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Ordinal efficiency under the lens of duality theory

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  • Athanassoglou, Stergios

Abstract

An allocation's ordinal efficiency deficit (OED) is defined as the greatest ordinal efficiency loss that can result from its application. More precisely, an allocation's OED is the negative of the greatest total amount by which it may be stochastically dominated by another feasible allocation. Thus, an allocation is ordinally efficient if and only if its OED is zero. Using this insight, we set up a linear program whose optimal objective value corresponds to a given allocation's OED. Furthermore, we show that the OED is a piecewise-linear convex function on the set of allocations. We use the optimal dual variables of the linear program to construct a profile of von Neumann-Morgenstern (vNM) utilities that is compatible with the underlying ordinal preferences, and which is a subgradient of the OED at the given allocation. When the given allocation is ordinally efficient, our analysis implies that it is ex-ante welfare maximizing at the constructed vNM profile, and we recover the ordinal efficiency theorem due to McLennan (2002)

Suggested Citation

  • Athanassoglou, Stergios, 2010. "Ordinal efficiency under the lens of duality theory," MPRA Paper 26331, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:26331
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    File URL: https://mpra.ub.uni-muenchen.de/26331/1/MPRA_paper_26331.pdf
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    Keywords

    random assignment; ordinal efficiency; linear programming; duality;

    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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