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Collective Choice under Dichotomous Preferences

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Author Info
Bogomolnaia, Anna (Rice U)
Moulin, Herve
Stong, Richard

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

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  1. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, 01. [Downloadable!] (restricted)
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  2. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December. [Downloadable!] (restricted)
  3. Barbera, Salvador, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Blackwell Publishing, vol. 46(2), pages 379-89, April. [Downloadable!] (restricted)
  4. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  6. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April. [Downloadable!] (restricted)
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  1. Arlegi, Ritxar & Dimitrov, Dinko, 2008. "Dichotomous Preferences and Power Set Extensions," Discussion Papers in Economics 6431, University of Munich, Department of Economics. [Downloadable!]
  2. 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). [Downloadable!]
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  3. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer, vol. 31(1), pages 151-162, June. [Downloadable!] (restricted)
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