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Efficient Random Assignment under a Combination of Ordinal and Cardinal Information on Preferences

Author

Listed:
  • Stergios Athanassoglou

    (Fondazione Eni Enrico Mattei and Euro-Mediterranean Center for Climate Change)

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 non-negative 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.

Suggested Citation

  • Stergios Athanassoglou, 2011. "Efficient Random Assignment under a Combination of Ordinal and Cardinal Information on Preferences," Working Papers 2011.11, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2011.11
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    Cited by:

    1. Aziz, Haris & Brandl, Florian & Brandt, Felix, 2015. "Universal Pareto dominance and welfare for plausible utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 123-133.
    2. Doğan, Battal & Yıldız, Kemal, 2016. "Efficiency and stability of probabilistic assignments in marriage problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 47-58.
    3. Haris Aziz, 2014. "A characterization of stochastic dominance efficiency," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 205-212, October.

    More about this item

    Keywords

    Random Assignment; Efficiency; Duality; Linear Programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D60 - Microeconomics - - Welfare Economics - - - General

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