IDEAS home Printed from https://ideas.repec.org/p/ecl/riceco/2003-09.html
   My bibliography  Save this paper

Collective Choice under Dichotomous Preferences

Author

Listed:
  • Bogomolnaia, Anna

    (Rice U)

  • Moulin, Herve
  • Stong, Richard

Abstract

Agents partition deterministic outcomes into good or bad. A direct revelation mechanism selects a lottery over outcomes - also interpreted as time-shares. Under such dichotomous preferences, the probability that the lottery outcome be a good one is a canonical utility representation. The utilitarian mechanism averages over all deterministic outcomes "approved" by the largest number of agents. It is efficient, strategy-proof and treats equally agents and outcomes. We reach the impossibility frontier if we also place the lower bound 1/n on each agent's utility, where n is the number of agents; or if this lower bound is the fraction of good outcomes to feasible outcomes. We conjecture that no ex-ante efficient and strategy-proof mechanism guarantees a strictly positive utility to all agents at all profiles, and prove a weaker version of this conjecture.

Suggested Citation

  • Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2003. "Collective Choice under Dichotomous Preferences," Working Papers 2003-09, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:2003-09
    as

    Download full text from publisher

    File URL: http://www.ruf.rice.edu/~econ/papers/2003papers/09bogomolnaia.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Salvador Barbera, 1979. "Majority and Positional Voting in a Probabilistic Framework," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 379-389.
    2. Barbera, Salvador & Bogomolnaia, Anna & van der Stel, Hans, 1998. "Strategy-proof probabilistic rules for expected utility maximizers," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 89-103, March.
    3. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
    4. Shasikanta Nandeibam, 1998. "An alternative proof of Gibbard's random dictatorship result," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 509-519.
    5. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
    6. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
    7. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    8. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    9. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    10. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhaskar Dutta & Hans Peters & Arunava Sen, 2008. "Strategy-proof cardinal decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 701-702, May.
    2. Wolitzky, Alexander, 2009. "Fully sincere voting," Games and Economic Behavior, Elsevier, vol. 67(2), pages 720-735, November.
    3. Shasikanta Nandeibam, 2013. "The structure of decision schemes with cardinal preferences," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 205-238, September.
    4. Barbera, Salvador & Bogomolnaia, Anna & van der Stel, Hans, 1998. "Strategy-proof probabilistic rules for expected utility maximizers," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 89-103, March.
    5. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
    6. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona School of Economics.
    7. 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.
    8. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    9. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
    10. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 227-245, March.
    11. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    12. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    13. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    14. Peter Fishburn & Steven Brams, 1984. "Manipulability of voting by sincere truncation of preferences," Public Choice, Springer, vol. 44(3), pages 397-410, January.
    15. Arlegi, Ritxar & Dimitrov, Dinko, 2016. "Power set extensions of dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 20-29.
    16. Felix Brandt & Patrick Lederer & Ren'e Romen, 2022. "Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes," Papers 2201.10418, arXiv.org.
    17. Ju, Biung-Ghi, 2011. "Collectively rational voting rules for simple preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 143-149, March.
    18. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    19. Felix Brandt & Patrick Lederer & René Romen, 2024. "Relaxed notions of Condorcet-consistency and efficiency for strategyproof social decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 19-55, August.
    20. Kaveh Madani & Laura Read & Laleh Shalikarian, 2014. "Voting Under Uncertainty: A Stochastic Framework for Analyzing Group Decision Making Problems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(7), pages 1839-1856, May.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecl:riceco:2003-09. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/dericus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.