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Register a new userThe Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally
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The long-term impact of algorithmic decision making is shaped by the dynamics between the deployed decision rule and individuals response. Focusing on settings where each individual desires a positive classification---including many important applications such as hiring and school admissions, we study a dynamic learning setting where individuals invest in a positive outcome based on their groups expected gain and the decision rule is updated to maximize institutional benefit. By characterizing the equilibria of these dynamics, we show that natural challenges to desirable long-term outcomes arise due to heterogeneity across groups and the lack of realizability. We consider two interventions, decoupling the decision rule by group and subsidizing the cost of investment. We show that decoupling achieves optimal outcomes in the realizable case but has discrepant effects that may depend on the initial conditions otherwise. In contrast, subsidizing the cost of investment is shown to create better equilibria for the disadvantaged group even in the absence of realizability.
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Society increasingly relies on machine learning models for automated decision making. Yet, efficiency gains from automation have come paired with concern for algorithmic discrimination that can systematize inequality. Recent work has proposed optimal post-processing methods that randomize classification decisions for a fraction of individuals, in order to achieve fairness measures related to parity in errors and calibration. These methods, however, have raised concern due to the information inefficiency, intra-group unfairness, and Pareto sub-optimality they entail. The present work proposes an alternative active framework for fair classification, where, in deployment, a decision-maker adaptively acquires information according to the needs of different groups or individuals, towards balancing disparities in classification performance. We propose two such methods, where information collection is adapted to group- and individual-level needs respectively. We show on real-world datasets that these can achieve: 1) calibration and single error parity (e.g., equal opportunity); and 2) parity in both false positive and false negative rates (i.e., equal odds). Moreover, we show that by leveraging their additional degree of freedom, active approaches can substantially outperform randomization-based classifiers previously considered optimal, while avoiding limitations such as intra-group unfairness.
Nowadays fairness issues have raised great concerns in decision-making systems. Various fairness notions have been proposed to measure the degree to which an algorithm is unfair. In practice, there frequently exist a certain set of variables we term as fair variables, which are pre-decision covariates such as users choices. The effects of fair variables are irrelevant in assessing the fairness of the decision support algorithm. We thus define conditional fairness as a more sound fairness metric by conditioning on the fairness variables. Given different prior knowledge of fair variables, we demonstrate that traditional fairness notations, such as demographic parity and equalized odds, are special cases of our conditional fairness notations. Moreover, we propose a Derivable Conditional Fairness Regularizer (DCFR), which can be integrated into any decision-making model, to track the trade-off between precision and fairness of algorithmic decision making. Specifically, an adversarial representation based conditional independence loss is proposed in our DCFR to measure the degree of unfairness. With extensive experiments on three real-world datasets, we demonstrate the advantages of our conditional fairness notation and DCFR.
The Arrow-Debreu extension of the classic Hylland-Zeckhauser scheme for a one-sided matching market -- called ADHZ in this paper -- has natural applications but has instances which do not admit equilibria. By introducing approximation, we define the $epsilon$-approximate ADHZ model, and we give the following results. * Existence of equilibrium under linear utility functions. We prove that the equilibrium satisfies Pareto optimality, approximate envy-freeness, and approximate weak core stability. * A combinatorial polynomial-time algorithm for an $epsilon$-approximate ADHZ equilibrium for the case of dichotomous, and more generally bi-valued, utilities. * An instance of ADHZ, with dichotomous utilities and a strongly connected demand graph, which does not admit an equilibrium. Since computing an equilibrium for HZ is likely to be highly intractable and because of the difficulty of extending HZ to more general utility functions, Hosseini and Vazirani proposed (a rich collection of) Nash-bargaining-based matching market models. For the dichotomous-utilities case of their model linear Arrow-Debreu Nash bargaining one-sided matching market (1LAD), we give a combinatorial, strongly polynomial-time algorithm and show that it admits a rational convex program.
This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.
Using the concept of principal stratification from the causal inference literature, we introduce a new notion of fairness, called principal fairness, for human and algorithmic decision-making. The key idea is that one should not discriminate among individuals who would be similarly affected by the decision. Unlike the existing statistical definitions of fairness, principal fairness explicitly accounts for the fact that individuals can be impacted by the decision. We propose an axiomatic assumption that all groups are created equal. This assumption is motivated by a belief that protected attributes such as race and gender should have no direct causal effects on potential outcomes. Under this assumption, we show that principal fairness implies all three existing statistical fairness criteria once we account for relevant covariates. This result also highlights the essential role of conditioning covariates in resolving the previously recognized tradeoffs between the existing statistical fairness criteria. Finally, we discuss how to empirically choose conditioning covariates and then evaluate the principal fairness of a particular decision.
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