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In observational studies of discrimination, the most common statistical approaches consider either the rate at which decisions are made (benchmark tests) or the success rate of those decisions (outcome tests). Both tests, however, have well-known statistical limitations, sometimes suggesting discrimination even when there is none. Despite the fallibility of the benchmark and outcome tests individually, here we prove a surprisingly strong statistical guarantee: under a common non-parametric assumption, at least one of the two tests must be correct; consequently, when both tests agree, they are guaranteed to yield correct conclusions. We present empirical evidence that the underlying assumption holds approximately in several important domains, including lending, education, and criminal justice -- and that our hybrid test is robust to the moderate violations of the assumption that we observe in practice. Applying this approach to 2.8 million police stops across California, we find evidence of widespread racial discrimination.

Regulatory efforts to protect against algorithmic bias have taken on increased urgency with rapid advances in large language models (LLMs), which are machine learning models that can achieve performance rivaling human experts on a wide array of tasks. A key theme of these initiatives is algorithmic "auditing," but current regulations -- as well as the scientific literature -- provide little guidance on how to conduct these assessments. Here we propose and investigate one approach for auditing algorithms: correspondence experiments, a widely applied tool for detecting bias in human judgements. In the employment context, correspondence experiments aim to measure the extent to which race and gender impact decisions by experimentally manipulating elements of submitted application materials that suggest an applicant's demographic traits, such as their listed name. We apply this method to audit candidate assessments produced by several state-of-the-art LLMs, using a novel corpus of applications to K-12 teaching positions in a large public school district. We find evidence of moderate race and gender disparities, a pattern largely robust to varying the types of application material input to the models, as well as the framing of the task to the LLMs. We conclude by discussing some important limitations of correspondence experiments for auditing algorithms.

The advent of large language models (LLMs) and their adoption by the legal community has given rise to the question: what types of legal reasoning can LLMs perform? To enable greater study of this question, we present LegalBench: a collaboratively constructed legal reasoning benchmark consisting of 162 tasks covering six different types of legal reasoning. LegalBench was built through an interdisciplinary process, in which we collected tasks designed and hand-crafted by legal professionals. Because these subject matter experts took a leading role in construction, tasks either measure legal reasoning capabilities that are practically useful, or measure reasoning skills that lawyers find interesting. To enable cross-disciplinary conversations about LLMs in the law, we additionally show how popular legal frameworks for describing legal reasoning -- which distinguish between its many forms -- correspond to LegalBench tasks, thus giving lawyers and LLM developers a common vocabulary. This paper describes LegalBench, presents an empirical evaluation of 20 open-source and commercial LLMs, and illustrates the types of research explorations LegalBench enables., Comment: 143 pages, 79 tables, 4 figures

There is debate over whether Asian American students are admitted to selective colleges and universities at lower rates than white students with similar academic qualifications. However, there have been few empirical investigations of this issue, in large part due to a dearth of data. Here we present the results from analyzing 685,709 applications from Asian American and white students to a subset of selective U.S. institutions over five application cycles, beginning with the 2015-2016 cycle. The dataset does not include admissions decisions, and so we construct a proxy based in part on enrollment choices. Based on this proxy, we estimate the odds that Asian American applicants were admitted to at least one of the schools we consider were 28% lower than the odds for white students with similar test scores, grade-point averages, and extracurricular activities. The gap was particularly pronounced for students of South Asian descent (49% lower odds). We trace this pattern in part to two factors. First, many selective colleges openly give preference to the children of alumni, and we find that white applicants were substantially more likely to have such legacy status than Asian applicants, especially South Asian applicants. Second, after adjusting for observed student characteristics, the institutions we consider appear less likely to admit students from geographic regions with relatively high shares of applicants who are Asian. We hope these results inform ongoing discussions on the equity of college admissions policies., Comment: 14 pages, 4 figures, 1 table + appendix: 42 pages, 5 figures, 21 tables

Millions of Americans must attend mandatory court dates every year. To boost appearance rates, jurisdictions nationwide are increasingly turning to automated reminders, but previous research offers mixed evidence on their effectiveness. In partnership with the Santa Clara County Public Defender Office, we randomly assigned 5,709 public defender clients to either receive automated text message reminders (treatment) or not receive reminders (control). We found that reminders reduced warrants issued for missed court dates by approximately 20%, with 12.1% of clients in the control condition issued a warrant compared to 9.7% of clients in the treatment condition. We further found that incarceration from missed court dates dropped by a similar amount, from 6.2% in the control condition to 4.8% in the treatment condition. Our results provide evidence that automated reminders can help people avoid the negative consequences of missing court.

There is active debate over whether to consider patient race and ethnicity when estimating disease risk. By accounting for race and ethnicity, it is possible to improve the accuracy of risk predictions, but there is concern that their use may encourage a racialized view of medicine. In diabetes risk models, despite substantial gains in statistical accuracy from using race and ethnicity, the gains in clinical utility are surprisingly modest. These modest clinical gains stem from two empirical patterns: first, the vast majority of individuals receive the same screening recommendation regardless of whether race or ethnicity are included in risk models; and second, for those who do receive different screening recommendations, the difference in utility between screening and not screening is relatively small. Our results are based on broad statistical principles, and so are likely to generalize to many other risk-based clinical decisions., Comment: 11 pages, 4 figures

In designing risk assessment algorithms, many scholars promote a "kitchen sink" approach, reasoning that more information yields more accurate predictions. We show, however, that this rationale often fails when algorithms are trained to predict a proxy of the true outcome, as is typically the case. With such "label bias", one should exclude a feature if its correlation with the proxy and its correlation with the true outcome have opposite signs, conditional on the other model features. This criterion is often satisfied when a feature is weakly correlated with the true outcome, and, additionally, that feature and the true outcome are both direct causes of the remaining features. For example, due to patterns of police deployment, criminal behavior and geography may be weakly correlated and direct causes of one's criminal record, suggesting one should exclude geography in criminal risk assessments trained to predict arrest as a proxy for behavior., Comment: 19 pages, 4 figures

Algorithmically optimizing the provision of limited resources is commonplace across domains from healthcare to lending. Optimization can lead to efficient resource allocation, but, if deployed without additional scrutiny, can also exacerbate inequality. Little is known about popular preferences regarding acceptable efficiency-equity trade-offs, making it difficult to design algorithms that are responsive to community needs and desires. Here we examine this trade-off and concomitant preferences in the context of GetCalFresh, an online service that streamlines the application process for California's Supplementary Nutrition Assistance Program (SNAP, formerly known as food stamps). GetCalFresh runs online advertisements to raise awareness of their multilingual SNAP application service. We first demonstrate that when ads are optimized to garner the most enrollments per dollar, a disproportionately small number of Spanish speakers enroll due to relatively higher costs of non-English language advertising. Embedding these results in a survey (N = 1,532) of a diverse set of Americans, we find broad popular support for valuing equity in addition to efficiency: respondents generally preferred reducing total enrollments to facilitate increased enrollment of Spanish speakers. These results buttress recent calls to reevaluate the efficiency-centric paradigm popular in algorithmic resource allocation., Comment: This paper will be presented at the 2023 International Conference on Web and Social Media (ICWSM'23)

Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the efficiency and equity of decision-making. At the same time, there is a danger that the algorithms themselves could entrench and exacerbate disparities, particularly along racial, ethnic, and gender lines. To help ensure their fairness, many researchers suggest that algorithms be subject to at least one of three constraints: (1) no use of legally protected features, such as race, ethnicity, and gender; (2) equal rates of "positive" decisions across groups; and (3) equal error rates across groups. Here we show that these constraints, while intuitively appealing, often worsen outcomes for individuals in marginalized groups, and can even leave all groups worse off. The inherent trade-off we identify between formal fairness constraints and welfare improvements -- particularly for the marginalized -- highlights the need for a more robust discussion on what it means for an algorithm to be "fair". We illustrate these ideas with examples from healthcare and the criminal-legal system, and make several proposals to help practitioners design more equitable algorithms.

Recent work highlights the role of causality in designing equitable decision-making algorithms. It is not immediately clear, however, how existing causal conceptions of fairness relate to one another, or what the consequences are of using these definitions as design principles. Here, we first assemble and categorize popular causal definitions of algorithmic fairness into two broad families: (1) those that constrain the effects of decisions on counterfactual disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions \emph{almost always} -- in a measure theoretic sense -- result in strongly Pareto dominated decision policies, meaning there is an alternative, unconstrained policy favored by every stakeholder with preferences drawn from a large, natural class. For example, in the case of college admissions decisions, policies constrained to satisfy causal fairness definitions would be disfavored by every stakeholder with neutral or positive preferences for both academic preparedness and diversity. Indeed, under a prominent definition of causal fairness, we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership. Our results highlight formal limitations and potential adverse consequences of common mathematical notions of causal fairness., Comment: ICML 2022. arXiv admin note: substantial text overlap with arXiv:1808.00023

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models., Comment: 15 pages, 2 figures

In an attempt to make algorithms fair, the machine learning literature has largely focused on equalizing decisions, outcomes, or error rates across race or gender groups. To illustrate, consider a hypothetical government rideshare program that provides transportation assistance to low-income people with upcoming court dates. Following this literature, one might allocate rides to those with the highest estimated treatment effect per dollar, while constraining spending to be equal across race groups. That approach, however, ignores the downstream consequences of such constraints, and, as a result, can induce unexpected harms. For instance, if one demographic group lives farther from court, enforcing equal spending would necessarily mean fewer total rides provided, and potentially more people penalized for missing court. Here we present an alternative framework for designing equitable algorithms that foregrounds the consequences of decisions. In our approach, one first elicits stakeholder preferences over the space of possible decisions and the resulting outcomes--such as preferences for balancing spending parity against court appearance rates. We then optimize over the space of decision policies, making trade-offs in a way that maximizes the elicited utility. To do so, we develop an algorithm for efficiently learning these optimal policies from data for a large family of expressive utility functions. In particular, we use a contextual bandit algorithm to explore the space of policies while solving a convex optimization problem at each step to estimate the best policy based on the available information. This consequentialist paradigm facilitates a more holistic approach to equitable decision-making.

In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day changes by the hour as new information becomes available. Given a collection of such probability paths, we introduce a Bayesian framework -- which we call the Gaussian latent information martingale, or GLIM -- for modeling the structure of dynamic predictions over time. Suppose, for example, that the likelihood of rain in a week is 50 %, and consider two hypothetical scenarios. In the first, one expects the forecast to be equally likely to become either 25 % or 75 % tomorrow; in the second, one expects the forecast to stay constant for the next several days. A time-sensitive decision-maker might select a course of action immediately in the latter scenario, but may postpone their decision in the former, knowing that new information is imminent. We model these trajectories by assuming predictions update according to a latent process of information flow, which is inferred from historical data. In contrast to general methods for time series analysis, this approach preserves important properties of probability paths such as the martingale structure and appropriate amount of volatility and better quantifies future uncertainties around probability paths. We show that GLIM outperforms three popular baseline methods, producing better estimated posterior probability path distributions measured by three different metrics. By elucidating the dynamic structure of predictions over time, we hope to help individuals make more informed choices.

The use of video surveillance in public spaces -- both by government agencies and by private citizens -- has attracted considerable attention in recent years, particularly in light of rapid advances in face-recognition technology. But it has been difficult to systematically measure the prevalence and placement of cameras, hampering efforts to assess the implications of surveillance on privacy and public safety. Here, we combine computer vision, human verification, and statistical analysis to estimate the spatial distribution of surveillance cameras. Specifically, we build a camera detection model and apply it to 1.6 million street view images sampled from 10 large U.S. cities and 6 other major cities around the world, with positive model detections verified by human experts. After adjusting for the estimated recall of our model, and accounting for the spatial coverage of our sampled images, we are able to estimate the density of surveillance cameras visible from the road. Across the 16 cities we consider, the estimated number of surveillance cameras per linear kilometer ranges from 0.2 (in Los Angeles) to 0.9 (in Seoul). In a detailed analysis of the 10 U.S. cities, we find that cameras are concentrated in commercial, industrial, and mixed zones, and in neighborhoods with higher shares of non-white residents -- a pattern that persists even after adjusting for land use. These results help inform ongoing discussions on the use of surveillance technology, including its potential disparate impacts on communities of color., Comment: We now credit Turtiainen et al. (2020) both for creating a state-of-the-art camera detection model and for suggesting that computer vision could, in theory, be applied to street view data to map surveillance cameras. Also, we discovered a coding error in our image sampling strategy that corrupted our analysis of camera density over time. We have now removed the results of that analysis

A potential voter must incur a number of costs in order to successfully cast an in-person ballot, including the costs associated with identifying and traveling to a polling place. In order to investigate how these costs affect voting behavior, we introduce two quasi-experimental designs that can be used to study how the political participation of registered voters is affected by differences in the relative distance that registrants must travel to their assigned Election Day polling place and whether their polling place remains at the same location as in a previous election. Our designs make comparisons of registrants who live on the same residential block, but are assigned to vote at different polling places. We find that living farther from a polling place and being assigned to a new polling place reduce in-person Election Day voting, but that registrants largely offset for this by casting more early in-person and mail ballots.

In studies of discrimination, researchers often seek to estimate a causal effect of race or gender on outcomes. For example, in the criminal justice context, one might ask whether arrested individuals would have been subsequently charged or convicted had they been a different race. It has long been known that such counterfactual questions face measurement challenges related to omitted-variable bias, and conceptual challenges related to the definition of causal estimands for largely immutable characteristics. Another concern, which has been the subject of recent debates, is post-treatment bias: many studies of discrimination condition on apparently intermediate outcomes, like being arrested, that themselves may be the product of discrimination, potentially corrupting statistical estimates. There is, however, reason to be optimistic. By carefully defining the estimand -- and by considering the precise timing of events -- we show that a primary causal quantity of interest in discrimination studies can be estimated under an ignorability condition that may hold approximately in some observational settings. We illustrate these ideas by analyzing both simulated data and the charging decisions of a prosecutor's office in a large county in the United States.

Public and private institutions must often allocate scare resources under uncertainty. Banks, for example, extend credit to loan applicants based in part on their estimated likelihood of repaying a loan. But when the quality of information differs across candidates (e.g., if some applicants lack traditional credit histories), common lending strategies can lead to disparities across groups. Here we consider a setting in which decision makers -- before allocating resources -- can choose to spend some of their limited budget further screening select individuals. We present a computationally efficient algorithm for deciding whom to screen that maximizes a standard measure of social welfare. Intuitively, decision makers should screen candidates on the margin, for whom the additional information could plausibly alter the allocation. We formalize this idea by showing the problem can be reduced to solving a series of linear programs. Both on synthetic and real-world datasets, this strategy improves utility, illustrating the value of targeted information acquisition in such decisions. Further, when there is social value for distributing resources to groups for whom we have a priori poor information -- like those without credit scores -- our approach can substantially improve the allocation of limited assets., Comment: To appear in Proceedings of the 2020 AAAI/ACM Conference on AI, Ethics, and Society (AIES). Update: Fully specified the definition of threshold policies

Several recent studies of online social networking platforms have found that adoption rates and engagement levels are positively correlated with structural diversity, the degree of heterogeneity among an individual's contacts as measured by network ties. One common theory for this observation is that structural diversity increases utility, in part because there is value to interacting with people from different network components on the same platform. While compelling, evidence for this causal theory comes from observational studies, making it difficult to rule out non-causal explanations. We investigate the role of structural diversity on retention by conducting a large-scale randomized controlled study on the Twitter platform. We first show that structural diversity correlates with user retention on Twitter, corroborating results from past observational studies. We then exogenously vary structural diversity by altering the set of network recommendations new users see when joining the platform; we confirm that this design induces the desired changes to network topology. We find, however, that low, medium, and high structural diversity treatment groups in our experiment have comparable retention rates. Thus, at least in this case, the observed correlation between structural diversity and retention does not appear to result from a causal relationship, challenging theories based on past observational studies., Comment: To appear in the Proceedings of International AAAI Conference on Web and Social Media (ICWSM 2020)

There is debate over whether Asian American students are admitted to selective colleges and universities at lower rates than white students with similar academic qualifications. However, there have been few empirical investigations of this issue, in large part due to a dearth of data. Here we present the results from analyzing 685,709 applications from Asian American and white students to a subset of selective U.S. institutions over five application cycles, beginning with the 2015-2016 cycle. The dataset does not include admissions decisions, and so we construct a proxy based in part on enrollment choices. Based on this proxy, we estimate the odds that Asian American applicants were admitted to at least one of the schools we consider were 28% lower than the odds for white students with similar test scores, grade-point averages, and extracurricular activities. The gap was particularly pronounced for students of South Asian descent (49% lower odds). We trace this pattern in part to two factors. First, many selective colleges openly give preference to the children of alumni, and we find that white applicants were substantially more likely to have such legacy status than Asian applicants, especially South Asian applicants. Second, after adjusting for observed student characteristics, the institutions we consider appear less likely to admit students from geographic regions with relatively high shares of applicants who are Asian. We hope these results inform ongoing discussions on the equity of college admissions policies.

Managers, employers, policymakers, and others often seek to understand whether decisions are biased against certain groups. One popular analytic strategy is to estimate disparities after adjusting for observed covariates, typically with a regression model. This approach, however, suffers from two key statistical challenges. First, omitted-variable bias can skew results if the model does not adjust for all relevant factors; second, and conversely, included-variable bias -- a lesser-known phenomenon -- can skew results if the set of covariates includes irrelevant factors. Here we introduce a new, three-step statistical method, which we call risk-adjusted regression, to address both concerns in settings where decision makers have clearly measurable objectives. In the first step, we use all available covariates to estimate the value, or inversely, the risk, of taking a certain action, such as approving a loan application or hiring a job candidate. Second, we measure disparities in decisions after adjusting for these risk estimates alone, mitigating the problem of included-variable bias. Finally, in the third step, we assess the sensitivity of results to potential mismeasurement of risk, addressing concerns about omitted-variable bias. To do so, we develop a novel, non-parametric sensitivity analysis that yields tight bounds on the true disparity in terms of the average gap between true and estimated risk -- a single interpretable parameter that facilitates credible estimates. We demonstrate this approach on a detailed dataset of 2.2 million police stops of pedestrians in New York City, and show that traditional statistical tests of discrimination can substantially underestimate the magnitude of disparities.

The field of fair machine learning aims to ensure that decisions guided by algorithms are equitable. Over the last decade, several formal, mathematical definitions of fairness have gained prominence. Here we first assemble and categorize these definitions into two broad families: (1) those that constrain the effects of decisions on disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions typically result in strongly Pareto dominated decision policies. For example, in the case of college admissions, adhering to popular formal conceptions of fairness would simultaneously result in lower student-body diversity and a less academically prepared class, relative to what one could achieve by explicitly tailoring admissions policies to achieve desired outcomes. In this sense, requiring that these fairness definitions hold can, perversely, harm the very groups they were designed to protect. In contrast to axiomatic notions of fairness, we argue that the equitable design of algorithms requires grappling with their context-specific consequences, akin to the equitable design of policy. We conclude by listing several open challenges in fair machine learning and offering strategies to ensure algorithms are better aligned with policy goals.

On a variety of complex decision-making tasks, from doctors prescribing treatment to judges setting bail, machine learning algorithms have been shown to outperform expert human judgments. One complication, however, is that it is often difficult to anticipate the effects of algorithmic policies prior to deployment, making the decision to adopt them risky. In particular, one generally cannot use historical data to directly observe what would have happened had the actions recommended by the algorithm been taken. One standard strategy is to model potential outcomes for alternative decisions assuming that there are no unmeasured confounders (i.e., to assume ignorability). But if this ignorability assumption is violated, the predicted and actual effects of an algorithmic policy can diverge sharply. In this paper we present a flexible, Bayesian approach to gauge the sensitivity of predicted policy outcomes to unmeasured confounders. We show that this policy evaluation problem is a generalization of estimating heterogeneous treatment effects in observational studies, and so our methods can immediately be applied to that setting. Finally, we show, both theoretically and empirically, that under certain conditions it is possible to construct near-optimal algorithmic policies even when ignorability is violated. We demonstrate the efficacy of our methods on a large dataset of judicial actions, in which one must decide whether defendants awaiting trial should be required to pay bail or can be released without payment.

To assess racial disparities in police interactions with the public, we compiled and analyzed a dataset detailing over 60 million state patrol stops conducted in 20 U.S. states between 2011 and 2015. We find that black drivers are stopped more often than white drivers relative to their share of the driving-age population, but that Hispanic drivers are stopped less often than whites. Among stopped drivers -- and after controlling for age, gender, time, and location -- blacks and Hispanics are more likely to be ticketed, searched, and arrested than white drivers. These disparities may reflect differences in driving behavior, and are not necessarily the result of bias. In the case of search decisions, we explicitly test for discrimination by examining both the rate at which drivers are searched and the likelihood searches turn up contraband. We find evidence that the bar for searching black and Hispanic drivers is lower than for searching whites. Finally, we find that legalizing recreational marijuana in Washington and Colorado reduced the total number of searches and misdemeanors for all race groups, though a race gap still persists. We conclude by offering recommendations for improving data collection, analysis, and reporting by law enforcement agencies.

Threshold tests have recently been proposed as a useful method for detecting bias in lending, hiring, and policing decisions. For example, in the case of credit extensions, these tests aim to estimate the bar for granting loans to white and minority applicants, with a higher inferred threshold for minorities indicative of discrimination. This technique, however, requires fitting a complex Bayesian latent variable model for which inference is often computationally challenging. Here we develop a method for fitting threshold tests that is two orders of magnitude faster than the existing approach, reducing computation from hours to minutes. To achieve these performance gains, we introduce and analyze a flexible family of probability distributions on the interval [0, 1] -- which we call discriminant distributions -- that is computationally efficient to work with. We demonstrate our technique by analyzing 2.7 million police stops of pedestrians in New York City., Comment: Accepted at AISTATS 2018; slightly shorter camera-ready version

From doctors diagnosing patients to judges setting bail, experts often base their decisions on experience and intuition rather than on statistical models. While understandable, relying on intuition over models has often been found to result in inferior outcomes. Here we present a new method, select-regress-and-round, for constructing simple rules that perform well for complex decisions. These rules take the form of a weighted checklist, can be applied mentally, and nonetheless rival the performance of modern machine learning algorithms. Our method for creating these rules is itself simple, and can be carried out by practitioners with basic statistics knowledge. We demonstrate this technique with a detailed case study of judicial decisions to release or detain defendants while they await trial. In this application, as in many policy settings, the effects of proposed decision rules cannot be directly observed from historical data: if a rule recommends releasing a defendant that the judge in reality detained, we do not observe what would have happened under the proposed action. We address this key counterfactual estimation problem by drawing on tools from causal inference. We find that simple rules significantly outperform judges and are on par with decisions derived from random forests trained on all available features. Generalizing to 22 varied decision-making domains, we find this basic result replicates. We conclude with an analytical framework that helps explain why these simple decision rules perform as well as they do.

Algorithms are now regularly used to decide whether defendants awaiting trial are too dangerous to be released back into the community. In some cases, black defendants are substantially more likely than white defendants to be incorrectly classified as high risk. To mitigate such disparities, several techniques recently have been proposed to achieve algorithmic fairness. Here we reformulate algorithmic fairness as constrained optimization: the objective is to maximize public safety while satisfying formal fairness constraints designed to reduce racial disparities. We show that for several past definitions of fairness, the optimal algorithms that result require detaining defendants above race-specific risk thresholds. We further show that the optimal unconstrained algorithm requires applying a single, uniform threshold to all defendants. The unconstrained algorithm thus maximizes public safety while also satisfying one important understanding of equality: that all individuals are held to the same standard, irrespective of race. Because the optimal constrained and unconstrained algorithms generally differ, there is tension between improving public safety and satisfying prevailing notions of algorithmic fairness. By examining data from Broward County, Florida, we show that this trade-off can be large in practice. We focus on algorithms for pretrial release decisions, but the principles we discuss apply to other domains, and also to human decision makers carrying out structured decision rules., Comment: To appear in Proceedings of KDD'17

Outcome tests are a popular method for detecting bias in lending, hiring, and policing decisions. These tests operate by comparing the success rate of decisions across groups. For example, if loans made to minority applicants are observed to be repaid more often than loans made to whites, it suggests that only exceptionally qualified minorities are granted loans, indicating discrimination. Outcome tests, however, are known to suffer from the problem of infra-marginality: even absent discrimination, the repayment rates for minority and white loan recipients might differ if the two groups have different risk distributions. Thus, at least in theory, outcome tests can fail to accurately detect discrimination. We develop a new statistical test of discrimination---the threshold test---that mitigates the problem of infra-marginality by jointly estimating decision thresholds and risk distributions via a hierarchical Bayesian latent variable model. Applying our test to a dataset of 4.5 million police stops in North Carolina, we find that the problem of infra-marginality is more than a theoretical possibility, and can cause the outcome test to yield misleading results in practice., Comment: To appear in The Annals of Applied Statistics, 2017

The only acceptable form of polling in the multi-billion dollar survey research field utilizes representative samples. We argue that with proper statistical adjustment, non-representative polling can provide accurate predictions, and often in a much more timely and cost-effective fashion. We demonstrate this by applying multilevel regression and post-stratification (MRP) to a 2012 election survey on the Xbox gaming platform. Not only do the transformed top-line projections from this data closely trend standard indicators, but we use the unique nature of the data's size and panel to answer a meaningful political puzzle. We find that reported swings in public opinion polls are generally not due to actual shifts in vote intention, but rather are the result of temporary periods of relatively low response rates among supporters of the reportedly slumping candidate. This work shows great promise for using non-representative polling to measure public opinion and the first product of this new polling technique raises the possibility that decades of large, reported swings in public opinion-including the perennial "convention bounce"-are mostly artifacts of sampling bias.

Classical multidimensional scaling (MDS) is a method for visualizing high-dimensional point clouds by mapping to low-dimensional Euclidean space. This mapping is defined in terms of eigenfunctions of a matrix of interpoint dissimilarities. In this paper we analyze in detail multidimensional scaling applied to a specific dataset: the 2005 United States House of Representatives roll call votes. Certain MDS and kernel projections output ``horseshoes'' that are characteristic of dimensionality reduction techniques. We show that, in general, a latent ordering of the data gives rise to these patterns when one only has local information. That is, when only the interpoint distances for nearby points are known accurately. Our results provide a rigorous set of results and insight into manifold learning in the special case where the manifold is a curve., Comment: Published in at http://dx.doi.org/10.1214/08-AOAS165 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

A deck of $n$ cards is shuffled by repeatedly moving the top card to one of the bottom $k_n$ positions uniformly at random. We give upper and lower bounds on the total variation mixing time for this shuffle as $k_n$ ranges from a constant to $n$. We also consider a symmetric variant of this shuffle in which at each step either the top card is randomly inserted into the bottom $k_n$ positions or a random card from the bottom $k_n$ positions is moved to the top. For this reversible shuffle we derive bounds on the $L^2$ mixing time. Finally, we transfer mixing time estimates for the above shuffles to the lazy top to bottom-$k$ walks that move with probability 1/2 at each step., Comment: Published at http://dx.doi.org/10.1214/10505160500000062 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)