Distributive Justice as the Foundational Premise of Fair ML: Unification, Extension, and Interpretation of Group Fairness Metrics
Authors: Joachim Baumann
Corinna Hertweck
Michele Loi
Christoph Heitz
Venue: NeurIPS 2022 Submitted (2022)
Keywords: algorithmic decision making
group fairness
distributive justice
welfare
egalitarianism
maximin
prioritarianism
sufficientarianism

Abstract: Group fairness metrics are an established way of assessing the fairness of prediction-based decision-making systems. However, these metrics are still insufficiently linked to philosophical theories, and their moral meaning is often unclear. We propose a general framework for analyzing the fairness of decision systems based on theories of distributive justice, encompassing different established "patterns of justice" that correspond to different normative positions. We show that the most popular group fairness metrics can be interpreted as special cases of our approach. Thus, we provide a unifying and interpretative framework for group fairness metrics that reveals the normative choices associated with each of them and that allows understanding their moral substance. At the same time, we provide an extension of the space of possible fairness metrics beyond the ones currently discussed in the fair ML literature. Our framework also allows overcoming several limitations of group fairness metrics that have been criticized in the literature, most notably (1) that they are parity-based, i.e., that they demand some form of equality between groups, which may sometimes be harmful to marginalized groups, (2) that they only compare decisions across groups, but not the resulting consequences for these groups, and (3) that the full breadth of the distributive justice literature is not sufficiently represented.

Distributive Justice as the Foundational Premise of Fair ML: Unification, Extension, and Interpretation of Group Fairness Metries
Anonymous Author(s)
Affiliation Address email
Abstract
Group fairness metrics are an established way of assessing the fairness of prediction- based decision-making systems. However, these metrics are still insufficiently linked to philosophical theories, and their moral meaning is often unclear. We propose general framework for analyzing the fairness of decision systems based on theories of distributive justice, encompassing different established "patterns of justice" that correspond to different normative positions. We show that the most popular group fairness metrics can be interpreted as special cases of our approach. Thus, provide unifying and interpretative framework for group fairness metrics that reveals the normative choices associated with each of them and that allows understanding their moral substance. At the same time, provide an extension of the space possible fairness metrics beyond the ones currently discussed in the fair ML literature. Our framework also allows overcoming several limitations of group fairness metrics that have been criticized in the literature, most notably (I) that they parity-based, i.e., that they demand some form of equality between groups, which may sometimes be harmful to marginalized groups, (2) that they only compare decisions across groups, but not the resulting consequences for these groups, and (3) that the full breadth of the distributive justice literature is not sufficiently represented.
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Introduction
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Supervised machine learning (ML) increasingly being used for prediction-basee decision making in various consequential applications, such as credit lending, school admission, and recruitment. Recent work has shown that the use of algorithms for decision making can reinforce existing biases or introduce new ones [8] Consequently, fairness has emerged as an important desideratum for automated decision making. As recent cases in practice have shown, this is crucial order to mitigate
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unjustified disadvantages towards certain demographic groups (see, e.g., [2] 46 21 40). However,
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quantifying the fairness of decision making systems not straightforward as any morally appropriate notion of fairness heavily depends on the given context.
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Many different measures have emerged in the algorithmic fairness literature assess and mitigate unfaimess towards marginalized groups in decision making systems. Many of the proposed notions of fairesss are in the category of so-called group faimess criteria (7]. some of which are mathematically
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incompatible in practice Kleinberg et al. [32), Chouldechova [14]. Therefore, satisfying such
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fairness criterion comes the expense of not being able satisfy others Kleinberg et al. (31. Wong
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AlMosst existing group faimess criteria demand equality of certain value between different
socio aaco-demoggappic groups [2]] However, our framework is also compatible with other notions of
Submitted to 36th Conference on Neural Information Processing Systems (NeurIPS 2022). Do not distribute.

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fairness that concern groups of individuals, such as preference-basee based fairness [56 30 However, this Hlands-whieh is in contrast to the comparison of individuals, as it is done with other types of fairness such as individual fairness 18 [2 envy-freeness 6 or counterfactual faimess Kusner
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al. 34 Readers unfamiliar with group fairness may refer B8 Chapter 21. [53 and 7 for an
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overview of the topic. We briefly introduce and formally define the most-discussed group faimess
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criteria in Appendix A
Much of the algorithmic fairness literature evolves around a limited set of group faimesss metrics and is often not clearly linked to the many philosophical theories of justice that have been well- discussed. Kuppler et al. [33 find that there is little to no overlap between philosophical theories 43
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of justice and metrics in the algorithmic fairness literature and conclude that "apparently, the fair machine learning literature has not taken full advantage of the rich and longstanding literature on distributive justice" [33 p. 17]. Therefore, the definitions of group fairnsss could be described as quite narrow when viewed from a philosophical perspective. This becomes evident when thinking about an example: Group fairness metries typically demand that groups are equal with respect to some metric. Demanding equality between groups often makes sense, but consider case in which we could increase the utility of one group without harming another: Should we do this? While we cannot
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51 say that this is always a good idea, it at least seems to be a reasonable objection to group fairness
52 metrics, which demand equality all costs. Therefore, this paper asks whether group fairness metrics
53 can be extended to compare groups in other ways.
54 As of today, only a limited number of faimess metrics have been discussed, forcing stakeholders to
55 choose between a set of pre-defined metrics that they then have to justify for their context. This paper,
56 in contrast, presents general framework for the derivation of targeted and context-specific fairness metrics, starting from values and moral views, and connects these to the philosophical literature, in particular to theories of distributive justice.
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Our main contributions can be summarized as follows:
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We propose a general framework for assessing the fairness of prediction-based decision systems, based theories of distributive justice, and allowing for different established "patterns of justice" that correspond to different normative positions. The framework is based on analysis of how utility is distributed between groups. "Pattern of justice" refers to normative ideas of what constitutes a just distribution.
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We show that the most popular group faimess metrics can be interpreted as special cases of this approach, which thus establishes a unifying framework that includes established metrics, but also shows how new ones can be constructed.
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We first present existing literature on group fairness (including its limitations) in Section 2 In Section we present our unified framework for utility-based defnnitoos of group fairness. We focus on the mathematical formalization of different aspects of the distributive justice literature while
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71 keeping the review of the philosophical side short. More details about the philosophical side can be found in the companion paper [3] Section thenn demonstrates that existing group fairness metrics
75 are special cases of our utility- based approach. Finally, we discuss the implications of this and possible future work in Section 5
2 Limitations of current group fairness criteria
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76 Existing group fairness criteria pursue an egalitarian approach. This means that they demand equality
77 of certain value between different socio-demographic groups [12]. The fulfillment of these criteria
78 is easy to assess, as this only requires access to a few variables (e.g., to check whether statistical
79 parity is satisfied, we only need the decisions and the group membership of individuals). However,
80 they also come with several limitations:
81 The "leveling down objection" As has been shown by (27. in some cases, enforcing group
82 fairness criteria can yield worse results for all groups in order to ensure parity between the groups
83 This is what is known the "leveling down objection", which is often brought forward to challenge 84 egalitarianism in philosophical literature 17]: In a case in which equality requires us to worsen the outcomes for everyone, should we really demand equality or should we rather tolerate some

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inequalities? As criticized by Cooper and Abrams [5], Weerts et al. [54] existing definitions of group faimess lack this differentiation as they always minimize inequality.
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No consideration of consequences As pointed out by Hertweck et al. [24] and Weerts et al. [54].
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a large part of the existing work on fairees criteria seems to focus on an equal distribution of
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favorable decisions and not on the consequences of these decisions. Binns [[T] notes that these criteria "[assume] a uniform valuation of decision outcomes across different populations" [1] p. 6], and notes that this assumption does not always hold. Whether a loan approval has a positive effect on one's life or not arguably depends on one's ability to repay this loan (and possibly on other individual attributes). This narrow focus on the algorithm's s decisions instead of its consequences makes difficult to use existing group faimess criteria for moral assessment of unfairness in decision making systems, Parity-based criteria that only consider the decisions but not their consequences do not allow us to deliberately give positive decisions to larger share of the disadvantaged group this would be a form of unequal treatment. However, Kasy and Abebe [29] argue that in such a case, unequal treatment can be required by justice to reduce overall inequalities. Several works have therefore taken a utility-bassed -aatiy view of fairness. Heidari et al. [22]'s 's utility- definitions of fairness focus on the effects of decisions while [33 developed a method that follows the Rawlsian leximin principle to increase the welfare of the worse off groups. However, none of them provides a general framework that encompasses different theories of distributive justice.
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Limited set of fairness definitions Another limitation of existing group fairness criteria is that they represent a limited set of alternatives. One has to choose one over the others, as they are
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mathematically incompatible [32 14). [47 28 have highlighted that the criteria differ with respect to underlying moral values. Thus, solely choosing one among the limited set of criteria might fail adequately represent a morally appropriate definition of fairness for a given context. Heidarí et al.
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23 show how existing group fairness criteria can be viewed as instantiations of the equality of 109
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opportunity (EOP) principle. Similarly, [I0] show that they can be viewed as special cases of a
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more general principle of fairness they call fair equality of chances (FEC). This way, they provide a framework through which the existing fairness criteria can be viewed. However, the conditions under which the existing fairness criteria map to EOP (or to FEC, respectively) are not always given. We cannot expect every application to fall neatly into one of these conditions and thus cannot expect to find a fitting fairness criterion among the ones already proposed in the group fairness literature.
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These more general notions of fairness might be suitable to grasp the different existing notions of group fairness. However, they do not adequately represent the complexity of the distributive justice literature Kuppler et al. [33] In this paper, want bridge the gap between fair machine learning and philosophical theories of distributive justice.
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A framework for fairness evaluations based on distributive justice
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As discussed in Section current group fairness criteria have some serious shortcomings. Clearly, they do not reflect the full breadth of the literature on distributive justice [33] To address this issue (at least partially), we propose a utility-based extension of group fairness. This section introduces this approach from rather technical perspective. More details on its links to the literature on distributive justice can be found in R. Our approach is based on the observation that each decision system creates a distribution of utility among individuals and groups. Theories of distributive justice are concerned with the question of when such a distribution can be considered just. As we will later
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show, some of these thcories can be mapped to classical group fairness concepts from the fair ML literature (see Section
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130 We consider decision making system that takes binary decisions D on decision subjects DS of a given population P. based on a decision rule r. The decision rule assigns each individual E P a binary decision d; E 1), applying the decision rule to some input data, which includes an unknown but decision-relevant binary random variable Y. It does not matter how the decision rule functions. It could, for example, be an automated rule that takes decisions based on predictions of Y
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from an MI. model or the decisions could be made by humans. We further assume that at least two social groups are defined, denoted with different values for the sensitive attribute A.
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3.1
Utility of the decision subjects
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As previously discussed, current definitions of group fairness only consider the decisions themselves, but not their consequences even though the same decision could be beneficial for some and harmful for others [54]. Our approach explicitly considers the consequences of decisions, i.c., the resulting utility (or welfare), which could be positive in the case of benefit or negative in the case of a harm. We model the consequences with a utility function u which, in our binary context, may depend on both the decision d, and the value y; of Y.
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The utility ups, of a decision subject is given by:
DSS = Wi1 d; Yi + who d; ( - ys) + wo1 .( -dd4) de) yi + 1000 (1 - (1-d))- (1 yi), (1)
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where the utility weights way denote the four different utility values that might be realized for the four combinations of the random variables Y and D
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The utility ups,; is a realization of a random variable UDS. For assessing the fairesss of a decision rule, we are interested in systemalic differences between groups. Our framework is based on the assumption that such differences correspond to differentThis- that we are intereste in the
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expectation values EsUDs) of the individual utility, for different groups in A. Note that this is
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normative choice and that other ways of comparing groups are imaginable, e.g., comparing their
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aggregated utilities.
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Relevant groups to compare
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Theories of distributive justice are typically concerned with individuals 48 while group fairness is concerned with socially salient groups. Group fairness focuses on comparisons of different groups as this is what theories of discrimination are concerned with [.] This poses the question of how the comparison of individuals distributive justice and the comparison of socially salient groups in group fairness can be combined? John Rawls's 's concept of "relevant positions" " [42, $16, pp. 81 81-86] is concept that unites both ideas. We view "relevant positions" as the groups whose expected utility we want to compare and refer to them as the relevant groups (to compare) As defined in 3. relevant groups to compare have comparable moral claims receive the same utility, but probably
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do not receive the same utility. Our approach thus views the theories of distributive justice, which we introduced in Section? 2 from the perspective of relevant groups to compare.
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164 To be more specific, relevant groups are defined by two concepts: (1) claims differentiator J: What makes the case that some people have the same claims utility while others have different claims to utility?: (2) causes of inequality (resulting in socially salient groups A): What are the most likely causes of inequalities?
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168 As described in 3 the claims differentiator identifies people who have equal moral claims. In other words, the utility should be distributed equally between these people. This means we only consider people with equal claims for our fairness evaluation 31 Within the group of all individuals that have equal claims to utility (i.e., that are equal in their value for J) we specify groups that are unlikely
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to end up receiving equal utility, on average, based on the known causes of inequality (i.e., that are different in their value for A, which is sometimes also referred to as protected attribute). J and A
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define the relevant groups that group fairness criteria compare. For simplicity, we will assume that there are only two groups = {0, 1} that are unlikely to receive the same utility. It is, for example, common to expect individuals of a different race or gender to not derive the same utility from decision systems.
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In practice, however, one could use a much more specific utility function, using other attributes as well. A rather simple extension would also take A into account and define these four utility weights for each group separately. That should be supported by an analysis of the inequality generated in the transition between the decision space and the utility space between different (socially salient other) groups. In philosophy and economics, the work of Amartya Sen explains why resources do not always convert into the same capabilities (options to be and do) (49, pp. 21-23].
"This builds on Anonymous 4 which refers to relevant positions "representative individuals".
3 For a philosophical analysis of comparable moral claims to good, see 25
"This concept is similar to the justifier described in [36 [0]

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The egalitarian fairness criterion is satisfied if the expected utility is equal for In the next step, we want to compare the utilities of the relevant groups. Specifically, we will compare the expectation value of utility over all decisions made for given population under a given decision rule. We denote this as the expected utility that takes the relevant groups into account, F[UDs| = j, = a), where J denotes the claims differentiator and j corresponds to a possible value of the variable J. and A denotes the different socially salient group to be compared with each other. In our framework, assessing fairness means comparing relevant groups with the same j. but different a, with respect to the distribution of utility.
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3.3
Patterns for just distribution of utility
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The claims differentiator tells us which individuals have equal moral claims to the utility distributed by the decision process. However, in some cases, an equal distribution of utility among the relevant groups (defined by and A) may not be the primary concern for justice (see below). Our approach offers different choices, which we refer to patterns of justice. For each of them, we will briefly explain their normative view of what constitutes justice. For each pattern, we formulate a fairness constraint and a fairness metric: A faimess constraint is mathematical formalization of pattern of justice, which can either be satisfied or not. A faimess metric F, on the other hand, can measure the degree to which this criterion is fulfilled. Note that construct faimess metrics for binary
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A = {0, 13. Therefore, all patterns of justice that we present compare the expected utility of 194
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two relevant groups: A 0 J j (i.e., F(UDs]] J j, A 0)) and A 1 A J j (i.e., F[UDs| = J. = ===11 1))- However, the patterns of justice that we introduce here (egalitarianism, maximin, prioritarianism, sufficientiarianismm) can easily be translated to cases of more groups.
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In the following, we introduce only a few patterns of justice (representing fairness principles for the allocation of goods) that are widely discussed in philosophical literature. However, our utility-based definition of group fairness should in no way be seen as limited to these patterns. Our approach easily be extended to other patterns of justice and one may also implement their own pattern of justice. Our goal here is simply to highlight a few popular patterns of justice and how they can be embedded in our approach.
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3.3.1
Egalitarianism
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Egalitarianism as the name suggests- - demands equality [5] Egalitarianism as a broad concept does not, however, specify what should be equalized. This is subject of the equality of what debate initiated by Sen [48). One could, for example, aim to equalize the opportunities (cquality of opportunity) or outcomes (equality of outcomes).
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Fairness criterion
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the relevant groups:
E(Uns!J j,A E(Uns]
(2)
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The degree to which egalitarianism is fulfilled is measured as the absolute differ- ence between the two groups' expected utilities (lower values are better)
Fairness metric
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F Fegalitarianism
[[UDs!]J j. A E(UDs]J j. A.A= 1)
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3.3.2
Maximin
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Maximin describes the principle that among set of possible distributions, the one that maximizes
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the expected utility of the relevant group that is worst-off should be chosen (35). In contrast to egalitarianism. inequalities are thus tolerated if the worst-off group benefits from them. This has been defended by Rawls in the form of the "difference principle" 42
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218 Fairness criterion The maximin faimess criterion is satisfied if there is no other possible distribu-
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tion that would lead to greater expected utility of the worst-off relevant group, which we denote by U wworst-oft minaes (E(UDs)J j.A= j. =.A=))). a)). It thus requires that the decision rule r' (which
'Here, we consider the absolute difference in expected utilities. Alternatively, we could also consider the ratio of the two expected utilities.
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Uwerst-off (r') that is greater or equal represents the decision taken for each individual) results in a DS 222 than the U 1 (r) for any other decision rule from the set of all possible decision rules R:
DS
Uforrt-off (r') 2 mazteR (Uwerst-off (r)
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Fairness metric The degree to which maximin is fulfilled is measured as the value of the lowest expected utility between all relevant groups (higher values are better):
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F maximmin minaed (E(UDS|J=3) = =iA =a)
(5)
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3.3.3
Prioritarianism
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Prioritarianism describes the principle that among set of possible distributions, the one that maxi-
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mizes the weighted sum of utilities across all people [26]. In contrast to egalitarianism, inequalities thus tolerated if they increase this weighted sum of expected utilities. In this weighted sum, the
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expected utility of the worst-off relevant groups is given higher weight (the maximin principle can
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be seen as the extreme version of this an infinite weight is given to the worst-off relevant groups).
Fairness criterion The prioritarian fairness criterion is satisfied if there is no other possible distribution that would lead to greater overall expected utility, which is measured as a weighted aggregation of the relevant groups' expected utilities, where the expected utility of the worst-off relevant group given a higher weight. It thus requires that the decision rule r' results weighted pbetter-off (r') that greater or equal than the Üns(r) for any other decision rule from the set of all possible decision rules R:
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utility (s"(r') = k -US Uoworsttoff off (r') + DS
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ÚDS(r') 2 mazren (ÜDs(r)),
(6)
237 where ÜDS denotes the sum of decision subject utilities for all groups with weight applied to the worst-off group.
239 Fairness metric The degree to which prioritarianism is fulfilled is measured as an aggregate the (weighted) expected utilities (higher values are better):
F prioritarianism = k min E(UDs) J = A E), --A-1))
+ mar E(Uns]] J[Uns[J=]:)
= = j. = =
=
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3.3.4 Sufficientarranismm
Sufficientarianism (50] describes the principle that there is minimum threshold of utility that should be reached by everyone expectation, Inequalities between relevant groups above this minimum threshold are acceptable according to this principle. Inequalities are thus tolerated as long as all groups achieve a minimum level utility in expectation.
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Fairness criterion The sufficientarian faimess criterion is satisfied if all groups' expected utilities are above given threshold
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Va E A E(UDs|J j.A= a)(r') 2
(8)
248 Fairness metric The degree to which sufficientarianism fulfilled measured as the number of groups whose expected utility is above the given threshold t (higher values are better):
[1, if E(UDs|J J = j, a)
Fusffcientarianisn Σ Ta. where T.
0, otherwise

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3,4
Extension of group fairness
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Based on the mathematical framework outlined in this section, we suggest an extension of the current understanding of group faimess as described in Section 2 Instead of seeing group fairnsss
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as demanding equality between socio-demographic groups with respect to some value, we instead propose the following definition:
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Definition (Group faimess). Group fairesss is the just distribution of utility among relevant groups.
What makes a distribution just depends the pattern of justice. Thus, our extended understanding of group faimess does not necessarily require equal expected utilities across groups. Furthermore, our definition ensures that only relevant groups are being compared (in the most familiar case, these correspond to socio-demographic groups).
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Group faireess criteria. in sense, specify when group fairness is satisfied by decision decision-making system. From this, it follows that there are more group faimess criteria than previously acknowledged. 281
This extension of group faimess criteria alleviates some of the criticisms of currently popular group fairness criteria as we will show in Section 5
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Relation to existing group fairness criteria
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Existing group fairness criteria are special cases of the utility-based extension we propose. In this section, we formally show under which conditions our approach maps to existing group faimess criteria (see Table [ for a summary of the results). In particular, we look at well-known group fairness criteria: (conditional) statistical parity, equality of opportunity, false positive rate (FPR) parity, equalized odds, predictive parity, false omission rate (FOR) parity, and sufficiency. The mathematical definitions of these criteria can be found in Table 2 in Appendix AA] Furthermore, we
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show how the utility-based group fairness metries relate to existing ones. In this section, we only demonstrate when our utility-based approach results in one of three often discussed group fairness criteria: statistical parity, equality of opportunity, and predictive parity. We refer the interested reader to the Appendix B.2 where we provide a similar mapping for other existing group fairness criteria.
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The findings we present in this section extend the ones of (3), 36), and [0O. While (23] consider the distribution of undeserved utility (what they call the difference between an individual's 's actual and effort- utility). (36) and [0 use the decision subject utility UDS to derive a morally appropriate group fairness definition. This is similar to our approach presented in this paper, however, they only consider two options UDS D and Ds = Y, while our approach allows for arbitrary functions f for the utility: UDs f(D,Y).
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Statistical parity (also called demographic parity or group fairness 1 is defined as P(D - 1/A 0) = P(D = 1|A = 1). For specific decision subject utility weights Way and without any claims differentiator J. the condition of our utility-based fairness criteria derived from our framework is equivalent to statistical parity:
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Proposition 2 (Statistical parity as utility-based fairness). If the utility weights of all possible outcomes (as described in Section [3.Tp do not depend on the group membership (Mad a), and 286
W11 W10 # wol woo. then the egalitarian pattern fairness condition with J 0 is equivalent to statistical parity.
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The formal proof of Proposition 2 can be found in Appendix B.I.I
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We use Win to denote the decision subject utility associated with a positive decision (D = 1) and Woy denote the decision subject utility associated with negative decision (D 0). As we showed above, requiring statistical parity can be equivalent to requiring the fulfillment of a utility-based group
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fairness criterion. However, even if the two criteria are equivalent, this is not necessarily true if we compare the group fairness metrics that specify the degree to which these two criteria are fulfilled, i.c., if we compare the degree to which statistical parity is fulfilled with the degree to which a utility-based faimnss metric is fulfilled:
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'Recall that utility weights are denoted by way. where both dl and y can take the value or 1. For simplicity, we use why as placeholder for utility weights of all outcomes with a positive decision (d = 1) and for individuals of any type (y E {0, 1)). Le., w1o w11.
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Corollary 3 (Partial fulfillment of statistical parity in terms of utility-based fairness), Suppose that the degree which statistical parity is fulfilled is defined as the absolute difference in decision ratios across groups, i.e., IP(D= = 1 = 0) P(D = 1|4 = ). If the utility weights of all possible outcomes do not depend on the group membership (w'd a), and wn1 = who o wp1 = woo (i.e., W1y # Way), and J = 0, then the degree to which egalitarianism is fulfilled is equivalent to the degree to which statistical parity is fulfilled, multiplied by |wiy - Woyl-
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The formal proof of Corollary can be found in Appendix B.1.2 Intuitively, F /'egaituriaaiiss which is derived from the sallit-bbased fairness approach and represents the degree to which egalitarianism is fulfilled, can be seen as the degree to which statistical parity is fulfilled, weighted by the absolute
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difference in utility for the decision received (decision subject utility for a positive versus a negative decision).
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Equality of opportunity (also called TPR parity) is defined as P(D = 1|Y 1, = =
-) P(D
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1| = 1, A = 1), i.e., it requires parity of true positive rates (TPR) across groups a E A 20)
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Proposition 4 (Equality of opportunity as utility-based fairness). If 111 and woi do not depend on the group membership (wa1 1 a), and wi * woi. then the egalitarian pattern fairness condition with J = Y and j = {1} is equivalent to equality of opportunity.
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The formal proof of Proposition Hean be found in Appendix 1.3 Compared to statistical parity, equality of opportunity only requires equal acceptance rates across those subgroups of A who are of type Y 1. This corresponds the claims differentiator = [1] for J = Y. Thus, we simply require the utility weights win and wor to be unequal and independent of (which means that the utility weights W11 and Wh1 are constant across groups). As is the case for statistical parity, there differences when looking at the degree to which the two notions of fairness are fulfilled (equality of opportunity and the utility-based fairness under the conditions specified in Proposition 4
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Corollary 5 (Partial fulfillment of equality of opportunity in terms of utility- -based faimness). Suppose
that the degree to which equality of opportunity is fulfilled is defined as the absolute difference in decision ratios for individuals of type Y -= across groups, i.e., IP(D = 1|Y = =1, A = 0) - P(D =
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Y 1, A 1)). If w11 and Won do not depend on the group membership (wan 1 a), 11 F wol.
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J = Y, and j = {1}, then the degree to which egalitarianism is fulfilled is equivalent to the degree
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to which equality of opportunity is fulfilled, multiplied by [wi - -Wo)]]
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The formal proof of Corollary 5 can be found in Appendix B.1.4
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Predictive parity (also called PPV parity 9 or outcome test (51) is defined as P(Y = 1|D = A
0) P(Y 1|D - 1, A 1), i.e., requires parity of positive predictive value (PPV) rates across
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groups a E A.
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Proposition 6 (Predictive parity utility-based fairness). If W11 and wio do not depend on the group membership (Wly 1 a), and W11 A W1o. then the egalitarian pattern fairness condition with D and
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{1} is equivalent predictive parity.
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Compared equality of opportunity, predictive parity requires an equal share of individuals to be of type Y = 1 among those subgroups of A who receive the decision D = This corresponds to the claims differentiator j {1} for J = D. Thus, we simply require the utility weights W11 and Who to be unequal and 336
The formal proof of Proposition 6 can be found in Appendix B.1.5|
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independent of a. As is the case for the other group fairness criteria, there are differences regarding the degree to which the two notions of fairness are fulfilled (predictive parity and the utility-based fairness under the conditions specified in Proposition 6):
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Corollary 7 (Partial fulfillment of predictive parity in terms of -based fairness). Suppose that
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the degree to which predictive parity is fulfilled is defined as the absolute difference in the ratio of individuals that are of type Y = 1 among all those that are assigned the decision D = 1 across groups i.e., IP(Y = 1 = 1, A = 0) P(Y = 1 = 1, = 1)}. If win and who do not depend on the group membership (wiy a), w11 * w1o. J = D, and j = (1), then the degree to which egalitarianism is fulfilled is equivalent to the degree to which predictive parity is fulfilled, multiplied
343
345
by W11 Wiol
347
The formal proof of Corollary can be found in Appendix B.1.6
348
Considering T we see that existing group fairness criteria have a narrow understanding of utility and do not tolerate incqualities, which can ultimately be harmful to already marginalized groups as
8

---

Table 1: Mapping of existing group fairness metries to our utility-based approach under Egalitarianism
Conditions
Equivalent fairness criterion
DS weights (for groups a E (0. 1))
j
W11 W1o # woo woo
Wdy
0
Statistical parity
W11 wio * wpl woo A wdy 1
L
Conditional statistical parity
W11 * Wuz A Wa1 1 a
Y
{1}
Equality of opportunity
W10 f woo A way 1
Y
{0]
False positive rate parity
W11 F wo1 A who * woo A Wdy 1.
y
1
Equalized odds
W11 * Whn A Wiy I a
D
{1}
Predictive parity
wo1 a woo A woy 1
D
{0]
False omission rate parity Sufficiency
W11 # Whu A wol o woo A Wdy La
D 10
350
previous work has shown [27]. Moreover, existing group fairness criteria embed assumptions about
who has equal different moral claims to utility. If we were to, for example, demand equalized odds for credit lending (where D is the bank's ' decision to either approve a loan (D = 1) or reject it
352
353
DD 0), and Y is the loan applicant's ability to repay the loan (Y =Y=1 1) or not (Y = 0)). would
354
make the following assumptions: People who are different in their ability to repay their loans have
355
different claims to utility. We must thus equalize the expected utilities between people who are able
358
to repay their loans and we must also equalize the expected utilities between people who are not able to repay their loans. However, the assumptions listed in Table may not be met for all decision making systems. Our utility- extension is thus necessary to implement other views of justice.
357
358
5
Discussion
As we have seen, existing group fairness criteria are special cases of our -baiid approach. This approach addresses several of the limitations of existing group fairness criteria that we discussed in Section 2
361
362
363
The "leveling down objection" The "leveling down objection" is a prevalent anti-egalitarianism argument [4 saying that less inequality is not desirable if this requires lowering the better-off group's 's welfare to match the one of the worse-off group. On this basis, choosing egalitarianism as the pattern of justice has been criticized in the algorithmic fairness literature (see, c.g., [36 27 54) ). Our approach allows using other patterns of justice, such as maximin, prioritarianism, or sufficientarianism (see Section 3.3). Other patterns that can be formalized mathematical formulas may also be used.
365
367
368
369
One could, for example, combine several patterns into one and require equal expected utilities across groups as long as none of the groups better off than it would be without any fairness requirement. This would represent combination of egalitarianism and group-specific baseline threshold (similar to sufficientarianism)) making a "leveling down" of the better-off group impossible and adhering
370
371
372
373
to the Pareto principle. Therefore, our approach links group fairness to a much larger part of the
374
literature on distributive justice than current group fairness criteria.
375 No consideration of consequences Existing group fairness criteria only consider the distribution of either D or Y. This could be interpreted as analyzing the distribution of utility but assuming that utility is equivalent to either D or Y instead of, for example, the combination of D and Y. Existing group faireess criteria thus represent a very confining definition of utility. Our approach acknowledges that the utility of the decision subjects does not only depend on the decision itself but also on other attributes such as one's 's ability to repay a loan or one's socioeconomic status (see, e.g..
378
377
378
379
380
381
24
54
This is represented through the utility function described in Section 3.1
382
Limited set of fairness definitions Previous attempts to guide stakeholders in choosing appropriate faimess criteria have taken on the form of explicit rules, such as in 45]
383
37 44
Such rules, however,
384
presuppose a limited set of fairness definitions berween which stakeholders can choose. Instead, we provide method to construct ad-hoc fairness criteria that reflect the values decided on by the stakeholders by combining the definition of the utility function for decision subjects (Section (3.] the
386
relevant groups to compare (Section 3.2) and the pattern for just distribution of utility (Section

---

388
Many important questions remain and may be the subject of future research: What are relevant trade- offs when imposing utility-based group fairness criteria requirements? Optimal decision rules for existing group fairness criteria have been derived by 20
389
do they change for the fairness criteria defined by our approach? Further, while our approach creates a link between group fairness
16 9
381
382
and different theories of justice, it does not cover theories of distributive justice that are structurally different from the ones we discussed, e.g., Nozick's entitlement theory [39]. It is unclear how such theories could be represented in formalized fairness criteria, Moreover, there is risk that decision approach to bluewash their decision making system, which they may claim to be "fair" and "unbiased" after coming up with a fairness criterion that neatly fits their own goals. This is issue with other fairness criteria well. Therefore, it is important make the process of defining fairness criteria accessible to the public, so that decision subjects can get involved and
388
394
makers simply
396
398
399
hold decision makers accountable. This raises the question: with utility functions being notoriously
400
hard to define [49 19], how could our approach be accessible enough for practical use? What may
be needed is a process for eliciting values from stakcholders. One may object that this makes group
402
faimness criteria similarly difficult to implement as individual fairness and counterfactual fairness.
403
Our response to this is that existing group fairness criteria might seem easier use, but they still
404
embed values and assumptions about the context in which they are used. Our approach helps to make
405
these assumptions explicit.
10

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407
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Checklist
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1. For all authors...
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes]
556
(b) Did you describe the limitations of your work? [Yes] The limitations are described in
Section [
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(c) Did you discuss any potential negative socictal impacts of your work? [Yes] The potential negative effect of decision makers misusing approach for bluewashing briefly discussed in Section 5 However, it should be noted that this is a potential negative effect of all approaches to measuring fairness.
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(d) Have you read the ethies review guidelines and ensured that your paper conforms to them? [Yes]
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2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Sections B
3
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(b) Did you include complete proof's of all theoretical results? [Yes] See Appendix B
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3. If you ran experiments..
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(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either in the supplemental material or as a URL)? [N/A]
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(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [N/A]
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(c) Did you report error bars (e-g., with respect to the random seed after running experi- ments multiple times)? [N/A]
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(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [N/A]
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4. If you are using existing assets code, data, models) or curating/releasing new assets...
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(a) If your work uses existing assets, did you cite the creators? [N/A]
(b) Did you mention the license of the assets? [N/A]
(c) Did you include any new assets either in the supplemental material or as URL? [N/A]
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(d) Did you discuss whether and how consent was obtained from people whose data you're using/curating? [N/A]
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(c) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
5B6
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5. If you used crowdsourcing or conducted research with human subjects...
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(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
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(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, applicable? [N/A]
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(c) Did you include the estimated hourly wage paid to participants and the total amount spent participant compensation? [N/A]
A Existing group fairness criteria
585
Here, we briefly introduce the most discussed group fairness criteria. Table list the parity require- ments associated with these criteria. Statistical parity demands that the share of positive decisions
14

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597
is equal between socio-demographic groups (defined by the sensitive attribute A = {0, 1)) 18 this is only required for set of so-called legitimate attributes L for the criterion conditional statistical parity [16]. Equality of opportunity, similarly, demands equal shares of positive decisions between deco-deemoga groups, but only for those whose target variable is positive (Y = =) [20]
596
600
thus, it is sometimes also referred to as true positive rate (TPR) parity. Equalized odds sometimes also called separation - requires both equality of opportunity and FPR parity (which is similar to equality of opportunity, however, it is limited to individuals of type Y 0). In contrast, predictive parity demands equal shares individuals of type Y = across socio-demographic groups, but only for those who received positive decision D 1 thus, it is sometimes also referred to as positive predictive value (PPV) parity. Sufficiency requires both PPV parity and false omission rate (FOR)
602
604
608
parity (which is similar to PPV parity, however, it is limited to individuals who received a negative decision = 0).
608
Table 2: Existing group faimess metrics
Fairness criterion
Parity requirement
Statistical parity
P(D =)D==
Conditional statistical parity
Equality of opportunity
False positive rate parity
Equalized odds
P(D= [DD=:\/=,,A=0==0>>\>>>>> 1), for E (0,1)
Predictive parity
False omission rate parity
Sufficiency
P(Y d======A====PV-=- d,A 1). for d E (0.1)
609
B
Mapping existing group fairness criteria to our utility-based approach
610
B.1
Omitted proof's
B.1.1
Proof of Proposition 2
612
Recall that the utility- based fairness following the pattern of egalitarianism requires equal expected utilities between groups:
E(UDS!J = A, = 0) E(UDs|J j j. A= 1)
(B.9)
614
Since there is no claims differentiator (i.e., J = 0). this can be simplified to:
E(UDs A = 0) = EUUDs|A = For Wi1 = W10 and wo1 = Woo, the decision subject utility (see Equation I is:
(B.10)
615
ups,
W0y (Wly - woy) di
(B.11)
616
where Why denotes the decision subject utility associated with a positive decision (D 1) and Way denotes the decision subject utility associated with a negative decision (D 0). Thus, the expected utility for individuals of group a can be written as:
617
618
E(U A a) way + (Wig Way) P(D 1|A =)) a).
(B.12)
619
If the utility weights of all possible outcomes do not depend on the group membership (way. a), and Wiy # wor then the utility- based faimess following the pattern of egalitarianism (see Equation 10
621
requires:
Woy
(Wiy woy) P(D = 1|A = 0) = -Woy + +Wiy - way) P(D = 1|A -A=1)
(Wiy Woy) P(D = 1/4 = 0) (Wig woy)) P(D = 1| 1))
(B.13)
+ P(D = 1|A = 0) = P(D =
=); 1|,
622
where the last line is identical to statistical parity.
'If Why Woy, then the -bied fairness following the pattern of egalitarianism would always be satisfied and the equivalence statistical parity would not hold.
15

---

623
B.1.2
Proof of Corollary 3
624
Recall that the degree to which egalitarianism is fulfilled is defined as F Fegalitariaanimm = |S(Ds
625
J. 0)- EU j.A A 1)] (see Equation 3 If the utility weights of all possible outcomes
do not depend on the group membership (Wa, at) and 20u1 -io + war = who (i.e., wly F way).
627
= 0, this can be written as (see Equations B. and B.12):
F eggalitarianism
(way + (wiy Woyy) P(D 1|A 0))
(way + (Wly - way) P(D =1
=
((Wly Way) P(D 1|A 0)) - ((wiy Woy) P(D 1/4 1))] (B.14)
= (wiy Way) (P(D=
-P(D = [|A=1))
628
where the last line corresponds to a multiplication of |wly - wayl with the degree to which statistical parity is fulfilled.
629
630
B.1.3
Proof of Proposition 4
631
Recall that the utility-basse fairness following the pattern of egalitarianism requires equal expected utilities between groups:
632
= -U
(B.15)
639
Since the claims differentiator is the same as the attribute Y == 1, i.e., J = Y and the only morally relevant value of Y is 1 (i.e., j (1)), ), this can be simplified to:
E(Uns|Y = 1, = = 0) E(UDs|Y = A, 1,, 1
(B.16)
For yi = 1, the decision subject utility (see Equation D is:
635
uDs, wol (w11 - Wo1) d;.
(B.17)
636
Thus, the expected utility for individuals of type Y = 1 in group a can be written E(UDS|Y = 1, A a) = (0o + (w11 Wo1) P(D 1 1 = a).
(B.18)
637
If wi and wor do not depend on the group membership (wai - a), and w1 # wp
then the
638 uuility-based fairness following the pattern of egalitarianism (see Equation B.16 requires:
wo1 + (wn wa1) P(D = 1/Y 1,4 0) Woo + (wi Wo1) P(D = 1111111114
= 1,,4=1
+ (wi win) P(D = 1|Y = 1, 0) (wi - wmm) P(D = 1|Y=1,A=1)
1,
+ P(D = 1|YY 11,4 0) P(D 1|Y = 1,A=11
(B.19)
639
where the last line is identical to equality of opportunity.
B.1.4 Proof of Corollary
Recall that the degree to which egalitarianism is fulfilled is defined as Fegalittaiiaiism = [s
642 j. A = 0)- - [UUDS|J = j, = 1)] (see Equation 3 If wi1 and wor do not depend on the group
membership (wai 1 a), wn1 + wol J Y, and j {1). this can be written as (see Equations B.
644 and B8I:
Pegalitarianism
(wo1 + (w11 wol) P(D 1/ = 1,4 0))
(Wor + (wi) - wol) PPD = 1,A
- 1))1
[(w11 wo1) P(D 11
(B.20)
- ((w11 - woo1) -[D==1I==1A==1])
[ -wo1) (P(D = 1|/Y =1,A= - P(D 1/ = 1,A=
where the last line corresponds to multiplication of |wn Wol with the degree which equality 646 of opportunity is fulfilled.
'If Wn = Wor. then the based faimess following the pattern of egalitarianism would always be satisfied and the equivalence equality of opportunity would not hold.
16

---

647
B.1.5
Proof of Proposition 6
648
Recall that the utility-basee faimess following the pattern of egalitarianism requires equal expected utilities between groups:
649
F [
(B.21)
650
Since the claims differentiator is the same as the decision D = 1, i.e., J = D and the only morally relevant value D is 1 (i.e.,) j = {1}), this can be simplified to:
651
DsUDs| D 1, A 0) E(Uns D 1, A 1)
(B.22)
For d, 1, the decision subject utility (see Equation ! is:
"DS W10 + (Wi1 - W10) Vi-
(B.23)
653 Thus, the expected utility for individuals in group a that are assigned the decision D = 1 can be written as:
D = B
a) = w10 + (w11 - w1o) P(Y = 1 = 1,A= a).
(B.24)
655
If u11 and Wio do not depend on the group membership (Wiy 1 a). and w1 * Wid muility-based fairness following the pattern of egalitarianism (see Equation B.22 requires:
then the
w10 + (wi1 - w1o) P(Y = 1|D = 1,4 = 0) = W10 + (w11 - w1o) P(Y = 11= 10==111111
+ (wi1 who) P(Y 1 1,A 0) (wi1 W1u) -0.-P((Y-- 1,
+ P(Y = 1|D = A1, = 0) -P(Y = = 1,
(B.25)
657
where the last line is identical to predictive parity.
658
B. Proof of Corollary 7
Recall that the degree to which egalitarianism is fulfilled is defined as F Fegulitariaanimm = |s J =
j. A = 0)- [s = j, = 1)] (see Equation 3. If W11 and wio do not depend on the group
660
membership (wly 1 a). W11 # w10. D, and {1}. this can be written as (see Equations B.22
662
and B B.24):
F eggalitarianism
(W10 + (W11 w1o) P(Y = = 1,A= 0))
[(w1 w16) P(Y = PPD==DD=-- 1| = 1))
(Wi0 + (wi1 - w10) P(Y =
(B.26)
((w11 - ((1) PPYY = [1]0==11=,,A1]]]] 1))
[w11 -W11) - 1 - P(Y 1|D 1, 1))
where the last line corresponds multiplication of |t11 w1ol with the degree which predictive parity is fulfilled.
684
685
B.2
Mapping to other group fairness criteria
In Section we mapped our utility- -baed approach to the three group fairness criteria statistical parity, equality of opportunity, and predictive parity. Here, we additionally show under which conditions our utility-based approach is equivalent to other group faimesss criteria: conditional statistical parity, false positive rate parity, equalized odds, false omission rate parity, and sufficiency.
667
669
B.2.1
Conditional statistical parity
Conditional statistical parity is defined as P(D 1 P
-,A 11==
1).
672
where L is what [16] refer to as the legitimate attributes. Thus, conditional statistical parity requires equality of acceptance rates across all subgroups in A 0 and A 1 who are equal in their value / 674 for L, where can be any (combination of) feature(s) besides D and A.
'If Wn = Wio. then the uullty-based faimess following the pattern of egalitarianism would always be satisfied and the equivalence predictive parity would not hold.
17

---

675
Proposition& 8 (Conditional statistical parity utility-basse based fairness). If the utility weights of all possible outcomes do not depend on the group membership (Way a), and w11 who wol = woo- then the egalitarian pattern fairness condition with J = I. is equivalent to conditional statistical parity.
678
677
678
The proof of Proposition g is similar to the one of Proposition 2
679
Under these conditions, the degree to which Fcgalittariaiimm is fulfilled is equivalent to the degree to which conditional statistical parity is fulfilled, multiplied by |Wig Woyl This could easily be proved similar to the proof of Corollary but with the conditions of the utility-based fairness stated in Proposition g
681
683
B.2.2
False positive rate (FPR) parity
FPR parity (also called predictive equality (16) is defined as P(D 1|Y 0, -- 0) P(D 1| 0, A = 1). i.e. it requires parity of false positive rates (FPR) across groups a E A.
686
Proposition 9 (FPR parity as utility-based fairness). If w1o and who do not depend on the group 688
membership (w 1 a), and wio # Woo. then the egalitarian pattern fairness condition with -= Y
and {0} is equivalent to FPR parity.
For y/ 0, the decision subject utility (see Equation D is:
680
"Ds Woo + (W10 - wooo dz.
(B.27)
691
Thus, the expected utility for individuals of type = 0 in group a can be written as:
E(UDs|Y = 0, A = a) = wpp + (W10- woo) P(D = 1|Y = 4-
(B.28)
692
Hence, we simply require the utility weights wio and woo to be unequal and independent of a. Then, the proof of Proposition is similar the one of Proposition
693
694
woo and who do not depend on the group membership (wis 1 a). and Wio * wgo, then the degree
to which Fegalitarianiam is fulfilled is equivalent to the degree to which FPR parity is fulfilled, multiplied
696
by W1o Woo This could easily be proved - similar to the proof of Corollary 5
687
B.2.3 Equalized odds
Equalized odds (sometimes also referred to separation 77) is defined as P(D = 1|Y = y, A 0) P(D = 1|Y = y, A 1), for y E {0, 1}.
689
Proposition 10 (Equalized odds as qullty-based fairness). If the utility weights of all possible outcomes do not depend on the group membership (Way 1 a), w11 * Wo1, and w'10 j Woo- then the egalitarian pattern fairness condition with J = Y and j {0, 1} is equivalent to equalized odds.
701
703
The conditions under which the utility- based fairness criteria is equivalent is shown separately for equality of opportunity (see Proposition 4) and FPR parity (see Proposition 99. Since equalized odds requires equality of opportunity and FPR parity, the the conditions for both fairness criteria must be met (i.e., Wdy 1 a), w11 * Wo1. who * won. J = Y, and {0, 1 1}), so that the utility-based fairness constraint is equivalent to equalized odds.
704
705
707
708
B.2.4
False omission rate (FOR) parity
709
= 0) = P(Y = 1D = 0, = =1), i.c. it requires FOR parity is defined as P(Y 1/D = A-
710
parity of false omission rates (FOR) across groups a E A.
711
Proposition 11 (FOR parity as utility-based faimess). If wo1 and woo do not depend on the group membership (Woy a), and Wt1 A wno. then the egalitarian pattern fairness condition with J = D, and
712
713
(0) is equivalent to FOR parity.
714
For d, 0, the decision subject utility (see Equation D is:
ups, w00 + (wo1 - woo) yi-
(B.29)
715
Thus, the expected utility for individuals in group a that are assigned the decision D -0 can be written as:
716
E(UDs) D= = A a) woo + (wo1 woo) P(Y 1|D 0, a).
(B.30)
18

---

717 Hence, we simply require the utility weights wol and Woo to be unequal and independent of a. Then, the proof of Proposition is similar to the one of Proposition 6
718
719
won and woo do not depend on the group membership (Wny 1 a), and Wol * woo. then the degree
which Pegalitarianism is fulfilled equivalent the degree which FoR parity is fulfilled, multiplied by |Woo- Woo This could easily be proved similar to the proof of Corollary
B.2.5 Sufficieney
723
Sufficiency is defined P(Y 1|D - d, P(Y 1D- d, d,
d {0, 77.
Proposition 12 (Sufficiency
tulity-bbsedd fairness). If the utility weights of all possible outcomes do not depend on the group membership (Way 1 a), W11 + w1o, and wo1 # woo. then the egalitarian pattern fairness condition with J D and (0, 1} is equivalent sufficiency.
725
727
The conditions under which the utility- based fairness criteria is equivalent is shown separately for predictive parity (see Proposition O and FOR parity (see Proposition TTp. Since sufficiency requires predictive parity and FOR parity, the the conditions for both fairness criteria must be met (i.e.,
729
730
Way a), Wi * wio. Wi1 woo. J = D, and {0, 1}), so that the utility-based fairness constraint is equivalent to sufficiency.
731
19


Reviews:
[{"review_id": "v8myW6SRewt", "reviewer": "Reviewer_aeFZ", "summary": "The authors propose a unifying framework for group fairness metrics which exposes different issues and justice patterns as choices in a mathematical equation. The key idea is to use explicitly the notion of utility (and expectation of it) in the definitions of fairness. By doing this they show that not only it is possible to represent all the most important fairness metrics in their formulation, but it is possible to construct new, more complex forms of fairness which address common criticisms of fairness criteria.", "questions": "Are there fairness formalisms and practical methods which are not covered by the unifying framework? Which are those? Why?  ", "limitations": "The authors should be more clear whether there are fairness formalisms which are not representable in their framework and why.", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\nThe article aims to be formal, mathematical, and precise. Within this goal, it works well, and reads as easily as it would be expected in this context. The authors make a good job of pointing to other articles (included in the additional material) which have a deeper philosophical perspective and are, to some extent, easier for a less technical audience to read.\n\nWeaknesses:\n\nIt would be really good to have the authors' view of what the drawbacks of their definition are. Often, unifying frameworks leave out some methods used in practice, and it would be great to have the authors' own view about what they have left behind. If nothing is left outside their framework, the authors' should clearly state that claim.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "XGkGgxBnTEE", "reviewer": "Reviewer_Votd", "summary": "The paper presents a general framework for understanding group fairness metrics that is connected to relevant literature in philosophy underpinning the relevant values and moral perspectives. Specifically, the paper proposes to interpret group fairness as the “just distribution of utility among relevant groups”, as opposed to simply “equality (of decisions) between socio-demographic groups”. This highlights the several components of the proposed approach:\n- utility (as opposed to decisions)\n- some notion of justice (as opposed to necessarily equality)\n- comparing relevant groups (as opposed to simply demographic groups)\n\nIn slightly more detail: The starting point of the proposed approach is to focus on the utility of the individuals (here referred to as decision subjects) and to introduce the concept of a “claims differentiator” J, which identifies individuals with equal claims utility for the sake of the evaluation. Technically,  this is a binary variable where now fairness means comparing the expected utilities of individuals with the same J=j but different group membership A=a. There is then the question of how to compare these quantities - here comes the component of “pattern of justice”. The paper considers several such patterns studied in the philosophical literature and studies their implications in terms of the implied fairness metrics. For example, “egalitarianism” would seek to equalize the above-mentioned quantities, but other principles (Maximin, Prioritarianism) could require different things. \n", "questions": "Minor points: \n- The notation U_{DS,i} seems overly complex, why not simply use u_i?\n- I couldn’t follow some of the choices for the degree to which fairness is fulfilled. For example in Maximin section, the choice of (5) seemed a bit weird - in particular, wouldn’t it be non-zero even if fairness is met? I would expect something like the difference in the terms in Eq (4).\n- Technically I think it would be helpful to clarify some of the mathematical notation. For example the notion of independence is used throughout for what I understand are realizations (e.g. w_dy independent of a in Table 1), and I’m not sure this is well-defined.\n", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths: The paper is generally clearly written, and bridging the gap between philosophical ideas and fair ML is an important objective.\n\nWeaknesses: The main weakness of the paper in my opinion is that the main contributions of the paper are w.r.t the authors’ portrayal of the notion of group fairness (“equality (of decisions) between socio-demographic groups”), which I’m not sure is a actually fair w.r.t the *current* state of the literature. Specifically:\n\n1. Confusion between group fairness as a metric and group fairness as an objective: Even with the narrow interpretation of equality of outcomes (or some other statistic that depends on the outcomes), an  important distinction in the literature is between group fairness as a metric and group fairness as an objective. I (and I believe many of my colleagues) view group notions of fairness as an important red flag, that if not satisfied, suggests one should look into the entire algorithmic pipeline for issues - be it the problem specification, the data collection, etc. In particular this means that the “solution” may be something like collecting better data, which does not require making any group’s welfare worse off. \n2. A narrow interpretation of group fairness: There are many more notions of fairness studied in the literature that (i) utility based, (ii) that take preferences into account, or (iii) that speak to notions of fairness that do not necessarily involve parity (such as making sure no groups is “worse off” than what it would be had there been no other groups).  None of them were mentioned in the paper, and I found the perspective that the proposed unifying view is novel to be hindered by this. \n\n\nAnother weakness is that while the approach sets out to expose the normative and moral assumptions under-pinning group fairness, there is a bit of a “pick and choose” nature to this, as some assumptions which I think are not inherent (and encode some moral assumptions) are taken for granted and not discussed. For example, it is stated that since we are interested in systematic differences between groups, fairness only means we are “interested in the expectation value E(U_DS) of the individual utility”. Isn’t this also an assumption? Two groups may very well be systematically different even if their expectations are similar (but their variance, for example, is not). Does this not come up in the philosophical literature? \t", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "OqvGvpOuxEB", "reviewer": "Reviewer_cmCu", "summary": "This paper proposes a general framework for evaluating the fairness of a decision-making system, based on concepts from theories of distributive justice. The authors first point out the limitations and shortcomings of the current fairness metrics used in the literature, namely “the levelling down objection”, “non-consideration of consequences”, and a limited set of fairness definitions in the literature of fairness in AI. The framework they propose is based on utility values for individuals based on different combinations of decision D and the variable Y. They show that most popular fairness metrics present in the literature can be interpreted as special cases of their proposed frameworks.  ", "questions": "Have the authors consider provide experimental comparison of the proposed metrics and the existing metrics? ", "limitations": "The paper lacks empirical evidence for their claims. While discussing downsides of current metrics, providing specific cases for which their claims might hold true would strengthen their claims. \nSimilarly, in addition to the theoretical and qualitative approach of their framework, providing empirical evidence for why and when their framework can be helpful in quantifying its effectiveness. \n", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Originality: This paper brings an interesting and fresh perspective to the discussion of fairness concept in AI field. I lack the understanding of ethics studies from the philosophical field that is discussed in this paper.  Therefore, I cannot comment on the originality of the ideas from that perspective. However, I believe that this paper would bring in an original enough perspective to the AI community working on fairness and ethical AI topics and would contribute to and enrich the discussions. \n\nQuality: The submission is technically sound. The claims appear to be theoretically supported but lacks the empirical evidence.  \n\nClarity: The paper is well written and organized. \n\nSignificance: This paper addresses an important issue, since most fairness metrics currently under consideration in the fairness literature suffer from levelling down objections. \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Reject