Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness conditions that lie at the heart of these debates, and we prove that except in highly constrained special cases, there is no method that can satisfy these three conditions simultaneously. Moreover, even satisfying all three conditions approximately requires that the data lie in an approximate version of one of the constrained special cases identified by our theorem. These results suggest some of the ways in which key notions of fairness are incompatible with each other, and hence provide a framework for thinking about the trade-offs between them.
propose a framework based on a task-specific externally defined similarity metric between individuals, seeking to achieve fairness through the goal that similar people [be] treated similarly'' @cite_30 . They strive towards individual fairness, which is a stronger notion of fairness than the definitions we use; however, our approach shares some of the underlying motivation (though not the specifics) in that our balance conditions for the positive and negative classes also reflect the notion that similar people should be treated similarly.
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We study fairness in classification, where individuals are classified, e.g., admitted to a university, and the goal is to prevent discrimination against individuals based on their membership in some group, while maintaining utility for the classifier (the university). The main conceptual contribution of this paper is a framework for fair classification comprising (1) a (hypothetical) task-specific metric for determining the degree to which individuals are similar with respect to the classification task at hand; (2) an algorithm for maximizing utility subject to the fairness constraint, that similar individuals are treated similarly. We also present an adaptation of our approach to achieve the complementary goal of "fair affirmative action," which guarantees statistical parity (i.e., the demographics of the set of individuals receiving any classification are the same as the demographics of the underlying population), while treating similar individuals as similarly as possible. Finally, we discuss the relationship of fairness to privacy: when fairness implies privacy, and how tools developed in the context of differential privacy may be applied to fairness. We propose a learning algorithm for fair classification that achieves both group fairness (the proportion of members in a protected group receiving positive classification is identical to the proportion in the population as a whole), and individual fairness (similar individuals should be treated similarly). We formulate fairness as an optimization problem of finding a good representation of the data with two competing goals: to encode the data as well as possible, while simultaneously obfuscating any information about membership in the protected group. We show positive results of our algorithm relative to other known techniques, on three datasets. Moreover, we demonstrate several advantages to our approach. First, our intermediate representation can be used for other classification tasks (i.e., transfer learning is possible); secondly, we take a step toward learning a distance metric which can find important dimensions of the data for classification. We consider the problem of fairly dividing a collection of indivisible goods among a set of players. Much of the existing literature on fair division focuses on notions of individual fairness. For instance, envy-freeness requires that no player prefer the set of goods allocated to another player to her own allocation. We observe that an algorithm satisfying such individual fairness notions can still treat groups of players unfairly, with one group desiring the goods allocated to another. Our main contribution is a notion of group fairness, which implies most existing notions of individual fairness. Group fairness (like individual fairness) cannot be satisfied exactly with indivisible goods. Thus, we introduce two “up to one good” style relaxations. We show that, somewhat surprisingly, certain local optima of the Nash welfare function satisfy both relaxations and can be computed in pseudo-polynomial time by local search. Our experiments reveal faster computation and stronger fairness guarantees in practice. The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier across these groups. Constraints of this form are susceptible to intentional or inadvertent "fairness gerrymandering", in which a classifier appears to be fair on each individual group, but badly violates the fairness constraint on one or more structured subgroups defined over the protected attributes. We propose instead to demand statistical notions of fairness across exponentially (or infinitely) many subgroups, defined by a structured class of functions over the protected attributes. This interpolates between statistical definitions of fairness and recently proposed individual notions of fairness, but raises several computational challenges. It is no longer clear how to audit a fixed classifier to see if it satisfies such a strong definition of fairness. We prove that the computational problem of auditing subgroup fairness for both equality of false positive rates and statistical parity is equivalent to the problem of weak agnostic learning, which means it is computationally hard in the worst case, even for simple structured subclasses. We then derive two algorithms that provably converge to the best fair classifier, given access to oracles which can solve the agnostic learning problem. The algorithms are based on a formulation of subgroup fairness as a two-player zero-sum game between a Learner and an Auditor. Our first algorithm provably converges in a polynomial number of steps. Our second algorithm enjoys only provably asymptotic convergence, but has the merit of simplicity and faster per-step computation. We implement the simpler algorithm using linear regression as a heuristic oracle, and show that we can effectively both audit and learn fair classifiers on real datasets.