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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.

Suggested Citation

  • 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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    1. Walter Briec & Kristiaan Kerstens & Octave Jokung, 2007. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Management Science, INFORMS, vol. 53(1), pages 135-149, January.
    2. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    3. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    4. Rawls, John, 1974. "Some Reasons for the Maximin Criterion," American Economic Review, American Economic Association, vol. 64(2), pages 141-146, May.
    5. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    6. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    7. Paul A. Samuelson, 1950. "Evaluation Of Real National Income," Oxford Economic Papers, Oxford University Press, vol. 2(1), pages 1-29.
    8. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    9. Chavas, Jean-Paul, 2008. "On fair allocations," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 258-272, October.
    10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    11. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    12. Luenberger, David G, 1996. "Welfare from a Benefit Viewpoint," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 445-462, April.
    13. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-136, February.
    14. David G. Luenberger, 1996. "Welfare from a benefit viewpoint (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 445-462.
    15. Xavier Ramos & Jacques Silber, 2005. "On The Application Of Efficiency Analysis To The Study Of The Dimensions Of Human Development," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 51(2), pages 285-309, June.
    16. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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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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