan, 2012. "Committee selection under weight constraints," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 48-56.
    4. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
    5. 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.
    6. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2014. "Random dictatorship domains," Games and Economic Behavior, Elsevier, vol. 86(C), pages 212-236.
    7. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    8. Chatterji, Shurojit & Roy, Souvik & Sen, Arunava, 2012. "The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 353-366.
    9. Martin Van der linden, 2016. "Impossibilities for strategy-proof committee selection mechanisms with vetoes," Vanderbilt University Department of Economics Working Papers 16-00018, Vanderbilt University Department of Economics.
    10. Wonki Jo Cho & Alejandro Saporiti, 2015. "Incentives, Fairness, and Efficiency in Group Identification," The School of Economics Discussion Paper Series 1501, Economics, The University of Manchester.
    11. John A. Weymark, 2008. "Strategy-Proofness and the Tops-Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    12. Reffgen, Alexander & Svensson, Lars-Gunnar, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, vol. 7(3), September.
    13. repec:eee:mateco:v:73:y:2017:i:c:p:111-121 is not listed on IDEAS

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    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making


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