One of the fundamental insights in the economics of information is the way in which assessing people (students, job applicants, employees) can serve two purposes simultaneously: it can identify the strongest performers, and it can also motivate people to invest effort in improving their performance [29]. This principle has only grown in importance with the rise in algorithmic methods for predicting individual performance across a wide range of domains, including education, employment, and finance. Akey challenge is that we do not generally have access to the true underlying properties that we need for an assessment; rather, they are encoded by an intermediate layer of features, so that the true properties determine the features, and the features then determine our assessment. Standardized testing in education is a canonical example, in which a test score serves as a proxy feature for a student's level of learning, mastery of material, and perhaps other properties we are seeking to evaluate as well. In this case, as in many others, the quantity we wish to measure is unobservable, or at the very least, difficult to accurately measure; the observed feature is a construct interposed between the decision rule and the intended quantity. This role that features play, as a kind of necessary interface between the underlying attributes and the decisions that depend on them, leads to a number of challenges. In particular, when an individual invests effort to perform better on a measure designed by an evaluator, there is a basic tension between effort invested to raise the true underlying attributes that the evaluator cares about, and effort that may serve to improve the proxy features without actually improving the underlying attributes. This tension appears in many contexts -- it is the problem of gaming the evaluation rule, and it underlies the formulation of Goodhart's Law, widely known in the economics literature, which states that once a proxy measure becomes a goal in itself, it is no longer a useful measure [17].

Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users for information that will lead to better decisions in the future. Recently, concerns have been raised about whether the process of exploration could be viewed as unfair, placing too much burden on certain individuals or groups. Motivated by these concerns, we initiate the study of the externalities of exploration - the undesirable side effects that the presence of one party may impose on another - under the linear contextual bandits model. We introduce the notion of a group externality, measuring the extent to which the presence of one population of users impacts the rewards of another. We show that this impact can in some cases be negative, and that, in a certain sense, no algorithm can avoid it. We then study externalities at the individual level, interpreting the act of exploration as an externality imposed on the current user of a system by future users. This drives us to ask under what conditions inherent diversity in the data makes explicit exploration unnecessary. We build on a recent line of work on the smoothed analysis of the greedy algorithm that always chooses the action that currently looks optimal, improving on prior results to show that a greedy approach almost matches the best possible Bayesian regret rate of any other algorithm on the same problem instance whenever the diversity conditions hold, and that this regret is at most $\tilde{O}(T^{1/3})$. Returning to group-level effects, we show that under the same conditions, negative group externalities essentially vanish under the greedy algorithm. Together, our results uncover a sharp contrast between the high externalities that exist in the worst case, and the ability to remove all externalities if the data is sufficiently diverse.

Over the past two decades, the notion of implicit bias has come to serve as an important component in our understanding of discrimination in activities such as hiring, promotion, and school admissions. Research on implicit bias posits that when people evaluate others -- for example, in a hiring context -- their unconscious biases about membership in particular groups can have an effect on their decision-making, even when they have no deliberate intention to discriminate against members of these groups. A growing body of experimental work has pointed to the effect that implicit bias can have in producing adverse outcomes. Here we propose a theoretical model for studying the effects of implicit bias on selection decisions, and a way of analyzing possible procedural remedies for implicit bias within this model. A canonical situation represented by our model is a hiring setting: a recruiting committee is trying to choose a set of finalists to interview among the applicants for a job, evaluating these applicants based on their future potential, but their estimates of potential are skewed by implicit bias against members of one group. In this model, we show that measures such as the Rooney Rule, a requirement that at least one of the finalists be chosen from the affected group, can not only improve the representation of this affected group, but also lead to higher payoffs in absolute terms for the organization performing the recruiting. However, identifying the conditions under which such measures can lead to improved payoffs involves subtle trade-offs between the extent of the bias and the underlying distribution of applicant characteristics, leading to novel theoretical questions about order statistics in the presence of probabilistic side information.

The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair." In this paper, we investigate the tension between minimizing error disparity across different population groups while maintaining calibrated probability estimates. We show that calibration is compatible only with a single error constraint (i.e. equal false-negatives rates across groups), and show that any algorithm that satisfies this relaxation is no better than randomizing a percentage of predictions for an existing classifier. These unsettling findings, which extend and generalize existing results, are empirically confirmed on several datasets.

The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair." In this paper, we investigate the tension between minimizing error disparity across different population groups while maintaining calibrated probability estimates. We show that calibration is compatible only with a single error constraint (i.e. equal false-negatives rates across groups), and show that any algorithm that satisfies this relaxation is no better than randomizing a percentage of predictions for an existing classifier. These unsettling findings, which extend and generalize existing results, are empirically confirmed on several datasets.

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.