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Directional distance functions and social welfare: Some axiomatic and dual properties

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  • Briec, Walter
  • Dumas, Audrey
  • Mekki, Ayman

Abstract

The paper introduces in social choice theory a directional distance function (DDF) that quantifies the level of inefficiency of a given allocation with respect to the utility possibilities frontier. The paper shows that the DDF has a simple geometric interpretation and involves a complete transitive preference relation. If the uility possibilities set is not convex, it is shown that the Rawls welfare function is dual (in a certain sense) to the DDF. Finally a more general class of distance functions is introduced that is shown to be closely related to a large class of welfare functions widely used in the study of economic inequality.

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  • Briec, Walter & Dumas, Audrey & Mekki, Ayman, 2021. "Directional distance functions and social welfare: Some axiomatic and dual properties," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 181-190.
    • Handle: RePEc:eee:matsoc:v:113:y:2021:i:c:p:181-190
    DOI: 10.1016/j.mathsocsci.2021.07.004
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    References listed on IDEAS

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    Cited by:

    1. Kerstens, Kristiaan & Mazza, Paolo & Ren, Tiantian & Van de Woestyne, Ignace, 2022. "Multi-Time and Multi-Moment Nonparametric Frontier-Based Fund Rating: Proposal and Buy-and-Hold Backtesting Strategy," Omega, Elsevier, vol. 113(C).
    2. Walter Briec, 2021. "Distance Functions and Generalized Means: Duality and Taxonomy," Papers 2112.09443, arXiv.org, revised May 2023.

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