The increasing application of artificial intelligence (AI) to healthcare raises both hope and ethical concerns. Some advanced machine learning methods provide accurate clinical predictions at the expense of a significant lack of explainability. Alex John London has defended that accuracy is a more important value than explainability in AI medicine. In this article, we locate the trade-off between accurate performance and explainable algorithms in the context of distributive justice. We acknowledge that accuracy is cardinal from outcome-oriented justice because it helps (...) to maximize patients’ benefits and optimizes limited resources. However, we claim that the opaqueness of the algorithmic black box and its absence of explainability threatens core commitments of procedural fairness such as accountability, avoidance of bias, and transparency. To illustrate this, we discuss liver transplantation as a case of critical medical resources in which the lack of explainability in AI-based allocation algorithms is procedurally unfair. Finally, we provide a number of ethical recommendations for when considering the use of unexplainable algorithms in the distribution of health-related resources. (shrink)

When artificial intelligence (AI) is used to make high-stakes decisions, some worry that this will create a morally troubling responsibility gap—that is, a situation in which nobody is morally responsible for the actions and outcomes that result. Since the responsibility gap might be thought to result from individuals lacking knowledge of the future behavior of AI systems, it can be and has been suggested that deploying explainable artificial intelligence (XAI) techniques will help us to avoid it. These techniques provide humans (...) with certain forms of understanding of the systems in question. In this paper, I consider whether existing XAI techniques can indeed close the responsibility gap. I identify a number of significant limits to their ability to do so. Ensuring that responsibility for AI-assisted outcomes is maintained may require using different techniques in different circumstances, and potentially also developing new techniques that can avoid each of the issues identified. (shrink)

Holm (2022) argues that a class of algorithmic fairness measures, that he refers to as the ‘performance parity criteria’, can be understood as applications of John Broome’s Fairness Principle. We argue that the performance parity criteria cannot be read this way. This is because in the relevant context, the Fairness Principle requires the equalization of actual individuals’ individual-level chances of obtaining some good (such as an accurate prediction from a predictive system), but the performance parity criteria do not guarantee any (...) such thing: the measures merely ensure that certain population-level ratios hold. (shrink)

A number of findings in the field of machine learning have given rise to questions about what it means for automated scoring- or decisionmaking systems to be fair. One center of gravity in this discussion is whether such systems ought to satisfy classification parity (which requires parity in accuracy across groups, defined by protected attributes) or calibration (which requires similar predictions to have similar meanings across groups, defined by protected attributes). Central to this discussion are impossibility results, owed to Kleinberg (...) et al. (2016), Chouldechova (2017), and Corbett-Davies et al. (2017), which show that classification parity and calibration are often incompatible. This paper aims to argue that classification parity, calibration, and a newer, interesting measure called counterfactual fairness are unsatisfactory measures of fairness, offer a general diagnosis of the failure of these measures, and sketch an alternative approach to understanding fairness in machine learning. (shrink)

Prediction-based decisions, which are often made by utilizing the tools of machine learning, influence nearly all facets of modern life. Ethical concerns about this widespread practice have given rise to the field of fair machine learning and a number of fairness measures, mathematically precise definitions of fairness that purport to determine whether a given prediction-based decision system is fair. Following Reuben Binns (2017), we take ‘fairness’ in this context to be a placeholder for a variety of normative egalitarian considerations. We (...) explore a few fairness measures to suss out their egalitarian roots and evaluate them, both as formalizations of egalitarian ideas and as assertions of what fairness demands of predictive systems. We pay special attention to a recent and popular fairness measure, counterfactual fairness, which holds that a prediction about an individual is fair if it is the same in the actual world and any counterfactual world where the individual belongs to a different demographic group (cf. Kusner et al. (2018)). (shrink)

Algorithms are used across a wide range of societal sectors such as banking, administration, and healthcare to make predictions that impact on our lives. While the predictions can be incredibly accurate about our present and future behavior, there is an important question about how these algorithms in fact represent human identity. In this paper, we explore this question and argue that machine learning algorithms represent human identity in terms of what we shall call the statistical individual. This statisticalized representation of (...) individuals, we shall argue, differs significantly from our ordinary conception of human identity, which is tightly intertwined with considerations about biological, psychological, and narrative continuity—as witnessed by our most well-established philosophical views on personal identity. Indeed, algorithmic representations of individuals give no special attention to biological, psychological, and narrative continuity and instead rely on predictive properties that significantly exceed and diverge from those that we would ordinarily take to be relevant for questions about how we are. (shrink)

In recent years, there has been a surge in research addressing the question which properties predictive algorithms ought to satisfy in order to be considered fair. Three of the most widely discussed criteria of fairness are the criteria called equalized odds, predictive parity, and counterfactual fairness. In this paper, I will present a new impossibility result involving these three criteria of algorithmic fairness. In particular, I will argue that there are realistic circumstances under which any predictive algorithm that satisfies counterfactual (...) fairness will violate both other fairness criteria, that is, equalized odds and predictive parity. As will be shown, this impossibility result forces us to give up one of four intuitively plausible assumptions about algorithmic fairness. I will explain and motivate each of the four assumptions and discuss which of them can plausibly be given up in order to circumvent the impossibility. (shrink)

The problem of algorithmic fairness is typically framed as the problem of finding a unique formal criterion that guarantees that a given algorithmic decision-making procedure is morally permissible. In this paper, I argue that this is conceptually misguided and that we should replace the problem with two sub-problems. If we examine how most state-of-the-art machine learning systems work, we notice that there are two distinct stages in the decision-making process. First, a prediction of a relevant property is made. Secondly, a (...) decision is taken based (at least partly) on this prediction. These two stages have different aims: the prediction is aimed at accuracy, while the decision is aimed at allocating a given good in a way that maximizes some context-relative utility measure. Correspondingly, two different fairness issues can arise. First, predictions could be biased in discriminatory ways. This means that the predictions contain systematic errors for a specific group of individuals. Secondly, the system’s decisions could result in an allocation of goods that is in tension with the principles of distributive justice. These two fairness issues are distinct problems that require different types of solutions. I here provide a formal framework to address both issues and argue that this way of conceptualizing them resolves some of the paradoxes present in the discussion of algorithmic fairness. (shrink)

An implicit ambiguity in the field of prediction-based decision-making concerns the relation between the concepts of prediction and decision. Much of the literature in the field tends to blur the boundaries between the two concepts and often simply refers to ‘fair prediction’. In this paper, we point out that a differentiation of these concepts is helpful when trying to implement algorithmic fairness. Even if fairness properties are related to the features of the used prediction model, what is more properly called (...) ‘fair’ or ‘unfair’ is a decision system, not a prediction model. This is because fairness is about the consequences on human lives, created by a decision, not by a prediction. In this paper, we clarify the distinction between the concepts of prediction and decision and show the different ways in which these two elements influence the final fairness properties of a prediction-based decision system. As well as discussing this relationship both from a conceptual and a practical point of view, we propose a framework that enables a better understanding and reasoning of the conceptual logic of creating fairness in prediction-based decision-making. In our framework, we specify different roles, namely the ‘prediction-modeler’ and the ‘decision-maker,’ and the information required from each of them for being able to implement fairness of the system. Our framework allows for deriving distinct responsibilities for both roles and discussing some insights related to ethical and legal requirements. Our contribution is twofold. First, we offer a new perspective shifting the focus from an abstract concept of algorithmic fairness to the concrete context-dependent nature of algorithmic decision-making, where different actors exist, can have different goals, and may act independently. In addition, we provide a conceptual framework that can help structure prediction-based decision problems with respect to fairness issues, identify responsibilities, and implement fairness governance mechanisms in real-world scenarios. (shrink)

This paper develops an account of how the implementation of ML models into healthcare settings requires revising the methodological apparatus of philosophical bioethics. On this account, ML models are cognitive interventions that provide decision-support to physicians and patients. Due to reliability issues, opaque reasoning processes, and information asymmetries, ML models pose inferential problems for them. These inferential problems lay the grounds for many ethical problems that currently claim centre-stage in the bioethical debate. Accordingly, this paper argues that the best way (...) to make progress in remedying these ethical problems is to distil their epistemic core and to identify appropriate epistemic norms as guardrails. The viability of this approach will be highlighted based on four key issues: trust, responsibility, paternalism, and fairness. In that respect, the paper also contributes to a more pronounced view of the specific methodological challenges for ethical theorizing, when the point of reference are complex statistical models that make predictions, rather than individual agents, acting for reasons. (shrink)

Where economists previously viewed the market as arising from a ‘spontaneous order’, antithetical to design, they now design markets to achieve specific purposes. This paper reconstructs how this change in what markets are and can do came about and considers some consequences. Two decisive developments in economic theory are identified: first, Hurwicz’s view of institutions as mechanisms, which should be designed to align incentives with social goals; and second, the notion of marketplaces – consisting of infrastructure and algorithms – which (...) should be designed to exhibit stable properties. These developments have empowered economists to create marketplaces for specific purposes, by designing appropriate algorithms. I argue that this power to create marketplaces requires a shift in ethical reasoning, from whether markets should reach into certain spheres of life, to how market algorithms should be designed. I exemplify this shift, focusing on bias, and arguing that transparency should become a goal of market design. (shrink)

Algorithmic discrimination has rapidly become a topic of intense public and academic interest. This article explores three issues raised by algorithmic discrimination: 1) the distinction between direct and indirect discrimination, 2) the notion of disadvantageous treatment, and 3) the moral badness of discriminatory automated decision-making. It argues that some conventional distinctions between direct and indirect discrimination appear not to apply to algorithmic discrimination, that algorithmic discrimination may often be discrimination between groups, as opposed to against groups, and that it is (...) not necessarily the case that morally bad algorithmic discrimination gives us reason to not use automated decision-making. For each of the three issues, the article explores implications for algorithmic discrimination, suggests some alternative answers, and clarifies how we may want to think of discrimination more broadly in light of lessons drawn from the context of algorithmic discrimination. (shrink)

Criminal justice systems have traditionally relied heavily on human decision-making, but new technologies are increasingly supplementing the human role in this sector. This paper considers what general limits need to be placed on the use of algorithms in sentencing decisions. It argues that, even once we can build algorithms that equal human decision-making capacities, strict constraints need to be placed on how they are designed and developed. The act of condemnation is a valuable element of criminal sentencing, and using algorithms (...) in sentencing – even in an advisory role – threatens to undermine this value. The paper argues that a principle of “meaningful public control” should be met in all sentencing decisions if they are to retain their condemnatory status. This principle requires that agents who have standing to act on behalf of the wider political community retain moral responsibility for all sentencing decisions. While this principle does not rule out the use of algorithms, it does require limits on how they are constructed. (shrink)

An Artificial Intelligence algorithm trained on data that reflect racial biases may yield racially biased outputs, even if the algorithm on its own is unbiased. For example, algorithms used to schedule medical appointments in the USA predict that Black patients are at a higher risk of no-show than non-Black patients, though technically accurate given existing data that prediction results in Black patients being overwhelmingly scheduled in appointment slots that cause longer wait times than non-Black patients. This perpetuates racial inequity, in (...) this case lesser access to medical care. This gives rise to one type of Accuracy-Fairness trade-off: preserve the efficiency offered by using AI to schedule appointments or discard that efficiency in order to avoid perpetuating ethno-racial disparities. Similar trade-offs arise in a range of AI applications including others in medicine, as well as in education, judicial systems, and public security, among others. This article presents a framework for addressing such trade-offs where Machine Learning and Optimization components of the algorithm are decoupled. Applied to medical appointment scheduling, our framework articulates four approaches intervening in different ways on different components of the algorithm. Each yields specific results, in one case preserving accuracy comparable to the current state-of-the-art while eliminating the disparity. (shrink)

Recent studies have shown that recidivism scoring algorithms like COMPAS have significant racial bias: Black defendants are roughly twice as likely as white defendants to be mistakenly classified as medium- or high-risk. This has led some to call for abolishing COMPAS. But many others have argued that algorithms should instead be given access to a defendant's race, which, perhaps counterintuitively, is likely to improve outcomes. This approach can involve either establishing race-sensitive risk thresholds, or distinct racial ‘tracks’. Is there a (...) moral difference between these two approaches? We first consider Deborah Hellman's view that the use of distinct racial tracks (but not distinct thresholds) does not constitute disparate treatment since the effects on individuals are indirect and does not rely on a racial generalization. We argue that this is mistaken: the use of different racial tracks seems both to have direct effects on and to rely on a racial generalization. We then offer an alternative understanding of the distinction between these two approaches—namely, that the use of different cut points is to the counterfactual comparative disadvantage, ex ante, of all white defendants, while the use of different racial tracks can in principle be to the advantage of all groups, though some defendants in both groups will fare worse. Does this mean that the use of cut points is impermissible? Ultimately, we argue, while there are reasons to be skeptical of the use of distinct cut points, it is an open question whether these reasons suffice to make a difference to their moral permissibility. (shrink)

Algorithmic predictions are promising for insurance companies to develop personalized risk models for determining premiums. In this context, issues of fairness, discrimination, and social injustice might arise: Algorithms for estimating the risk based on personal data may be biased towards specific social groups, leading to systematic disadvantages for those groups. Personalized premiums may thus lead to discrimination and social injustice. It is well known from many application fields that such biases occur frequently and naturally when prediction models are applied to (...) people unless special efforts are made to avoid them. Insurance is no exception. In this paper, we provide a thorough analysis of algorithmic fairness in the case of insurance premiums. We ask what “fairness” might mean in this context and how the fairness of a premium system can be measured. For this, we apply the established fairness frameworks of the fair machine learning literature to the case of insurance premiums and show which of the existing fairness criteria can be applied to assess the fairness of insurance premiums. We argue that two of the often-discussed group fairness criteria, independence (also called statistical parity or demographic parity) and separation (also known as equalized odds), are not normatively appropriate for insurance premiums. Instead, we propose the sufficiency criterion (also known as well-calibration) as a morally defensible alternative that allows us to test for systematic biases in premiums towards certain groups based on the risk they bring to the pool. In addition, we clarify the connection between group fairness and different degrees of personalization. Our findings enable insurers to assess the fairness properties of their risk models, helping them avoid reputation damage resulting from potentially unfair and discriminatory premium systems. (shrink)

This article presents a fairness principle for evaluating decision-making based on predictions: a decision rule is unfair when the individuals directly impacted by the decisions who are equal with respect to the features that justify inequalities in outcomes do not have the same statistical prospects of being benefited or harmed by them, irrespective of their socially salient morally arbitrary traits. The principle can be used to evaluate prediction-based decision-making from the point of view of a wide range of antecedently specified (...) substantive views about justice in outcome distributions. (shrink)

Algorithm-assisted decision procedures—including some of the most high-profile ones, such as COMPAS—have been described as unfair because they compound injustice. The complaint is that in such procedures a decision disadvantaging members of a certain group is based on information reflecting the fact that the members of the group have already been unjustly disadvantaged. I assess this reasoning. First, I distinguish the anti-compounding duty from a related but distinct duty—the proportionality duty—from which at least some of the intuitive appeal of the (...) former illegitimately derives. Second, I distinguish between different versions of the anti-compounding duty, arguing that, on some versions, uses of algorithm-assisted decision procedures rarely clash with the anti-compounding duty. Third, drawing on examples of algorithm-assisted decision procedures, I present three objections to the idea that there is a reason not to compound injustice. The most important of these is that one can compound injustice in a non-disrespectful way, and that the wrongfulness of non-disrespectfully compounding injustice is fully explained by the proportionality duty. (shrink)

Increasing concerns have been raised regarding artificial intelligence (AI) bias, and in response, efforts have been made to pursue AI fairness. In this paper, we argue that the idea of structural injustice serves as a helpful framework for clarifying the ethical concerns surrounding AI bias—including the nature of its moral problem and the responsibility for addressing it—and reconceptualizing the approach to pursuing AI fairness. Using AI in healthcare as a case study, we argue that AI bias is a form of (...) structural injustice that exists when AI systems interact with other social factors to exacerbate existing social inequalities, making some groups of people more vulnerable to undeserved burdens while conferring unearned benefits to others. The goal of AI fairness, understood this way, is about pursuing a more just social structure with the development and usage of AI systems when appropriate. We further argue that all participating agents in the unjust social structure associated with AI bias bear a shared responsibility to join collective action with the goal of reforming the social structure, and we provide a list of practical recommendations for agents in various social positions to contribute to this collective action. (shrink)

Optimism about our ability to enhance societal decision‐making by leaning on Machine Learning (ML) for cheap, accurate predictions has palled in recent years, as these ‘cheap’ predictions have come at significant social cost, contributing to systematic harms suffered by already disadvantaged populations. But what precisely goes wrong when ML goes wrong? We argue that, as well as more obvious concerns about the downstream effects of ML‐based decision‐making, there can be moral grounds for the criticism of these predictions themselves. We introduce (...) and defend a theory of predictive justice, according to which differential model performance for systematically disadvantaged groups can be grounds for moral criticism of the model, independently of its downstream effects. As well as helping resolve some urgent disputes around algorithmic fairness, this theory points the way to a novel dimension of epistemic ethics, related to the recently discussed category of doxastic wrong. (shrink)

The use of machine learning systems for decision-support in healthcare may exacerbate health inequalities. However, recent work suggests that algorithms trained on sufficiently diverse datasets could in principle combat health inequalities. One concern about these algorithms is that their performance for patients in traditionally disadvantaged groups exceeds their performance for patients in traditionally advantaged groups. This renders the algorithmic decisions unfair relative to the standard fairness metrics in machine learning. In this paper, we defend the permissible use of affirmative algorithms; (...) that is, algorithms trained on diverse datasets that perform better for traditionally disadvantaged groups. Whilst such algorithmic decisions may be unfair, the fairness of algorithmic decisions is not the appropriate locus of moral evaluation. What matters is the fairness of final decisions, such as diagnoses, resulting from collaboration between clinicians and algorithms. We argue that affirmative algorithms can permissibly be deployed provided the resultant final decisions are fair. (shrink)

This paper examines racial discrimination and algorithmic bias in predictive policing algorithms (PPAs), an emerging technology designed to predict threats and suggest solutions in law enforcement. We first describe what discrimination is in a case study of Chicago’s PPA. We then explain their causes with Broadbent’s contrastive model of causation and causal diagrams. Based on the cognitive science literature, we also explain why fairness is not an objective truth discoverable in laboratories but has context-sensitive social meanings that need to be (...) negotiated through democratic processes. With the above analysis, we next predict why some recommendations given in the bias reduction literature are not as effective as expected. Unlike the cliché highlighting equal participation for all stakeholders in predictive policing, we emphasize power structures to avoid hermeneutical lacunae. Finally, we aim to control PPA discrimination by proposing a governance solution—a framework of a social safety net. (shrink)

Artificial intelligence (AI) and machine learning (ML) systems increasingly purport to deliver knowledge about people and the world. Unfortunately, they also seem to frequently present results that repeat or magnify biased treatment of racial and other vulnerable minorities. This paper proposes that at least some of the problems with AI’s treatment of minorities can be captured by the concept of epistemic injustice. To substantiate this claim, I argue that (1) pretrial detention and physiognomic AI systems commit testimonial injustice because their (...) target variables reflect inaccurate and unjust proxies for what they claim to measure; (2) classification systems, such as facial recognition, commit hermeneutic injustice because their classification taxonomies, almost no matter how they are derived, reflect and perpetuate racial and other stereotypes; and (3) epistemic injustice better explains what is going wrong in these types of situations than does the more common focus on procedural (un)fairness. (shrink)

With the increasing use of algorithms in high-stakes areas such as criminal justice and health has come a significant concern about the fairness of prediction-based decision procedures. In this article I argue that a prominent class of mathematically incompatible performance parity criteria can all be understood as applications of John Broome’s account of fairness as the proportional satisfaction of claims. On this interpretation these criteria do not disagree on what it means for an algorithm to be _fair_. Rather they express (...) different understandings of what grounds a claim to a good being allocated by an algorithmic decision procedure. I then argue that an important implication of the Broomean interpretation is that it strengthens the case for outcome-based criteria. Finally, I consider how a version of the levelling-down objection to performance parity criteria arises within the Broomean account. (shrink)

The use of algorithms to support prediction-based decision-making is becoming commonplace in a range of domains including health, criminal justice, education, social services, lending, and hiring. An assumption governing such decisions is that there is a property Y such that individual a should be allocated resource R by decision-maker D if a is Y. When there is uncertainty about whether a is Y, algorithms may provide valuable decision support by accurately predicting whether a is Y on the basis of known (...) features of a. Based on recent work on statistical evidence in epistemology this article presents an argument against relying exclusively on algorithmic predictions to allocate resources when they provide purely statistical evidence that a is Y. The article then responds to the objection that any evidence that will increase the proportion of correct decisions should be accepted as the basis for allocations regardless of its epistemic deficiency. Finally, some important practical aspects of the conclusion are considered. (shrink)

What does it mean for algorithmic classifications to be fair to different socially salient groups? According to classification parity criteria, what is required is equality across groups with respect to some performance measure such as error rates. Critics of classification parity object that classification parity entails that achieving fairness may require us to choose an algorithm that makes no group better off and some groups worse off than an alternative. In this article, I interpret the problem of algorithmic fairness as (...) a case concerning the ethics of the distribution of algorithmic classifications across groups (as opposed to, e.g., the fairness of data collection). I begin with a short introduction of algorithmic fairness as a problem discussed in machine learning. I then show how the criticism raised against classification parity is a form of leveling down objection, and I interpret the egalitarianism of classification parity as deontic egalitarianism. I then discuss a challenge to this interpretation and suggest a revision. Finally, I examine how my interpretation provides proponents of classification parity with a response to the leveling down criticism and how it relates to a recent suggestion to evaluate fairness for automated decision-making systems based on risk and welfare considerations from behind a veil of ignorance. (shrink)

Statistical criteria of fairness are formal measures of how an algorithm performs that aim to help us determine whether an algorithm would be fair to use in decision-making. In this paper, I introduce a new version of the criterion known as “Equalized Odds,” argue that it is a requirement of procedural fairness, and show that it is immune to a number of objections to the standard version.

With increasing use of automated algorithmic decision-making, issues of algorithmic fairness have attracted much attention lately. In this growing literature, existing concepts from ethics and political philosophy are often applied to new contexts. The reverse—that novel insights from the algorithmic fairness literature are fed back into ethics and political philosophy—is far less established. However, this short commentary on Baumann and Loi (Philosophy & Technology, 36(3), 45 2023) aims to do precisely this. Baumann and Loi argue that among algorithmic group fairness (...) measures proposed, one—sufficiency (well-calibration) is morally defensible for insurers to use, whereas independence (statistical parity or demographic parity) and separation (equalized odds) are not normatively appropriate in the insurance context. Such a result may seem to be of relatively narrow interest to insurers and insurance scholars only. We argue, however, that arguments such as that offered by Baumann and Loi have an important but so far overlooked connection to the derivation of the minimal state offered by Nozick (1974) and thus to political philosophy at large. (shrink)

In this paper I argue that some examples of what we label ‘algorithmic bias’ would be better understood as cases of institutional bias. Even when individual algorithms appear unobjectionable, they may produce biased outcomes given the way that they are embedded in the background structure of our social world. Therefore, the problematic outcomes associated with the use of algorithmic systems cannot be understood or accounted for without a kind of structural account. Understanding algorithmic bias as institutional bias in particular (as (...) opposed to other structural accounts) has at least two important upshots. First, I argue that the existence of bias that is intrinsic to certain institutions (whether algorithmic or not) suggests that at least in some cases, the algorithms now substituting as pieces of institutional norms or rules are not “fixable” in the relevant sense, because the institutions they help make up are not fixable. Second, I argue that in other cases, changing the algorithms being used within our institutions (rather than getting rid of them entirely) is essential to changing the background structural conditions of our society. (shrink)

The literature on algorithmic fairness has examined exogenous sources of biases such as shortcomings in the data and structural injustices in society. It has also examined internal sources of bias as evidenced by a number of impossibility theorems showing that no algorithm can concurrently satisfy multiple criteria of fairness. This paper contributes to the literature stemming from the impossibility theorems by examining how informational richness affects the accuracy and fairness of predictive algorithms. With the aid of a computer simulation, we (...) show that informational richness is the engine that drives improvements in the performance of a predictive algorithm, in terms of both accuracy and fairness. The centrality of informational richness suggests that classification parity, a popular criterion of algorithmic fairness, should be given relatively little weight. But we caution that the centrality of informational richness should be taken with a grain of salt in light of practical limitations, in particular, the so-called bias-variance trade off. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)