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Efficiency under a combination of ordinal and cardinal information on preferences

  • Athanassoglou, Stergios

Abstract Consider a collection of m indivisible objects to be allocated to n agents, where m>=n. Each agent falls in one of two distinct categories: either he (a) has a complete ordinal ranking over the set of individual objects, or (b) has a set of "plausible" benchmark von Neumann-Morgenstern (vNM) utility functions in whose positive span his "true" utility is known to lie. An allocation is undominated if there does not exist a preference-compatible profile of vNM utilities at which it is Pareto dominated by another feasible allocation. Given an undominated allocation, we use the tools of linear duality theory to construct a profile of vNM utilities at which it is ex-ante welfare maximizing. A finite set of preference-compatible vNM utility profiles is exhibited such that every undominated allocation is ex-ante welfare maximizing with respect to at least one of them. Given an arbitrary allocation, we provide an interpretation of the constructed vNM utilities as subgradients of a function which measures worst-case domination.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 2 (March)
Pages: 180-185

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Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:180-185
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Yeon-Koo Che & Fuhito Kojima, 2008. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Discussion Papers 0809-06, Columbia University, Department of Economics.
  2. Mihai Manea, 2008. "Random serial dictatorship and ordinally efficient contracts," International Journal of Game Theory, Springer, vol. 36(3), pages 489-496, March.
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  4. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
  5. Manea, Mihai, 2009. "Asymptotic ordinal inefficiency of random serial dictatorship," Theoretical Economics, Econometric Society, vol. 4(2), June.
  6. Carroll, Gabriel, 2010. "An efficiency theorem for incompletely known preferences," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2463-2470, November.
  7. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
  8. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
  9. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
  10. Manea, Mihai, 2008. "A constructive proof of the ordinal efficiency welfare theorem," Journal of Economic Theory, Elsevier, vol. 141(1), pages 276-281, July.
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