TY - JOUR
T1 - A guide to formulating fairness in an optimization model
AU - Xinying Chen, Violet
AU - Hooker, J. N.
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/7
Y1 - 2023/7
N2 - Optimization models typically seek to maximize overall benefit or minimize total cost. Yet fairness is an important element of many practical decisions, and it is much less obvious how to express it mathematically. We provide a critical survey of various schemes that have been proposed for formulating ethics-related criteria, including those that integrate efficiency and fairness concerns. The survey covers inequality measures, Rawlsian maximin and leximax criteria, convex combinations of fairness and efficiency, alpha fairness and proportional fairness (also known as the Nash bargaining solution), Kalai–Smorodinsky bargaining, and recently proposed utility-threshold and fairness-threshold schemes for combining utilitarian with maximin or leximax criteria. The paper also examines group parity metrics that are popular in machine learning. We present what appears to be the best practical approach to formulating each criterion in a linear, nonlinear, or mixed integer programming model. We also survey axiomatic and bargaining derivations of fairness criteria from the social choice literature while taking into account interpersonal comparability of utilities. Finally, we cite relevant philosophical and ethical literature where appropriate.
AB - Optimization models typically seek to maximize overall benefit or minimize total cost. Yet fairness is an important element of many practical decisions, and it is much less obvious how to express it mathematically. We provide a critical survey of various schemes that have been proposed for formulating ethics-related criteria, including those that integrate efficiency and fairness concerns. The survey covers inequality measures, Rawlsian maximin and leximax criteria, convex combinations of fairness and efficiency, alpha fairness and proportional fairness (also known as the Nash bargaining solution), Kalai–Smorodinsky bargaining, and recently proposed utility-threshold and fairness-threshold schemes for combining utilitarian with maximin or leximax criteria. The paper also examines group parity metrics that are popular in machine learning. We present what appears to be the best practical approach to formulating each criterion in a linear, nonlinear, or mixed integer programming model. We also survey axiomatic and bargaining derivations of fairness criteria from the social choice literature while taking into account interpersonal comparability of utilities. Finally, we cite relevant philosophical and ethical literature where appropriate.
KW - Distributive justice
KW - Fairness
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U2 - 10.1007/s10479-023-05264-y
DO - 10.1007/s10479-023-05264-y
M3 - Article
AN - SCOPUS:85152080891
SN - 0254-5330
VL - 326
SP - 581
EP - 619
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1
ER -