We derive an accounting identity for predictive models that links accuracy with common fairness criteria. The identity shows that for globally calibrated models, the weighted sums of miscalibration within groups and error imbalance across groups is equal to a "total unfairness budget." For binary outcomes, this budget is the model's mean-squared error times the difference in group prevalence across outcome classes. The identity nests standard impossibility results as special cases, while also describing inherent tradeoffs when one or more fairness measures are not perfectly satisfied. The results suggest that accuracy and fairness are best viewed as complements in binary prediction tasks: increasing accuracy necessarily shrinks the total unfairness budget and vice-versa. Experiments on benchmark data confirm the theory and show that many fairness interventions largely substitute between fairness violations, and when they reduce accuracy they tend to expand the total unfairness budget. The results extend naturally to prediction tasks with non-binary outcomes, illustrating how additional outcome information can relax fairness incompatibilities and identifying conditions under which the binary-style impossibility does and does not extend to regression tasks.

We study the identification of individual-level associations when only aggregate data are available. We characterize the biases of, and relationships among, canonical ecological inference (EI) estimators. We use these results to develop a partial identification approach: monotone EI. The approach exploits information about one or both of the following conditional associations: (1) outcome differences between groups within the same neighborhood and (2) outcome differences within the same group between neighborhoods with different group compositions. We show how assumptions about the sign of these conditional associations, whether individually or in relation to one another, can yield informative sharp bounds. We illustrate our results using county-level data to study differences in COVID-19 vaccination rates among Republicans and Democrats in the United States.

We study monotone ecological inference, a partial identification approach to ecological inference. The approach exploits information about one or both of the following conditional associations: (1) outcome differences between groups within the same neighborhood, and (2) outcomes differences within the same group across neighborhoods with different group compositions. We show how assumptions about the sign of these conditional associations, whether individually or in relation to one another, can yield informative sharp bounds in ecological inference settings. We illustrate our proposed approach using county-level data to study differences in Covid-19 vaccination rates among Republicans and Democrats in the United States.

The vast majority of techniques to train fair models require access to the protected attribute (e.g., race, gender), either at train time or in production. However, in many practically important applications, this protected attribute is largely unavailable. Still, AI systems used in sensitive business and government applications — such as housing, ad delivery, and credit underwriting — are increasingly required by law to measure and mitigate their bias. In this paper, we develop methods for measuring and reducing fairness violations in a setting with limited access to protected attribute labels. Specifically, we assume access to protected attribute labels on a small subset of the dataset of interest, but only probabilistic estimates of protected attribute labels (e.g., via Bayesian Improved Surname Geocoding) for the rest of the dataset. With this setting in mind, we propose a method to estimate bounds on common fairness metrics for an existing model, as well as a method for training a model to limit fairness violations by solving a constrained non-convex optimization problem. Unlike existing approaches, our methods take advantage of contextual information – specifically the relationships between a model’s predictions and the probabilistic prediction of protected attributes, given the true protected attribute, and vice versa – to provide tighter bounds on the true disparity. We provide an empirical illustration of our methods using voting data as well as the COMPAS dataset. First, we show that our measurement method can bound the true disparity up to 5.5x tighter than previous methods in these applications. Then, we demonstrate that our training technique effectively reduces disparity in comparison to an unconstrained model while often incurring less severe fairness-accuracy trade-offs than other fair optimization methods with limited access to protected attributes.

Tax authorities around the world rely on audits to detect underreported tax liabilities and to verify that taxpayers qualify for the benefits they claim. We study differences in Internal Revenue Service audit rates between Black and non-Black taxpayers. Because neither we nor the IRS observe taxpayer race, we propose and use a novel partial identification strategy to estimate these differences. Despite race-blind audit selection, we find that Black taxpayers are audited at 2.9 to 4.7 times the rate of non-Black taxpayers. An important driver of the disparity is differing audit rates by race among taxpayers claiming the Earned Income Tax Credit (EITC). Using counterfactual audit selection models to explore why the disparity arises, we find that maximizing the detection of underreported taxes would not lead to Black EITC claimants being audited at higher rates. Rather, the audit disparity among EITC claimants stems largely from a policy decision to prioritize detecting overclaims of refundable credits over other forms of noncompliance. Modifying the audit selection algorithm to target total underreported taxes while holding fixed the number of audited EITC claimants would reduce the share of audited taxpayers who are Black and would lead to more audits focused on accurate reporting of business income and deductions, fewer audits focused on the eligibility of claimed dependents, higher per audit costs, and more detected noncompliance.

We study the problem faced by a data analyst or platform that wishes to collect private data from privacy-aware agents. To incentivize participation, in exchange for this data, the platform provides a service to the agents in the form of a statistic computed using all agents' submitted data. The agents decide whether to join the platform (and truthfully reveal their data) or not participate by considering both the privacy costs of joining and the benefit they get from obtaining the statistic. The platform must ensure the statistic is computed differentially privately and chooses a central level of noise to add to the computation, but can also induce personalized privacy levels (or costs) by giving different weights to different agents in the computation as a function of their heterogeneous privacy preferences (which are known to the platform). We assume the platform aims to optimize the accuracy of the statistic, and must pick the privacy level of each agent to trade-off between i) incentivizing more participation and ii) adding less noise to the estimate. We provide a semi-closed form characterization of the optimal choice of agent weights for the platform in two variants of our model. In both of these models, we identify a common nontrivial structure in the platform's optimal solution: an instance-specific number of agents with the least stringent privacy requirements are pooled together and given the same weight, while the weights of the remaining agents decrease as a function of the strength of their privacy requirement. We also provide algorithmic results on how to find the optimal value of the noise parameter used by the platform and of the weights given to the agents.

This paper studies equilibrium quality of semi-separable position auctions (known as the Ad Types setting [9]) with greedy or optimal allocation combined with generalized second-price (GSP) or Vickrey-Clarke-Groves (VCG) pricing. We make three contributions: first, we give upper and lower bounds on the Price of Anarchy (PoA) for auctions which use greedy allocation with GSP pricing, greedy allocation with VCG pricing, and optimal allocation with GSP pricing. Second, we give Bayes-Nash equilibrium characterizations for two-player, two-slot instances (for all auction formats) and show that there exists both a revenue hierarchy and revenue equivalence across some formats. Finally, we use no-regret learning algorithms and bidding data from a large online advertising platform to evaluate the performance of the mechanisms under semi-realistic conditions. We find that the VCG mechanism tends to obtain revenue and welfare comparable to or better than that of the other mechanisms. We also find that in practice, each of the mechanisms obtains significantly better welfare than our worst-case bounds might suggest.

This study examines issues of algorithmic fairness in the context of systems that inform tax audit selection by the United States Internal Revenue Service (IRS). While the field of algorithmic fairness has developed primarily around notions of treating like individuals alike, we instead explore the concept of vertical equity -- appropriately accounting for relevant differences across individuals -- which is a central component of fairness in many public policy settings. Applied to the design of the U.S. individual income tax system, vertical equity relates to the fair allocation of tax and enforcement burdens across taxpayers of different income levels. Through a unique collaboration with the Treasury Department and IRS, we use access to anonymized individual taxpayer microdata, risk-selected audits, and random audits from 2010-14 to study vertical equity in tax administration. In particular, we assess how the use of modern machine learning methods for selecting audits may affect vertical equity. First, we show how the use of more flexible machine learning (classification) methods -- as opposed to simpler models -- shifts audit burdens from high to middle-income taxpayers. Second, we show that while existing algorithmic fairness techniques can mitigate some disparities across income, they can incur a steep cost to performance. Third, we show that the choice of whether to treat risk of underreporting as a classification or regression problem is highly consequential. Moving from classification to regression models to predict underreporting shifts audit burden substantially toward high income individuals, while increasing revenue. Last, we explore the role of differential audit cost in shaping the audit distribution. We show that a narrow focus on return-on-investment can undermine vertical equity. Our results have implications for the design of algorithmic tools across the public sector.

We consider a variation on the classical finance problem of optimal portfolio design. In our setting, a large population of consumers is drawn from some distribution over risk tolerances, and each consumer must be assigned to a portfolio of lower risk than her tolerance. The consumers may also belong to underlying groups (for instance, of demographic properties or wealth), and the goal is to design a small number of portfolios that are fair across groups in a particular and natural technical sense. Our main results are algorithms for optimal and near-optimal portfolio design for both social welfare and fairness objectives, both with and without assumptions on the underlying group structure. We describe an efficient algorithm based on an internal two-player zero-sum game that learns near-optimal fair portfolios ex ante and show experimentally that it can be used to obtain a small set of fair portfolios ex post as well. For the special but natural case in which group structure coincides with risk tolerances (which models the reality that wealthy consumers generally tolerate greater risk), we give an efficient and optimal fair algorithm. We also provide generalization guarantees for the underlying risk distribution that has no dependence on the number of portfolios and illustrate the theory with simulation results.

We propose and analyze differentially private (DP) mechanisms for call auctions as an alternative to the complex and ad-hoc privacy efforts that are common in modern electronic markets. We prove that the number of shares cleared in the DP mechanisms compares favorably to the non-private optimal and provide a matching lower bound. We analyze the incentive properties of our mechanisms and their behavior under natural no-regret learning dynamics by market participants. We include simulation results and connections to the finance literature on market impact.

Recent work has documented instances of unfairness in deployed machine learning models, and significant researcher effort has been dedicated to creating algorithms that intrinsically consider fairness. In this work, we highlight another source of unfairness: market forces that drive differential investment in the data pipeline for differing groups. We develop a high-level model to study this question. First, we show that our model predicts unfairness in a monopoly setting. Then, we show that under all but the most extreme models, competition does not eliminate this tendency, and may even exacerbate it. Finally, we consider two avenues for regulating a machine-learning driven monopolist - relative error inequality and absolute error-bounds - and quantify the price of fairness (and who pays it). These models imply that mitigating fairness concerns may require policy-driven solutions, not only technological ones.

The Keynesian Beauty Contest is a classical game in which strategic agents seek to both accurately guess the true state of the world as well as the average action of all agents. We study an augmentation of this game where agents are concerned about revealing their private information and additionally suffer a loss based on how well an observer can infer their private signals. We solve for an equilibrium of this augmented game and quantify the loss of social welfare as a result of agents acting to obscure their private information, which we call the 'price of privacy'. We analyze two versions of this this price: one from the perspective of the agents measuring their diminished ability to coordinate due to acting to obscure their information and another from the perspective of an aggregator whose statistical estimate of the true state of the world is of lower precision due to the agents adding random noise to their actions. We show that these quantities are high when agents care very strongly about protecting their personal information and low when the quality of the signals the agents receive is poor.

Settings such as lending and policing can be modeled by a centralized agent allocating a resource (loans or police officers) amongst several groups, in order to maximize some objective (loans given that are repaid or criminals that are apprehended). Often in such problems fairness is also a concern. A natural notion of fairness, based on general principles of equality of opportunity, asks that conditional on an individual being a candidate for the resource, the probability of actually receiving it is approximately independent of the individual's group. In lending this means that equally creditworthy individuals in different racial groups have roughly equal chances of receiving a loan. In policing it means that two individuals committing the same crime in different districts would have roughly equal chances of being arrested. We formalize this fairness notion for allocation problems and investigate its algorithmic consequences. Our main technical results include an efficient learning algorithm that converges to an optimal fair allocation even when the frequency of candidates (creditworthy individuals or criminals) in each group is unknown. The algorithm operates in a censored feedback model in which only the number of candidates who received the resource in a given allocation can be observed, rather than the true number of candidates. This models the fact that we do not learn the creditworthiness of individuals we do not give loans to nor learn about crimes committed if the police presence in a district is low. As an application of our framework, we consider the predictive policing problem. The learning algorithm is trained on arrest data gathered from its own deployments on previous days, resulting in a potential feedback loop that our algorithm provably overcomes. We empirically investigate the performance of our algorithm on the Philadelphia Crime Incidents dataset.

We study a game between two firms which each provide a service based on machine learning.  The firms are presented with the opportunity to purchase a new corpus of data, which will allow them to potentially improve the quality of their products. The firms can decide whether or not they want to buy the data, as well as which learning model to build on that data. We demonstrate a reduction from this potentially complicated action space  to a one-shot, two-action game in which each firm only decides whether or not to buy the data. The game admits several regimes which depend on the relative strength of the two firms at the outset and the price at which the data is being offered. We analyze the game's Nash equilibria in all parameter regimes and demonstrate that, in expectation, the outcome of the game is that the initially stronger firm's market position weakens whereas the initially weaker firm's market position becomes stronger. Finally, we consider the perspective of the users of the service and demonstrate that the expected outcome at equilibrium is not the one which maximizes the welfare of the consumers.

Inspired by the successes of AlphaGo, AlphaGo Zero, and Libratus, which have resulted in superhuman performance in the games Go and Poker, we study the game Four Hundred. Four Hundred is a team-based trick-taking card game similar to Spades, and has not been widely studied to our knowledge. The game contains many interesting aspects. Notably, the game has hidden information (since hands are not revealed and communication is forbidden), is cooperative (players are split into two teams which compete), and players must bet, ex ante, the tricks they win expect to win (and are punished if they fail to take these tricks). In this work, we discuss an AI, Over400, which has learned how to play the game via self-play. Over400 uses deep reinforcement learning techniques to identify optimal actions in playing rounds and supervised learning to make optimal bets given its strategy. Training over 100,000 games, we find that Over400 defeats heuristic algorithms based on human knowledge and performs competitively against human players.