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Collective choice under dichotomous preferences

  • Bogomolnaia, Anna
  • Moulin, Herve
  • Stong, Richard

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 122 (2005)
Issue (Month): 2 (June)
Pages: 165-184

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Handle: RePEc:eee:jetheo:v:122:y:2005:i:2:p:165-184
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  1. 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).
  2. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
  3. Moulin, Herve & Bogomolnaia, Anna, 2001. "Random Matching under Dichotomous Preferences," Working Papers 2001-03, Rice University, Department of Economics.
  4. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  5. Shasikanta Nandeibam, 1998. "An alternative proof of Gibbard's random dictatorship result," Social Choice and Welfare, Springer, vol. 15(4), pages 509-519.
  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. Barbera, Salvador, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 379-89, April.
  8. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
  9. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
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