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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. Barbera, Salvador, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 379-89, April.
  2. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
  3. 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.
  4. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, 01.
  5. Barbera, S & Bogomolnaia, A & van der Stel, H, 1996. "Strategy-Proof Probabilistic Rules for Expected Utility Maximizers," UFAE and IAE Working Papers 330.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
  7. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  8. Shasikanta Nandeibam, 1998. "An alternative proof of Gibbard's random dictatorship result," Social Choice and Welfare, Springer, vol. 15(4), pages 509-519.
  9. 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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Citations

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Cited by:
  1. Salvador Barberà & Lars Ehlers, 2003. "Free Triples, Large Indifference Classes and the Majority Rule," UFAE and IAE Working Papers 599.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Feb 2007.
  2. 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.
  3. Jordi Massó & Marc Vorsatz, 2006. "Weighted Approval Voting," UFAE and IAE Working Papers 668.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. repec:lmu:muenec:6431 is not listed on IDEAS
  5. Marc Vorsatz, 2004. "Scoring Rules on Dichotomous Preferences," UFAE and IAE Working Papers 617.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Wolitzky, Alexander, 2009. "Fully sincere voting," Games and Economic Behavior, Elsevier, vol. 67(2), pages 720-735, November.
  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. Sato, Shin, 2009. "Strategy-proof social choice with exogenous indifference classes," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 48-57, January.
  9. 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.
  10. 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.
  11. 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.
  12. Aziz, Haris & Brandt, Felix & Brill, Markus, 2013. "The computational complexity of random serial dictatorship," Economics Letters, Elsevier, vol. 121(3), pages 341-345.
  13. Jérémy Picot, 2012. "Random aggregation without the Pareto principle," Review of Economic Design, Springer, vol. 16(1), pages 1-13, March.

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