Utility as Fair Pricing
Keywords: Fairness, generalised entropy, inequality, classification, imbalanced data, cost sensitive learning, fair pricing, utility.
TL;DR: Examination of the use of generalised entropy indices as utility functions.
Abstract: In 2018, researchers proposed the use of generalized entropy indices as a unified approach to quantifying algorithmic \emph{unfairness} at both the group and individual levels. Using this metric they empirically evidenced a trade-off between the two notions of fairness. The definition of the index introduces an array of new parameters; thus, while the construction of the metric is principled, its behavior is opaque. Since its publication, the metric has been highly reproduced in the literature, researched and implemented in open source libraries by IBM, Microsoft and Amazon; thus demonstrating traction among researchers, educators and practitioners. Advice or grounded justification around appropriate parameter selection, however, remains scarce. Nevertheless, the metric has been implemented in libraries with default or hard-coded parameter settings from the original paper with little to no explanation.
In this article we take an intentionally data agnostic (rational, rather than empirical) approach to understanding the index, illuminating its behavior with respect to different error distributions and costs, and the effect of placing constraints on it. By adding the simple requirement that the the resulting fairness metric should be independent of model accuracy, we demonstrate consistency between cost sensitive learning and individual fairness in this paradigm. By viewing a classification decision as a transaction between the individual and the decision maker, and accounting for both perspectives, we prove that, with careful parameter selection, the concepts of utility and (group and individual) fairness can be firmly aligned, establishing generalized entropy indices as an efficient, regulatable parametric model of risk, and method for mitigating bias in machine learning.
Primary Area: optimization
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Submission Number: 12523
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