The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two special cases: when the prevalence of the outcome being predicted is equal across groups, or when a perfectly accurate predictor is used. However, theory does not always translate to practice. In this work, we challenge the implications of the impossibility theorem in practical settings. First, we show analytically that, by slightly relaxing the impossibility theorem (to accommodate a \textit{practitioner's} perspective of fairness), it becomes possible to identify a large set of models that satisfy seemingly incompatible fairness constraints. Second, we demonstrate the existence of these models through extensive experiments on five real-world datasets. We conclude by offering tools and guidance for practitioners to understand when -- and to what degree -- fairness along multiple criteria can be achieved. For example, if one allows only a small margin-of-error between metrics, there exists a large set of models simultaneously satisfying \emph{False Negative Rate Parity}, \emph{False Positive Rate Parity}, and \emph{Positive Predictive Value Parity}, even when there is a moderate prevalence difference between groups. This work has an important implication for the community: achieving fairness along multiple metrics for multiple groups (and their intersections) is much more possible than was previously believed.

The error of an estimator can be decomposed into a (statistical) bias term, a variance term, and an irreducible noise term. When we do bias analysis, formally we are asking the question: "how good are the predictions?" The role of bias in the error decomposition is clear: if we trust the labels/targets, then we would want the estimator to have as low bias as possible, in order to minimize error. Fair machine learning is concerned with the question: "Are the predictions equally good for different demographic/social groups?" This has naturally led to a variety of fairness metrics that compare some measure of statistical bias on subsets corresponding to socially privileged and socially disadvantaged groups. In this paper we propose a new family of performance measures based on group-wise parity in variance. We demonstrate when group-wise statistical bias analysis gives an incomplete picture, and what group-wise variance analysis can tell us in settings that differ in the magnitude of statistical bias. We develop and release an open-source library that reconciles uncertainty quantification techniques with fairness analysis, and use it to conduct an extensive empirical analysis of our variance-based fairness measures on standard benchmarks.

Counterfactuals are often described as 'retrospective,' focusing on hypothetical alternatives to a realized past. This description relates to an often implicit assumption about the structure and stability of exogenous variables in the system being modeled -- an assumption that is reasonable in many settings where counterfactuals are used. In this work, we consider cases where we might reasonably make a different assumption about exogenous variables, namely, that the exogenous noise terms of each unit do exhibit some unit-specific structure and/or stability. This leads us to a different use of counterfactuals -- a 'forward-looking' rather than 'retrospective' counterfactual. We introduce "counterfactual treatment choice," a type of treatment choice problem that motivates using forward-looking counterfactuals. We then explore how mismatches between interventional versus forward-looking counterfactual approaches to treatment choice, consistent with different assumptions about exogenous noise, can lead to counterintuitive results.

Automated hiring systems are among the fastest-developing of all high-stakes AI systems. Among these are algorithmic personality tests that use insights from psychometric testing, and promise to surface personality traits indicative of future success based on job seekers' resumes or social media profiles. We interrogate the validity of such systems using stability of the outputs they produce, noting that reliability is a necessary, but not a sufficient, condition for validity. Our approach is to (a) develop a methodology for an external audit of stability of predictions made by algorithmic personality tests, and (b) instantiate this methodology in an audit of two systems, Humantic AI and Crystal. Crucially, rather than challenging or affirming the assumptions made in psychometric testing -- that personality is a meaningful and measurable construct, and that personality traits are indicative of future success on the job -- we frame our methodology around testing the underlying assumptions made by the vendors of the algorithmic personality tests themselves. In our audit of Humantic AI and Crystal, we find that both systems show substantial instability with respect to key facets of measurement, and so cannot be considered valid testing instruments. For example, Crystal frequently computes different personality scores if the same resume is given in PDF vs. in raw text format, violating the assumption that the output of an algorithmic personality test is stable across job-irrelevant variations in the input. Among other notable findings is evidence of persistent -- and often incorrect -- data linkage by Humantic AI.

A significant body of research in the data sciences considers unfair discrimination against social categories such as race or gender that could occur or be amplified as a result of algorithmic decisions. Simultaneously, real-world disparities continue to exist, even before algorithmic decisions are made. In this work, we draw on insights from the social sciences and humanistic studies brought into the realm of causal modeling and constrained optimization, and develop a novel algorithmic framework for tackling pre-existing real-world disparities. The purpose of our framework, which we call the "impact remediation framework," is to measure real-world disparities and discover the optimal intervention policies that could help improve equity or access to opportunity for those who are underserved with respect to an outcome of interest. We develop a disaggregated approach to tackling pre-existing disparities that relaxes the typical set of assumptions required for the use of social categories in structural causal models. Our approach flexibly incorporates counterfactuals and is compatible with various ontological assumptions about the nature of social categories. We demonstrate impact remediation with a real-world case study and compare our disaggregated approach to an existing state-of-the-art approach, comparing its structure and resulting policy recommendations. In contrast to most work on optimal policy learning, we explore disparity reduction itself as an objective, explicitly focusing the power of algorithms on reducing inequality.

Recent interest in codifying fairness in Automated Decision Systems (ADS) has resulted in a wide range of formulations of what it means for an algorithmic system to be fair. Most of these propositions are inspired by, but inadequately grounded in, political philosophy scholarship. This paper aims to correct that deficit. We introduce a taxonomy of fairness ideals using doctrines of Equality of Opportunity (EOP) from political philosophy, clarifying their conceptions in philosophy and the proposed codification in fair machine learning. We arrange these fairness ideals onto an EOP spectrum, which serves as a useful frame to guide the design of a fair ADS in a given context. We use our fairness-as-EOP framework to re-interpret the impossibility results from a philosophical perspective, as the in-compatibility between different value systems, and demonstrate the utility of the framework with several real-world and hypothetical examples. Through our EOP-framework we hope to answer what it means for an ADS to be fair from a moral and political philosophy standpoint, and to pave the way for similar scholarship from ethics and legal experts.

In this paper we propose a causal modeling approach to intersectional fairness, and a flexible, task-specific method for computing intersectionally fair rankings. Rankings are used in many contexts, ranging from Web search results to college admissions, but causal inference for fair rankings has received limited attention. Additionally, the growing literature on causal fairness has directed little attention to intersectionality. By bringing these issues together in a formal causal framework we make the application of intersectionality in fair machine learning explicit, connected to important real world effects and domain knowledge, and transparent about technical limitations. We experimentally evaluate our approach on real and synthetic datasets, exploring its behaviour under different structural assumptions.

Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the overall representativeness of the selected set. An unintended consequence of these constraints, however, is reduced in-group fairness: the selected candidates from a given group may not be the best ones, and this unfairness may not be well-balanced across groups. In this paper we study this phenomenon using datasets that comprise multiple sensitive attributes. We then introduce additional constraints, aimed at balancing the \in-group fairness across groups, and formalize the induced optimization problems as integer linear programs. Using these programs, we conduct an experimental evaluation with real datasets, and quantify the feasible trade-offs between balance and overall performance in the presence of diversity constraints.

We develop a novel framework that aims to create bridges between the computational social choice and the database management communities. This framework enriches the tasks currently supported in computational social choice with relational database context, thus making it possible to formulate sophisticated queries about voting rules, candidates, voters, issues, and positions. At the conceptual level, we give rigorous semantics to queries in this framework by introducing the notions of necessary answers and possible answers to queries. At the technical level, we embark on an investigation of the computational complexity of the necessary answers. We establish a number of results about the complexity of the necessary answers of conjunctive queries involving positional scoring rules that contrast sharply with earlier results about the complexity of the necessary winners.

Distributions over rankings are used to model user preferences in various settings including political elections and electronic commerce. The Repeated Insertion Model (RIM) gives rise to various known probability distributions over rankings, in particular to the popular Mallows model. However, probabilistic inference on RIM is computationally challenging, and provably intractable in the general case. In this paper we propose an algorithm for computing the marginal probability of an arbitrary partially ordered set over RIM. We analyze the complexity of the algorithm in terms of properties of the model and the partial order, captured by a novel measure termed the "cover width." We also conduct an experimental study of the algorithm over serial and parallelized implementations. Building upon the relationship between inference with rank distributions and counting linear extensions, we investigate the inference problem when restricted to partial orders that lend themselves to efficient counting of their linear extensions.