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Collective Choice under Dichotomous Preferences

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  • 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.

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Bibliographic Info

Paper provided by Rice University, Department of Economics in its series Working Papers with number 2003-09.

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Date of creation: Aug 2003
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Handle: RePEc:ecl:riceco:2003-09

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  1. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
  2. Shasikanta Nandeibam, 1998. "An alternative proof of Gibbard's random dictatorship result," Social Choice and Welfare, Springer, vol. 15(4), pages 509-519.
  3. Moulin, Herve & Bogomolnaia, Anna, 2001. "Random Matching under Dichotomous Preferences," Working Papers 2001-03, Rice University, Department of Economics.
  4. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
  5. Barbera, Salvador, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 379-89, April.
  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. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  8. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
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Cited by:
  1. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer, vol. 31(1), pages 151-162, June.
  2. Aziz, Haris & Brandt, Felix & Brill, Markus, 2013. "The computational complexity of random serial dictatorship," Economics Letters, Elsevier, vol. 121(3), pages 341-345.
  3. EHLERS, Lars & BARBERÀ, Salvador, 2007. "Free Triples, Large Indifference Classes and the Majority Rule," Cahiers de recherche 2007-02, Universite de Montreal, Departement de sciences economiques.
  4. Jérémy Picot, 2012. "Random aggregation without the Pareto principle," Review of Economic Design, Springer, vol. 16(1), pages 1-13, March.
  5. Massó, Jordi & Vorsatz, Marc, 2006. "Weighted Approval Voting," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Mariotti, Marco & Veneziani, Roberto, 2012. "Allocating chances of success in finite and infinite societies: The utilitarian criterion," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 226-236.
  7. Ju, Biung-Ghi, 2011. "Collectively rational voting rules for simple preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 143-149, March.
  8. Wolitzky, Alexander, 2009. "Fully sincere voting," Games and Economic Behavior, Elsevier, vol. 67(2), pages 720-735, November.
  9. Picot, Jérémy & Sen, Arunava, 2012. "An extreme point characterization of random strategy-proof social choice functions: The two alternative case," Economics Letters, Elsevier, vol. 115(1), pages 49-52.
  10. Sato, Shin, 2009. "Strategy-proof social choice with exogenous indifference classes," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 48-57, January.
  11. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs, Spanish Economic Association, vol. 3(1), pages 227-245, March.
  12. 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.
  13. repec:lmu:muenec:6431 is not listed on IDEAS

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