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Measuring unfairness feeling in allocation problems

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  • Hoang, Lê Nguyên
  • Soumis, François
  • Zaccour, Georges

Abstract

In this paper, we introduce a new measure of social fairness based on unfairness feelings of the players involved in an allocation problem, e.g., cake-cutting problem or shift scheduling. We only require that each player be described by a von Neumann–Morgenstern utility function. Next, we propose a social normalization of each player׳s utility function, based on how each player sees the other players׳ shares through her own utility function. Further, we extend this normalization idea to a setting where the players are represented by a weighted oriented graph, where the weights assess the relatedness of (or similarities between) the agents. Among other results, we establish some links between our measures of fairness and those classically used in the cake-cutting-problem literature.

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  • Hoang, Lê Nguyên & Soumis, François & Zaccour, Georges, 2016. "Measuring unfairness feeling in allocation problems," Omega, Elsevier, vol. 65(C), pages 138-147.
    • Handle: RePEc:eee:jomega:v:65:y:2016:i:c:p:138-147
    DOI: 10.1016/j.omega.2016.01.005
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    1. Arnsperger, Christian, 1994. "Envy-Freeness and Distributive Justice," Journal of Economic Surveys, Wiley Blackwell, vol. 8(2), pages 155-186, June.
    2. Varian, Hal R., 1976. "Two problems in the theory of fairness," Journal of Public Economics, Elsevier, vol. 5(3-4), pages 249-260.
    3. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    4. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    5. Chen, Yiling & Lai, John K. & Parkes, David C. & Procaccia, Ariel D., 2013. "Truth, justice, and cake cutting," Games and Economic Behavior, Elsevier, vol. 77(1), pages 284-297.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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    Cited by:

    1. Shen, Yuelin, 2018. "Pricing contracts and planning stochastic resources in brand display advertising," Omega, Elsevier, vol. 81(C), pages 183-194.
    2. Sanja Petrovic, 2019. "“You have to get wet to learn how to swim” applied to bridging the gap between research into personnel scheduling and its implementation in practice," Annals of Operations Research, Springer, vol. 275(1), pages 161-179, April.

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