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From “appropriate” means to desired aims

On instrumental justification in discrimination cases
Alejo Joaquín Giles
This article is a translation of:
De medios “adecuados” a fines anhelados []

Abstract

Legal rules prohibiting discrimination often make this mandate subject to the condition that the difference of treatment in question is not considered justified. Typically, a difference of treatment must be considered justified if, among other factors, it pursues a legitimate aim and is an “appropriate” means to achieve it. But what does “appropriate” mean in such a context? My answer in this article develops over three steps. The first step is to elucidate the vague requirement of “appropriateness” as a given causal contribution. The second step is to reconstruct the content assigned to the notion of causal contribution by two conceptions of causality: the regularistic and the probabilistic. The third step is to argue for an understanding of the requirement of “appropriateness” as a probabilistic causal contribution. After establishing these grounds, I turn to the regulatory opportunities that the choice in the third step opens regarding the strategy, common in anti-discrimination law, of requiring a more robust justification for certain kinds of cases. As I will show, the gradual character of the notion of probabilistic causal contribution allows for the formulation of different levels of “appropriateness” that are sufficient for justificatory purposes. In relation to the non-basic levels, a dilemma may arise.

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1 Introduction

  • 1 See Giles 2023 for a more detailed analysis of the elements of the generic concept of discriminat (...)
  • 2 This is a weak permission (a non-prohibition): if the conduct were considered justified, there wo (...)

1Legal rules prohibiting discrimination often make this mandate subject to the condition that the difference of treatment in question is not considered justified according to its proportionality.1 Typically, a difference of treatment must be considered justified if, among other factors, it pursues a legitimate aim and is an “appropriate” means to achieve it. In addition, some provisions state that to be considered justified, the inequality must also be the most efficient means of achieving its aim and must be proportionate (stricto sensu) to it. If a difference of treatment satisfies these conditions, and even if it harms a protected group, it is legally permitted.2

2European and Inter-American supranational anti-discrimination law provide remarkable examples of what has just been characterised. Starting in Europe, let us consider the interpretation of Article 14 (“Prohibition of discrimination”) of the European Convention on Human Rights. In interpreting this provision, the European Court of Human Rights (ECtHR) has repeatedly held that a distinction qualifies as discriminatory if, among other conditions, it “has no objective and reasonable justification”. The Court has also made it clear that:

  • 3 ECtHR, “Belgian Linguistic case”, 1968, p. 34, §10. The ECtHR has reiterated this interpretation (...)

The existence of such a justification must be assessed in relation to the aim and effects of the measure under consideration […]. A difference of treatment in the exercise of a right laid down in the Convention must not only pursue a legitimate aim: Article 14 (art. 14) is likewise violated when it is clearly established that there is no reasonable relationship of proportionality between the means employed and the aim sought to be realised.3

  • 4 As in the following European Directives: 2000/43/EC (2.2.b; 4); 2000/78/EC (2.2.b.i; 4.1); 2004/1 (...)
  • 5 As in “Bilka-Kaufhaus”, 1986, §37; “Johnston v Chief Constable of the Royal Ulster Constabulary”, (...)
  • 6 The UK’s Equality Act (2010) is a clear example. The only cases of direct discrimination that all (...)

3The same idea is found in many provisions of European law4 and interpretations of the Court of Justice of the European Union (CJEU).5 However, for some types of cases, some sources omit this requirement and prohibit unfavourable differences of treatment based on certain grounds, regardless the reason(s) that could be invoked to justify them.6

  • 7 See “Schuler-Zgraggen v. Switzerland”, 1993, §67; “Abdulaziz, Cabales and Balkandali v. The Unite (...)
  • 8 See “Karner v. Austria”, 2003, §37; “Vallianatos and Others v. Greece”, 2013, §77, and citations.
  • 9 See “Karner v. Austria”, 2003, §41, “Vallianatos and Others v. Greece”, 2013, §85, and citations; (...)

4Furthermore, the ECtHR has established a stricter level of scrutiny for differences of treatment based on certain grounds, such as sex7 and sexual orientation:8 they require “very weighty” reasons to justify them. With regard to the relationship between means and ends, the measure adopted must be more than merely “appropriate” to achieve the aim pursued; it must be “necessary” to that goal.9 The following extract from a decision of the Grand Chamber of the ECtHR illustrates this point:

  • 10 ECtHR, “Vallianatos and Others v. Greece”, 2013, §85.

In cases in which the margin of appreciation afforded to States is narrow, as is the position where there is a difference in treatment based on sex or sexual orientation, the principle of proportionality does not merely require the measure chosen to be suitable in principle for achievement of the aim sought. It must also be shown that it was necessary, in order to achieve that aim, to exclude certain categories of people […] from the scope of application of the provisions in issue.10

  • 11 See 2000/43/EC (2.2.b); 2000/78/EC (2.2.b.i; 6.1); 2004/113/EC (2.b); 2006/54/EC (2.1.b).
  • 12 See CJEU, “Johnston v Chief Constable of the Royal Ulster Constabulary”, 1986, §38.

5The European anti-discrimination directives11 and the case law of their main interpreter, the CJEU,12 seem to require this combination of “appropriateness” and “necessity” in all cases.

  • 13 Generally, see OC-4/84, §56; OC-17/02, §46-48; “Espinoza Gonzáles vs. Perú”, 2014, §219; “Flor Fr (...)

6On the other side of the Atlantic ocean, the Inter-American Court of Human Rights (CorteIDH) has generally adopted a similar approach.13 The Court seems to agree with the ECtHR in interpreting that, with regard to differences of treatment based on the grounds protected by Article 1(1) of the American Convention on Human Rights, the evaluation of their justification must be guided by “a strict scrutiny that incorporates particularly demanding elements into the analysis”. While the aim pursued must be imperative, the means chosen

  • 14 CorteIDH, “Pavez Pavez vs. Chile”, 2022, §69. The Court had already expressed the same idea in “G (...)

must not only be appropriate and effective, but also necessary, that is, it must not be substitutable by a less harmful alternative. In addition, it involves the application of a strict proportionality test, according to which the benefits of adopting the measure in question must clearly outweigh the restrictions it imposes on the conventional principles it affects.14

  • 15 As the CorteIDH states in the extract just quoted.
  • 16 See CJEU, “‘CHEZ Razpredelenie Bulgaria AD’ v. Komisia za zashtita ot diskriminatsia”, Grand Cham (...)
  • 17 This seems to be the common understanding of the term in the literature on proportionality. Two n (...)

7In this framework, the requirement that the contested factor be “necessary” to achieve a particular goal is often understood to mean that it must be the least harmful15 or least restrictive16 of the possible means.17

  • 18 On the concept of effectiveness, understood as “to lead to” given results, see Fernández Blanco 2 (...)
  • 19 According to Barak (2012: 305, 320), what distinguishes the necessity and appropriateness criteri (...)
  • 20 Similar arguments can be found in CJEU, “Reinhard Prigge v. Lufthansa”, 2011, §64. This judgment (...)

8Summarising somewhat superficially, we could say that the “appropriateness” of a means refers to its effectiveness18 and the “necessity” to a certain efficiency.19 A difference of treatment may be “appropriate” to achieve an aim but not “necessary” because there are other, less harmful means. For example, it may be “appropriate” to require workers in an organisation to retire at 60 to guarantee the quality of the service for which they are responsible, if this depends on skills that decline over time. However, if the relevant skills are not lost until the age of 65, the retirement five years earlier would be “unnecessary”. There would be a less harmful means of achieving the purpose of this unequal treatment: to provide for retirement at age 65 rather than earlier.20

  • 21 What I will say does not apply to discrimination cases mentioned in a previous footnote where (...)
  • 22 Or “suitable”, “proper”, “adequate”, and other terms used as synonyms.
  • 23 See CJEU, “CJ v. TGSS”, 2022, §48, and citations.

9In what follows, I will elucidate the requirement (or basic element) of “appropriateness” for discrimination cases involving general rules or practices, focusing on legal provisions with the characteristics just described.21 What does the requirement that the relationship between a means and its end must be “appropriate”22 mean? Following a CJEU definition, it could be that the means in question must “genuinely reflect a concern to attain” the objective pursued.23 But under what conditions can we say that this is the case?

10My main objective will be to elucidate the problematic “appropriateness” requirement with the help of contributions from the philosophy of science. As a starting point, I will understand the requirement of “appropriateness” as a certain causal contribution (§2). I will then reconstruct the content that two conceptions of causality – the regularistic (§3) and the probabilistic (§5) – assign to that idea. Both provide a basis for formulating two different models of instrumental justification. Because it fits better with some theses about what should be required to justify general rules or practices, as well as what is actually required by courts for this effect, I will argue (§4 and §6) that the idea of probabilistic causal contribution is best suited to elucidating what the “appropriateness” required for justificatory purposes means.

11Finally, I will also explore some of the regulatory opportunities that arise from my proposed understanding of the “appropriateness” requirement (§7). In particular, I will consider the opportunities that arise for the strategy, common in anti-discrimination law, of requiring more robust justification (“very weighty” reasons) for certain kinds of cases by introducing different levels of the justification requirement. As I will show, the gradual character of the notion of probabilistic causal contribution allows for, among other uses, the formulation of different levels of “appropriateness” that are sufficient for justification purposes. At the high (or non-basic) levels, as I will emphasise, there is a potential dilemma between choosing a fixed threshold of sufficiency and delegating this assessment to interpreters.

  • 24 The relevance of factual statements in constitutional argumentation, a phenomenon that emerges in (...)
  • 25 I will explain these limits in the final paragraphs of §2.
  • 26 See pp. 3, 23-26, 32-35, 58-60. Carter’s distinction between “judicial facts” and “legislative fa (...)

12Insofar as justification in cases of discrimination is understood as it usually is as a special case of the proportionality test, which is applied in assessing the limitations of fundamental rights, what I will say about the requirement of “appropriateness” for the species also applies to the respective element of its genus. What follows could therefore also be read as a contribution to the study and characterisation of the (mostly neglected) factual side of the proportionality test.24 In Proportionality and Facts in Constitutional Adjudication (2021), A. Carter has recently addressed this issue and made a remarkable contribution. The argument I will present in this article is narrower, limited to the element of “appropriateness” and to a particular class of instrumental relations.25 However, this limitation has the advantage of allowing for a more detailed approach than in the above-mentioned work, where the elements of “appropriateness” and “necessity” are defined in causal terms (such as “lead to”, “contribute to”, “be able to achieve”, etc.), but without specifying what kind of causal contributions they refer to.26

13Let’s start with the detailed itinerary.

2 “Appropriateness” and instrumental justification

14The requirement that a means be “appropriate” to an end is as we shall understand it synonymous with the requirement that the two factors be instrumentally related. The property of instrumentality is usually ascribed to a thing according to its aptitude for achieving something else. This predicate can refer to a variety of entities, three of which are of particular interest to us. Someone is said to be instrumentally rational if he or she uses means that contribute to achieving what he or she wants to achieve. An argument is said to be instrumentally rational if its conclusion is an assertion about how to act and its premises establish a certain relationship between that action and an intended state of affairs. Finally, an action or a rule of conduct is said to be instrumentally justified if it contributes to the achievement of a certain goal (for the achievement of which there are sufficient reasons).

  • 27 I will deal here exclusively with means-ends relationships of an empirical nature. But these are (...)

15In general, instrumental reasoning is understood to be composed of statements that refer to at least three elements: a state of affairs to be achieved, the end (or aim or goal) (E); an action directed towards it, the means (M); and a relationship between the means and its end.27 If we take the basic schema of such an argument and slightly modify the conclusion, we get the basic schema of instrumental justification with which we shall work. It is as follows:

(a) It is intended to bring about a state of affairs, E.

(b) Action M is appropriate to bring about E.

Therefore:

(c) Performing action M is instrumentally justified.

  • 28 “To bring about a state of affairs” or “to perform an act” is understood here as producing an “ev (...)

16“E” denotes a generic state of affairs and “M” a generic action. Premise (a) describes − or ascribes − an end (or aim or goal), whose content is the realisation of a state of affairs. Premise (b) describes the performance of an action as an “appropriate” means to achieve what is intended. “To act” is understood here as producing a change from one (initial) state of affairs to another (final) state of affairs.28 Statement (c), the conclusion of the argument, is to be read as a particular rule derived from statements (a) and (b) in conjunction with an implicit normative premise, according to which any action that is “appropriate” to bring about the content of a legitimate aim must be considered instrumentally justified. As we saw at the beginning, this premise often finds support in jurisprudential discourse and in legal provisions.

  • 29 In its full version, the schema looks like this:

17As presented, the argument is enthymematic. It lacks some premises from which the conclusion would follow deductively. I omit them for simplicity and to highlight only what we will deal with here.29 The notation used could be more detailed, but it is sufficient for our objective.

18I will focus here on premise (b). What does it mean to require a relation of “appropriateness” between a means and its end? I will answer this question with two successive premises. I will state the first immediately and then only sketch the second, which will be elaborated in the following sections.

19First premise: in the present discursive context, to require a relation of “appropriateness” between a means and its end is to require that the means makes a causal contribution to bringing about the end.

20When two events always occur together, or occur together with some frequency, they are said to be correlated or associated. For example, “Most top footballers own luxury watches” is a clear example of a statement involving correlations. If this were true, and we were bored with our jobs and wanted to move up to the top leagues of football, would it be a good strategy to invest our life savings into the purchase of one of these accessories? Definitely not. If we really wanted to be a top footballer, we should think about the conditions that, in addition to those merely associated with being an elite footballer, explain why people become elite footballers; the conditions that, if present, would lead or contribute to achieving that goal. Amongst so many other factors, one could think of constant and intense training and the possession of some innate talent. A lot of training and talent, but not a luxury watch, would contribute to the realisation of our dream. These are what we would call the causes, or some of the causes, of such a projection.

  • 30 For the causal language, see Hitchcock 2003: 2-3.
  • 31 Similarly, von Wright (1963b) has pointed out that one of the premises of the argument he calls “ (...)

21Well, when we talk about the “appropriate” means to achieve something, we are generally talking about factors such as training or talent, not watches, in relation to being an elite footballer. In general, we mean that the means, if used, would in some way lead to (or contribute to) the end, and that if the means had been used, the contribution would have been made. In short, we are saying that the two factors are not just correlated, but causally related. This is the kind of relationship that is expressed in the language of causality by terms such as “lead to”, “contribute to”, “help to”, “bring about”, “produce” and, above all, “cause”.30 It is also what seems to be required for an action to be considered instrumentally justified: not only that it merely coincides with the achievement of a legitimate end, but that it contributes to it.31

  • 32 With regard to the proportionality test, this view is expressed, for example, in Bernal Pulido 20 (...)
  • 33 For present purposes, we are leaving aside the meaning of “appropriate” that is sometimes used in (...)

22On this basis, it seems plausible to understand the required “appropriateness” of a means to an end as follows: a means is “appropriate” to an end if it makes a causal contribution to the end.32 Thus, to say that “Action M is appropriate to bring about E” is equivalent to saying that “Action M makes certain causal contribution to bring about E”.33

  • 34 In the sense of Tarski 1994: 110.

23To organise ideas, I will hereafter speak of two events as being linked by a causal relationship when one of them makes a causal contribution to the occurrence of the other. Thus, in the following discourse, this last concept will fulfil the function of a basic or primitive concept.34 As can be seen, the approach still leaves open the definition of how the aforementioned contribution is to be characterised: exactly how two factors must be related in order to be considered causally related. This leads to premise number two.

24Second premise: depending on the underlying conception of causality, different relations of causal contribution of one event to another can be characterised; this provides a basis for formulating correlative models of instrumental justification.

25If the translation just suggested is accepted, the task of clarification can be continued by moving into the realm of philosophy of science and stopping at studies of causal relations. I will now take up some of these contributions to place them in the arena of instrumental justification for the purpose already explained. In particular, I will present a reconstruction of two conceptions of causality, which applied to our focus of interest, give content to the idea of causal contribution and at the same time provide a basis for the formulation of two models of instrumental justification, a regularistic one (§3) and a probabilistic one (§5), depending on whether we are dealing with a universal or a frequentist means-ends relationship, respectively.

26Before proceeding, it is worth making some clarifications and pointing out some limitations of the proposed project. First, I will speak of “conceptions” − also “approaches” or “standpoints” − of causality in a very broad sense, to refer to discourses that attempt to explain causal contributions between events. Among their variants, I will not distinguish between conceptual (which try to define causal contributions) or epistemological (which investigate what we can know about these relations) approaches and those that make more ambitious ontological claims (which try to figure out what causality means in objects). For the purposes of this paper, conceptual approximations will suffice. Their conclusions are independent of how the dispute about the ontology of causality is resolved.

  • 35 As, for example, in Cartwright 2004: §6 and Hitchcock 2003: 1, 21-22.

27Second, I want to emphasise that the fact that I present only two approaches to causality does not mean I claim they are the only admissible approaches, or that only one of them is correct in relation to the others. Rather, I see them as two discourses explaining different systems of causal relations to which they are bound in their domain. One might say, then, that I take a pluralist view of the issue.35 In the context of discrimination cases, the system of causal relations relevant for assessing the justification of a difference of treatment − an elementary piece of information for choosing the most appropriate model to explain it − depends on something that cannot be defined a priori: the nature of the events to be linked. This in turn depends on how the goals are specified and the means chosen to achieve them. These factors may relate to a biological phenomenon (e.g., the relationship between increasing age and the loss of certain abilities), to a social phenomenon (e.g., the relationship between the rate of migration and the rate of unemployment in a particular place), and so on. Here, I will deal with a certain class of causal relations between events, those that are dealt with by the theses and cases I will mention in time (§4). My conclusions will be limited to these theses and cases.

  • 36 This is emphasised, for example, by Cartwright 2004: §6 and Frosini 2006: 313. This choice leaves (...)
  • 37 For the merits of adapting one model or the other, see the counterpoint between the position pres (...)
  • 38 E. Eells addresses this problem in Eells 1991: 6.

28Third, and finally, I will consider relations between events that are generic cases or types of cases, such as those associated with the claim “smoking causes lung cancer”. This is important because the question of which causal approaches are more suitable for explaining particular relationships depends, among other things, on the generic or specific character of those relationships.36 The reason for the restriction to generic cases is that my main interest here is the justification of legal rules and general practices. One of the consequences of this limitation is that the discourse presented here will be useful for generalist decision-making methods. That is, for methods that, in assessing the justification of a behaviour, seek its justification in general, and not for its application to a particular case taking into account all the properties present in that case.37 Particularistic decision-making methods would need to be complemented by reflections on the gap between the levels of general causality and specific causality.38 With that, let us now move on to the detailed plan.

3 Regularistic instrumental justification

29I will call regularistic instrumental justification any argument according to which performing an action is instrumentally justified because it is a universal or regular “condition” for achieving a legitimate end. In this model, premise (b) of the basic schema is modified as follows: “Action M is a universal or regular condition for bringing about E”.

30The elusive idea of causal relation or causal contribution is a source of seemingly never-ending debate in the philosophy of science. One influential approach proposes understanding it through the notion of condition, that is, as a regular conditional relationship between two events: the condition (C) and its effect or consequence (E). This approach is based on a solid conceptual framework that includes a typology of conditions. I will take part of this typology here from the work of G. H. von Wright.

31As a general feature, the relations we are talking about are regular or universal, which means that they occur always, invariably, and not only with some frequency. If eating (C) is a regular condition for appetite satisfaction (E), then this effect always occurs when you eat.

  • 39 Below, I follow von Wright 1971: 38-41, 2001: 66-77.
  • 40 Cf. von Wright 2001: 66-67. In the following, symbols expressing conditional (→) and biconditiona (...)

32Von Wright begins with the well-known distinction between two basic types of conditions, “necessary” and “sufficient”;39 each characterised by a different role in producing an event. He defines them as follows:40

33(1) To say that C is a sufficient condition for E is to say that if C occurs, E will also occur. The presence of C is sufficient to ensure that E occurs. (Although E could occur even without C.) In this sense, we say that eating a home-made pizza (C) is a (sufficient) condition for appetite satisfaction (E), even if the same thing can be achieved in another way (e.g., by eating another food). The logical form of this kind of condition can be expressed as follows:

C → E (sufficient condition)

34(2) On the other hand, to say that C is a necessary condition for E is to say that if E occurs, C will also occur. The occurrence of E requires the occurrence of C. (Although C could occur without E.) In this sense we say that heating the oven (C) is a (necessary) condition for cooking the home-made pizza (E), regardless of the fact that other conditions (such as preparing the dough, putting the pizza in the oven, etc.) must also occur for the latter to occur. The logical form of this kind of condition can be expressed as follows:

  • 41 This relationship can be expressed, perhaps more intuitively for the study of causal relationship (...)

E → C (necessary condition)41

35(3) Combining the concepts, to say that C is a necessary and sufficient condition for E, means that if and only if C is given, then E is also given. In this sense we say that the absorption of water into the body (C) is a (necessary and sufficient) condition for hydration (E), because only in this way is this effect achieved. The logical form of this kind of condition can be expressed as follows:

C ↔ E (necessary and sufficient condition)

  • 42 Cf. von Wright 1971: 38-39, 2001: 70-71.

36Based on this typology, further conditional relations are defined to cover various cases of plurality of conditions where an event has more than one necessary or sufficient condition. Let us consider some of them:42

  • 43 Its logical form is as follows: (C1 · C2) → E.
  • 44 Its logical form is as follows: (C1 ∨ C2) → E.
  • 45 Its logical form is as follows: E → (C1 · C2).
  • 46 Its logical form is as follows: E → (C1 ∨ C2 ).

37(4) For simplicity, let us take only two conditions, C1 and C2. They are said to be jointly sufficient for E if E occurs whenever they occur together. Individually, they do not guarantee the occurrence of E, but together they do.43 They are said to be disjunctively sufficient with respect to E if whenever at least one of them occurs, E also occurs. Each by itself is sufficient to produce E.44 On the other hand, they are said to be jointly necessary together for E if, whenever E occurs, both also occur together. Each by itself is necessary to produce E.45 They are said to be disjunctively necessary with respect to E if, whenever E occurs, at least one of them occurs. The occurrence of E does not require that one of them in particular occurs, but that at least one of them occurs.46

38Von Wright calls the disjunction of all sufficient conditions for E within a set of logically independent properties a “total sufficient condition”; and the conjunction of all necessary conditions for E within a set of logically independent properties is called a “total necessary condition”. From this (relative) perspective, one can see how many sufficient conditions a given event E has, how many its necessary conditions there are, and what form each of them takes.

  • 47 The application of this model in discrimination cases will be illustrated by an example in sectio (...)

39In short, a regularistic model of instrumental justification links means and ends through regular or universal conditional relations, such as those just characterised.47

4 Limits of the regularistic model

40The scope of the regularistic model of justification is, nevertheless, limited. Broadly speaking, it expresses the pattern of reasoning when it is required for the justification of certain actions that always lead to the realisation of their aims. However, in discrimination cases (and beyond) something else seems to be generally required, which this model does not capture.

41As I will show below, there are important theses that hold that what matters in assessing the justification of general rules is not a regular or universal instrumental relation, but one of a frequentist character. These theses are in line with what courts actually require in many cases. Even if this is not or should not be required in all cases (admitting this would not undermine my main argument), it invites us to think about more suitable models of justification to account for such requirements when they apply.

  • 48 This imperfect character is commonplace among those who study the phenomenon of legislation, some (...)

42(1) The first thesis I would like to emphasise deals, in a broad sense, with decision-making based on rules or general criteria. Its starting point is the systematic fallibility of this activity: the fact that such a process usually covers cases that should not be covered according to the reasons for adopting the rules that guide the decisions. It is a more or less imperfect mechanism.48

  • 49 Behind this assertion lies an assumption that is worth revealing, according to which legislators (...)
  • 50 Cf. Schauer 1991: 25-31.
  • 51 Cf. Schauer 1991: 31-34. Tussman & tenBroek (1948: 347-353) already considered these alternatives (...)
  • 52 Cf. Schauer 1991: 27, 29, 31.
  • 53 Cf. Schauer 2003: 117. Notwithstanding this point, it is important to note that when the challeng (...)

43It is precisely this feature that led Schauer to propose that the content of general rules be understood as empirical generalisations of a probabilistic nature. If the possession of such-and-such properties is chosen as the antecedent of a rule, he claims, it is because it is causally relevant to the achievement of a particular goal.49 And, such a relation is not regularistic but probabilistic: the instances of the rule’s content do not always lead to the achievement of its goal, but only with a certain frequency.50 Hence, such generalisations can be both over- and under-inclusive with respect to individual cases.51 On this basis, Schauer takes a second interpretive step: he argues that it is precisely this kind of relationship between a rule and its underlying reasons that determines the correctness of the rule.52 Following the same idea, he has suggested that the prohibition of “arbitrary discrimination”, found in the US Age Discrimination in Employment Act, should not be interpreted as prohibiting any generalisation that is not universal, but rather as prohibiting any generalisation that, being frequentist, has no empirical support.53

44(2) The second thesis I would like to highlight concerns the proportionality test. In examining its elements, Barak refers to the requirement of “appropriateness” as the one according to which the use of a means would “rationally lead” to the realization of the purpose of the means, in the sense that the means “increases the likelihood of realizing its purpose”. Indeed, according to the author, it should not be required “that the means chosen fully realize the purpose. A partial realization of the purpose – provided that this realization is not marginal or negligible – satisfies the rational connection requirement” (2012: 303-305). Similarly, Bernal Pulido understands the requirement of “appropriateness” as requiring that the measure in question “has some positive relationship with its immediate objective, that is, that it facilitates its realisation in some way, regardless of its degree of effectiveness, rapidity, completeness and security” (2014: 916).

45The above theses are in line with the justification requirement actually applied by the courts in certain cases, as the following examples show.

  • 54 I am referring to CJEU, “Wolf v. Stadt Frankfurt am Main”, 2010, decided by the Grand Chamber of (...)
  • 55 CJEU, “Wolf v. Stadt Frankfurt am Main”, §37-39.
  • 56 CJEU, “Wolf v. Stadt Frankfurt am Main”, §44.
  • 57 CJEU, “Wolf v. Stadt Frankfurt am Main”, §40.

46(3) Let us start with a CJEU case in which a difference of treatment based on age was challenged.54 A city was sued for setting an age limit of 30 years for the recruitment of staff for the “intermediate career in the fire service”, a force responsible, inter alia, for firefighting and rescue services. The purpose of this age limit, which the Court recognised as legitimate, was “to guarantee the operational capacity and proper functioning of the professional fire service”.55 The CJEU stated that the difference of treatment at issue was “appropriate” and “necessary” to achieve its objective56 on the basis of the following interrelated reasons. First, because, given the characteristics of the activities to be performed by those workers, “the possession of especially high physical capacities may be regarded as a genuine and determining occupational requirement.”57

47Second, because, according to “data deriving from studies in the field of industrial and sports medicine” provided by the German Government,

  • 58 CJEU, “Wolf v. Stadt Frankfurt am Main”, §41, emphasis mine.

respiratory capacity, musculature and endurance diminish with age. Thus very few officials over 45 years of age have sufficient physical capacity to perform the fire-fighting part of their activities. As for rescuing persons, at the age of 50 the officials concerned no longer have that capacity. Officials who have passed those ages work in the other branches of activities mentioned above.58

  • 59 CJEU, “Wolf v. Stadt Frankfurt am Main”, §43. The reasons for this can be read in the same paragr (...)

48Third, and finally, because, in order to “ensure the efficient functioning of the intermediate career in the fire service”, it is necessary that those who enter this career are able to perform the corresponding duties “for a minimum of 15 to 20 years.”59 According to the information available, only those recruited before the age of 30 could do so; if they entered at that age, they could fight fires for a maximum of 15 years.

  • 60 I will return to this in section §6.

49As can be seen from the long passage I have quoted, the CJEU held that the age limit was “appropriate” because (it held that it proved that) there is a conditional relationship − in a broad sense − between the age of persons and certain physical abilities required for the performance of fire service activities. What is interesting for us is that, according to the information provided, this relationship is not regular or universal. That is, it is not the case that all officers over 45 years of age (C) lose these abilities (E), so that the former is a “sufficient condition” for the latter (C → E). What happens, however, is that “very few officials over 45 years” continue to have these skills. This is sufficient, according to the CJEU, to qualify the age limit in question as “appropriate”.60

  • 61 The case is ECtHR, “Abdulaziz, Cabales and Balkandali v. The United Kingdom”, 1985.
  • 62 Quotations are from §74-75 of the judgment.
  • 63 According to some information, 90 percent of the men and (only) 63 percent of the women qualify a (...)
  • 64 See §79 of the judgment. Being “economically active”, the Court emphasised, does not mean (only) (...)

50(4) Let us now examine an ECtHR case on sex discrimination. In the early 1980s, the UK introduced certain immigration rules for family reunification between married persons. These rules were more restrictive for men who applied for entry because they were married to a resident, than for women who applied for the same reasons. A discrimination case was brought against this unequal treatment, which reached the ECtHR.61 In its defence, the UK Government argued that one purpose of the impugned legislation was “to protect the domestic labour market at a time of high unemployment”, which the Court found legitimate. And that since “men were more likely to seek work than women”, “male immigrants would have a greater impact than female immigrants on the said market”. The debate focused on whether the difference of treatment on this basis “had an objective and reasonable justification”.62 The ECtHR ruled that it did not, employing as one of its main arguments that available information on the difference between “economically active”63 men and women did not show that similar differences existed or would have existed in the respective impact of a husband’s or wife’s immigration on the labour market had the contested provisions not been applied.64

  • 65 The ECtHR questioned the government’s failure to demonstrate that. This suggests that if the gove (...)
  • 66 Cf. §79 of the judgment. I will return to this argument in section §7.

51What is remarkable about the case, for our purposes, is the nature of the instrumental assertions that were discussed, which dealt with relationships which, it can be assumed, the Court would have regarded as “appropriate” if it had considered them proved. The hypotheses put forward by the UK Government can be reconstructed purely in frequency terms. One of the most important reconstructions can be formulated as follows: “An increase in the family reunification income rate of male migrants contributes to an increase (or no decrease) in the unemployment rate”.65 This claims that there is a conditional relationship in a broad sense between one rate and the other. However, this does not mean that any increase in the former always leads to a corresponding increase in the other. Nor does it mean that every change in the unemployment rate can be explained by a change in the family income rate. It does mean, however, that the family income rate is a factor that contributes to a greater or lesser extent, and together with other variables, to explaining changes in the unemployment rate. It is the partial extent to which it explains it that determines its relative causal contribution. This is precisely the point of the ECtHR’s other main argument against the UK government’s defence: Notwithstanding, the Court was also not convinced “that the difference that may nevertheless exist between the respective impact of men and of women on the domestic labour market is sufficiently important to justify the difference of treatment.”66

  • 67 I am referring to the tobacco labelling case, 95 BVerfGE 173, 1997, cited by authors such as Alex (...)

52(5) Finally, consider the decision of the German Federal Constitutional Court in a well-known case on the restriction of other fundamental rights.67 The case dealt with a regulation requiring the labelling of tobacco product packaging with warnings about the health risks of tobacco consumption. The commercial freedom of tobacco manufacturers was restricted in the interest of protecting human health. The “appropriateness” of such a measure depended (among other things) on the existence of a certain relationship between smoking tobacco and acquiring health problems such as lung cancer. If one did not lead to the other, there would be nothing to warn about and no health benefit from not smoking.

  • 68 See §55 of the judgment.
  • 69 Cf. Doll et al. 1994: 901.

53What kind of relationship would be required to argue, in the context of such a case, that “smoking causes lung cancer” (or any other disease)? It is plausible to think that the two factors would not have to be invariably related, so that someone who smokes (C) will also get cancer (E). That is, a relationship of the type C → E. Instead, a less close relationship seems acceptable, in which smoking makes some contribution to the disease and increases the probability of getting it. Indeed, it was precisely this type of relationship that the German Federal Constitutional Court considered “appropriate” to justify the labelling requirement. In the 1997 case, it found that a causal relationship had been established between smoking and cancer and other diseases and cited as evidence three research studies published in reputable scientific journals.68 The distinctive feature of these sources for us is that they did not prove nor did they claim to prove that smoking inevitably leads to cancer. Rather, they have used statistical methods to show general associations of a frequentist nature, such as that “about half of all regular cigarette smokers will eventually be killed by their habit.”69

54In short, the examples show that there are cases where adopting a means to an end is accepted as instrumentally justified, even if there is no regular relationship between the instances of the two. That is, even if it is not the case that every worker over the age of 45 loses the skills needed by the fire service, or that every new male migrant who enters the country is another person looking for work and not getting it, or that every person who is persuaded not to smoke is a person who is saved from contracting diseases that he would certainly have contracted if he had continued the habit.

55In such cases it is sufficient that the means-end relationship is frequentist or probabilistic, either because it is assumed that the connection between the relevant factors consists in itself of nothing else, or because, assuming that they are connected in a regular or universal way, only incomplete causal laws are known, without all the conditions which, given together, would ensure that a certain effect always occurs. Therefore to account for requirements such as those contained in the above theses and judgments, it is necessary to consider other models of justification more suitable than the regularistic one. To this end, I will examine a conception of causality, which as its name suggests, has the advantage of being based on relations of the same kind as those required to justify the differences of treatment in the examples that have attracted our attention.

5 Probabilistic instrumental justification

56I will call probabilistic instrumental justification any argument according to which performing an action is instrumentally justified because it produces a difference in the probability that the instances of the content of a legitimate end will occur. In this model, premise (b) of the basic schema is modified as follows: “The instances of action M produce a difference in the probability that the instances of E will bring about”.

  • 70 A probability function assigns a real number to an event that represents the probability of its o (...)
  • 71 I will deal mainly with the contributions of P. Suppes 1970, N. Cartwright 1979, and E. Eells 199 (...)

57Reconstructing some features of probabilistic approaches to causality will provide some insight into the meaning of the key terms in the previous paragraph. These conceptions understand causal relationships as relative frequencies between types of events and represent them through a probability function.70 Their basic idea is that “causes” make a difference in the probability of their effects, even if they do not always lead to them.71 It can be expressed, in principle, as Pr(E|C) ≠ Pr(E) and reads as follows: The probability of the occurrence of E (the effect) given C (the cause) is different from the probability of the occurrence of E. Based on this conceptual stipulation, and having observed that smoking does makes a difference to the probability of getting lung cancer, it is correct to say that “smoking causes lung cancer”.

  • 72 The problem regularistic approaches have in explaining imperfect regularities (as in the example) (...)

58In contrast to regularistic conceptions, probabilistic conceptions allow relationships in which the factors involved (their instances) that are not connected in an invariant or regular way to be qualified as causal. They allow the claim “smoking causes lung cancer” even if the disease also occurs in people who have never smoked (the condition is not necessary for the effect) and even if there are regular smokers who never get it (the condition is not sufficient for the effect). Proponents of probabilistic conceptions see this as a comparative advantage for both epistemological reasons (we would normally only be able to know imperfect regularities) and ontological reasons (in reality, there would be no deterministic relationships between the phenomena we can try to know).72

59As I have introduced it, the basic idea of difference-in-probability is only an approximation to the way probabilistic approaches understand what I have called the “causal contribution” of one factor to another. How useful such an approach is for our purposes becomes clear when we consider some further details. For simplicity, I will refer to the positive causal contribution, i.e., the raise in the probability of the effect due to the cause: Pr(E|C) > Pr(E).

60The rise-in-probability we are concerned with is, basically, what is known as a positive correlation. If C and E are positively correlated and follow each other in time in that order, we could say, in the words of Suppes (1970: 12), that C is a “prima facie cause” of E. The expression is a good way of highlighting that something else is missing, that not every correlation translates linearly as a causal contribution. There are still several clarifications that need to be made. Of interest now are those that refer to the need to exclude so-called “spurious correlations”.

  • 73 See Eells 1991: 59, 62 and Suppes 1970: 21.
  • 74 The use of the expression “screening off” in the statistical literature to refer to the mentioned (...)
  • 75 That is: Pr(E|C·T) = Pr(E|T).

61One factor may be correlated with another because it causes it, or because both are caused by a common third factor. In the second hypothesis, and for the purposes of causal attribution, the association is called “spurious”.73 In probabilistic terms, a correlation between two factors (C and E) is called “spurious” if a third factor (T), when considered and included in the equation, screens off the apparent causal contribution of one to the other.74 This means that the probability of E given C and T is equal to the probability of E given T.75 Given T, the occurrence of C makes no difference to the probability of E.

  • 76 There is an exception to this, pointed out by authors such as Eells 1991: 59, 167 ff. If there is (...)

62Based on these concepts, the first important refinement of the idea of probabilistic causal contribution is that if a factor C is screened off in its correlation with a factor E by another factor, then C cannot be qualified as the cause of E.76 If not, C is what Suppes (1970: 10, 21-25) calls a “genuine cause” of E. According to this approach, the probabilistic causal contribution, understood as an unscreened-off positive correlation, is the exclusive contribution of one factor to the rise in the probability of the other. This idea, which is more complete than the first approach, has been further refined. Let us look at two lines of refinement.

  • 77 See Eells 1991: 1.1.

63On the one hand, attention has been drawn to the fact that the truth value of any causal assertion depends, among other things, on the population to which it refers, or as it is also called, its reference class.77 A change in the reference class may lead to a change in the conditional probability of the associated factors. For example, the probability of suffering a heart attack as a smoker tends to vary with age: it is not the same for someone in their thirties as it is for someone in their sixties. It is therefore suggested that any causal claim, even if implicit, should be understood as referring to a specific population group.

  • 78 See Cartwright 1979: 422 and Eells 1991: 72. According to Eells, “it is within the appropriate su (...)

64On the other hand, it has been pointed out that not every population or reference class is suitable for establishing the causal contribution of one factor to another.78 Any association between two factors observed in a population or set may be reversed in its subgroups by the effect of a third factor correlated with both. This phenomenon is called Simpson’s paradox (or reversal paradox) and raises the question of which correlations are appropriate for causal statements.

  • 79 See Bickel et al. 1975. This study has been cited by Cartwright to illustrate the problem we are (...)

65A well-known case is helpful in understanding the problem. It comes from a 1973 study of admission at UC Berkeley, which attempted to clarify the influence of the sex of applicants on admissions.79 Looking at the total number of applications, it was found that women were admitted at a lower rate than men. However, looking at the same data at the level of individual departments, it was found somewhat simplified that in each department the proportion of men and women admitted was the same. Although it may not seem so, the two observations at the university and departmental levels are compatible; they can be true at the same time without contradicting each other. In this case, the result was explained by the effect of a third factor: women tended to apply to departments with a higher rejection rate.

  • 80 Cf. Cartwright 1979: 423. W. Salmon (1971: 42-43, 2006: 63) has employed the idea of homogeneity (...)

66The question, then, is which correlation the one that belongs to which reference class should be used to establish causal relationships. The answer that has been given is, in simple terms, that one must rely on the correlation that is predicted on a causally homogeneous reference class (or population, or set). So, “C causes E if and only if C increases the probability of E in every situation that is otherwise causally homogeneous with respect to E”.80 This can be expressed as follows:

Pr(E|C·Kj) > Pr(E|Kj)

  • 81 Cartwright (1979: 423) makes a clear distinction between the set of properties that make a causal (...)
  • 82 This can be expressed as follows: Pr(E|T·Kj) = Pr(E|Kj), where “T” denotes any other property not (...)

67A population or reference class is causally homogeneous if and only if it is composed of the affirmation or negation of each of the properties that make a causal contribution to the production of factor E, with the exception of factor C, whose relevance is to be established. This description is denoted Kj.81 If a reference class is homogeneous, there is no additional property that can be introduced into the description that would divide it into two subclasses in which the probability of E is different (which would make it inhomogeneous). In such a class, any additional property is always screened off by the properties that make it homogeneous.82 So the only factor that could introduce a change in the probability of E, if it contributes causally to E (and that is what we want to determine), is C.

  • 83 In this sense, see Eells 1991: 85-86. There is discussion regarding whether C must increase the p (...)

68The suitable reference class for determining causal contributions, the causally homogeneous one, is called the background causal context of the corresponding causal assertion.83 In such an operation, the properties constituting the suitable reference class are said to be held fixed or constant, which means that the contribution of C to the probability of E is measured in a context in which they (its affirmation or negation) occur. Thus, every probabilistic causal statement always includes an implicit ceteris paribus clause.

69In short, if it is observed that C increases the probability of E, regardless of what other factors are present in the background causal context (which are independent and make a causal contribution), then C is said to make a causal contribution to E. There is a probabilistic causal contribution if, and only if, we have Pr(E|C·Kj) > Pr(E|Kj).

  • 84 I simplify here the notation used in Eells 1991: 88.

70The method we are discussing here, by overcoming the problems introduced above, enables us to distinguish between the degree of correlation of C and E and what may be called the degree of causal contribution of C to E. The magnitude of the causal contribution of C to E is equivalent to the correlation between C and E that is not screened off by Kj. That is, the result of the following operation: Pr(E|C·Kj) Pr(E|Kj).84

71Returning to the example of university admissions, we see that the factor “applying to the most selective departments” makes a causal contribution to the factor-effect “rejection of application” and, as we have seen, we should hold it constant as part of the background context. Once we have done this, we find that the correlation between the factor “sex of the applicant” and the effect is screened off: both are statistically independent given the first factor.

  • 85 In a similar but not identical sense, see Salmon 1971: 44, 2006: 63. A suggestion in this directi (...)

72Before concluding this section, it is worth moving from the conceptual level to the level of causal inquiry and noting the distinction between the set of properties whose possession actually makes a causal contribution to a factor E, and the properties whose possession we believe makes a causal contribution to E, given the information available at a given time. We might refer to the former as the “objective” homogeneity of a reference class, and to the latter as the “epistemic” homogeneity of a reference class.85 Causal inquiries are based on epistemically homogeneous reference classes that are selected according to the background information available to us at a given time and in a given context. This suggests that a causal claim can always be false because it was made without sufficient information, i.e., when we think we know all the properties whose possession makes a causal contribution to the phenomenon of interest, but we overlook some of them.

73In short, a probabilistic instrumental justification model links means to ends through probabilistic dependencies as characterised here.

6 Advantages of the probabilistic model

74Having formulated a model of justification based on the idea of probabilistic causal contribution, it seems useful to recover some examples to better illustrate the advantages of this model over the regularistic model when it is used to account for what is usually required in discrimination cases (and beyond) when assessing the justification of general rules or practices. This brings us back to what was suggested in §4.

75I will take as my main example the CJEU case challenging an age limit of 30 years for recruitment to the “intermediate career in the fire service”. I am talking about “Wolf v. Stadt Frankfurt am Main” (2010). Let us briefly recall that, according to the Court, the restriction was an “appropriate” and “necessary” difference of treatment to ensure that those entering the service could perform the relevant activities “for a minimum of 15 to 20 years” in order to guarantee its proper functioning.

76Now, the point I have been trying to make could essentially be refocused as a question of how the contribution that a difference of treatment must make to its end in order to be considered justified (for the sake of simplicity, I will hereafter speak of “the required contribution”) is specified or can be reconstructed. When this contribution is specified in an unrestricted or categorical way, without allowing for partial concreteness, the regularistic model of justification seems suitable for evaluating the means by which it is pretended to be achieved. If, on the other hand, it is frequently specified, this model becomes too demanding.

77In the fire recruitment case, the required contribution to the age limit would be unrestrictedly specified if it consisted of “ensuring that all persons entering the intermediate career in the fire service maintain the required physical condition for at least 15 years”. This would only be successful if none of the new members lost the physical ability to perform their duties fifteen years after recruitment.

  • 86 Assuming that this means is the only one that is used to achieve the purpose
  • 87 Which can also be expressed (as we saw in §3) as E → C.

78If the rule setting the age limit was intended to produce, by itself, an unrestricted contribution like the one just mentioned, the fact that a recruited person does not exceed the age of 30 (C) would have to be at least a “necessary condition” (in the sense analysed in §3) for him to retain physical ability after 15 years of incorporation (E).86 Thus, if someone older than that age (~C) were to join in violation of the limit, that person would not retain the required capacity beyond that time (~E). It is thus assumed that there is a regular or universal relationship between the two factors, age and maintenance of fitness, of the type ~C→~E.87

79If we make the proper adaptations, we can introduce what has been said into our basic schema of instrumental justification (presented in §2). To this end, by “AL” we denote the state in which all entrants would have been recruited at the age of 30 or less, and by “Action M” we denote the transition from the state “~AL”, in which this criterion was not met, to the state AL. We also denote by “E” the situation in which, 15 years after entry, all new recruits have the physical ability to perform their duties. With these adaptations, the schema would read as:

(a) It is intended to bring about a state of affairs, E.

  • 88 This can be read as follows: If people over 30 are hired (~LE), then not all new recruits will ha (...)

(b) ~AL → ~E.88

Therefore:

(c) Performing action M is instrumentally justified.

80This justification schema, based on universal or regularistic causal contributions such as ~ AL → ~E, is suitable to account for the reasoning when the required contribution is specified, as we have just done in an unrestricted way (“ensuring that all persons entering…”).

81Now consider the frequentist alternative for specifying the required contribution. It could be formulated as follows: “raising the probability that all persons entering the intermediate career in the fire service will maintain the required physical ability for at least 15 years”. The required contribution would thus be presented as something gradual, whose unit of measurement is the frequency of occurrence of certain types of events.

  • 89 CJEU, “Wolf v. Stadt Frankfurt am Main”, §41.

82By setting the contribution in this way, the legal rule could achieve it and thus be justified even if not all persons over the age of 30 would lose the required physical ability before completing 15 years of service (the condition is not sufficient), or if not all persons who would lose the required physical ability before 15 years of service would have entered the service after 30 years of age (the condition is not necessary). It would be sufficient if the probability of losing these capacities increased with age over 45. Or, in other words, that “very few officials over 45 years” still have them, as the CJEU stated.89

83If by “AL” we denote the condition that all recruits must be recruited at the age of 30 or younger, and by “E” the condition that all recruits must still be physically able to perform their duties after 15 years of service, the required contribution, expressed in frequency terms, could be formalised in the following way:

Pr(E | AL · Kj) > Pr(E | ~AL · Kj)

84It reads as follows: Holding the background causal context (Kj) fixed, the probability of E occurring when AL occurs is greater than the probability of E occurring when AL does not occur.

85If we call again “Action M” the transition from the state of affairs ~AL to the state of affairs AL, we can introduce these expressions into our basic schema of instrumental justification:

(a) It is intended to bring about a state of affairs, E.

(b) Pr(E | AL · Kj) > Pr(E | ~AL · Kj).

Therefore:

(c) Performing action M is instrumentally justified.

86This justification schema, based on probabilistic causal contributions of the type Pr(E|C·Kj) > Pr(E|Kj), is the suitable model to account for the type of reasoning when the required contribution is specified in a frequentist way (“raising the probability that…”).

  • 90 This premise about the systematic fallibility of the mechanism of decision making based on genera (...)

87As we have seen, each alternative for determining the required contribution has its own model of justification. But which of the two alternatives (and their respective models) is preferable? In the judgement we examined, the CJEU clearly opted for the second alternative, the frequentist version. Although it did not justify this selction, I believe there are reasons for it: It is an excellent way to deal with the consequences of the epistemological problem that follows. At least for generic cases, it is very difficult to know which conditions alone or in combination with others are sufficient and necessary to produce this or that effect on a regular basis, that is, to obtain justified and true beliefs about complete causal laws. Therefore, to require as a condition of justification for any difference of treatment that it be shown to make a regularistic causal contribution to its goal would be asking too much and would completely hamper the systematically fallible mechanism of decision-making based on general rules or criteria.90

88The above problem arises in relation to the nature of the causal relationship relevant to the resolution of the case under consideration. It is very difficult, if not impossible, to know the combination of circumstances that must be present for someone to inevitably lose the physical fitness required to be a firefighter after 15 years. Recruitment at over 30 years of age is a factor which, according to the scientific information available to the CJEU, is not in itself sufficient to ensure this outcome. It does not appear to be a “necessary condition” (in the sense discussed in §3) for someone to lose the required skills. It is not unreasonable to assume that some people may become unfit well before their 45th birthday. Moreover, this factor does not seem to be a “sufficient condition” (again in the sense discussed in §3). It is not unreasonable to imagine cases, albeit exceptional, where officers have such privileged anatomy and training that they can live beyond the age of 45 in a condition that still allows them to carry out activities such as firefighting.

89Thus, if the CJEU had applied a regularistic model of instrumental justification, it would have had to declare the introduction of the age limit at issue in this case discriminatory because it lacks “appropriateness”. And arguably, more broadly, most differences of treatment established by general rules. But as we know, the Court did not so rule. Instead, it applied a probabilistic model of instrumental justification (in a way that can be reconstructed, as I did a few paragraphs ago). It was enough for the Court that the means in question made a probabilistic causal contribution to the achievement of its objective.

  • 91 See §4(5).
  • 92 See §4(4).

90The advantages of the probabilistic model for capturing the requirements in discrimination cases when assessing the justification of general rules or practices, as illustrated by the above case, are also evident in other relevant examples, such as the German Federal Constitutional Court case on tobacco labelling91 or the ECtHR case on sex discrimination against migrants.92 In this respect, the probabilistic model better expresses the reasoning that the courts actually used or would have used given sufficient evidence than the regularistic model. In the first case, a regularistic contribution between smoking (C) and cancer (E) of type C→E was not required, but a probabilistic contribution of type Pr(E|C·Kj) > Pr(E|Kj) was. In the second case, no regularistic contribution of type C→E would have been required between being a male migrant (C) and looking for work but not getting work, but a probabilistic contribution of type Pr(E|C·Kj) > Pr(E|Kj). A contribution, according to the ECtHR, that should have been “sufficiently important”. This brings us to the issue we will address below.

7 Formulating levels of justification

91In sections §3 and §5 I characterised two different versions of the idea of causal contribution. For the reasons explained in §4 and §6, I have focused on the probabilistic version. I will now consider some of the regulatory opportunities that arise from understanding the “appropriateness” required to justify differences of treatment as a probabilistic causal contribution. In particular, I will look at the opportunities that arise for the strategy, common in anti-discrimination law, of requiring more robust justification (“very weighty” reasons) for certain kinds of cases by introducing different levels of the justification requirement.

  • 93 If Pr(E|C·Kj) Pr(E|Kj) were equal to 0, we would say that C makes no causal contribution to E. (...)

92To recapitulate, in §5 we found that the probabilistic causal contribution (P-CC) consists of a probabilistic dependence. An event C makes a P-CC to another event E if it produces a difference in the probability of the occurrence of instances of E, without being fully screened off by the causal contributions of the events that are part of the background causal context. As a concept, the P-CC has a quantitative and gradual character. It is expressed by probability functions, which, being positive, can take any numerical value in a range from above 0 to below 1. Its instances are graded by this measure: the higher the value, the greater the degree of contribution.93

93When we combine this with the other pieces we have been working on, an issue arises that deserves attention. Instrumental justification in cases of discrimination is based on the premise that any action that is “appropriate” to achieve a legitimate aim is to be considered i-justified (if other conditions are also met). Now, we note that if “appropriate” is understood in terms of probabilistic causal contributions, and given the gradual nature of the latter notion, it could always be asked how much contribution should be required? i.e., how much is enough? Anyone who has to decide whether a means-end relationship is “appropriate” will therefore inevitably have to assume, even if implicitly, some answer to this question: whether to accept that any contribution meets the requirement, or only a contribution above a certain (what?) degree. This decision would then involve two types of judgements: an empirical one about the degree of P-CC of a means in relation to an end, and an evaluative one about how much P-CC is sufficient for justification purposes.

  • 94 On the predictability of judicial decisions and their value in terms of autonomy and power distri (...)

94If one wanted to avoid the case-by-case evaluative judgement and the unpredictability that this involves,94 one could try albeit with limited effectiveness, as we shall see to define the P-CC required for justification as a categorical rather than a gradual concept. The point is to establish, at the regulatory stage, the level of justificatory requirement to be applied in each case, that is, the degree of P-CC to be considered sufficient and thus “appropriate” in this or that class of cases.

95The solution can ride on a strategy well known in anti-discrimination law, while also contributing to its refinement. As I pointed out in the introductory section (§1), it is common to require a more robust justification for certain kinds of discrimination cases those considered particularly harmful to the principle of equality than for others: “very weighty” reasons. The case law and provisions I have mentioned thus far seem to specify this higher requirement by demanding not only an “appropriate” but also a “necessary” relationship between means and ends.

  • 95 The picture is different, but only partially, in US jurisprudence. The US Supreme Court applies d (...)

96However, this way of increasing the justification requirement − by directly including the requirement of “necessity” − fails to take advantage of a regulatory opportunity that arises from the gradual nature of the P-CC, a feature that would allow for a higher causal contribution to be required (in addition to some efficiency), if deemed pertinent.95 The greater the sacrifice to values other than the achievement of the objective of a difference of treatment, the stricter the scrutiny that could be applied and the higher the means-end contribution that could be required as a condition for it to be considered “appropriate” for the purposes of justification.

97In what follows, I will present and analyse two ways of categorically defining when there is a sufficient causal contribution (hereafter SuffCC) between a means and an end. One will represent a basic requirement, the other a high one. We will see that in both cases, the strategy of requiring different levels of justifiability is refined with regard to the requirement of “appropriateness”. That is, the idea that some differences of treatment should make a greater contribution to the achievement of its end to be considered justified is given a more precise meaning. However, this raises other, not insignificant issues, which I will address in due course.

98Let’s turn to definitions, starting with the basic requirement:

D1 (basic level). There is a SuffCC between a means (M) and an end (E) if the former makes any positive causal contribution to the latter.

99This could be formalised as SuffCC(M, E) ≡ [Pr(E|M·Kj) Pr(E|Kj)] > 0.

100Under D1, the statement “The action M is SuffCC to bring about a state of affairs E” consists exclusively in a description of reality, that is, in the utterance of a statement with a descriptive function.

101Considering that “any positive P-CC” means producing any unscreened-off increase in probability, we can note that the definition expresses a basic level of requirement, since it is compatible with the contribution having a minimum degree even slightly higher than 0. For D1, any contribution should be considered sufficient.

  • 96 Cf. “Abdulaziz, Cabales and Balkandali v. The United Kingdom”, 1985, §79.

102While the definition serves as a default criterion, we have already seen that for some differences of treatment it is not considered acceptable to require such a weak justification; instead, a more robust one is expected: “very weighty” reasons. This is what the ECtHR and other courts have expressed in some of the judgments cited in §1. It is also what the Plenary of the ECtHR suggested in the example discussed above (§4) about the admission of male migrants: even if they were found to have a greater negative impact on the labour market than the admission of female migrants, the Court was not convinced that this was “sufficiently important to justify the difference of treatment” in the interests of employment protection.96

  • 97 A difference on grounds of gender, race, etc.
  • 98 For example, by not having a universal or near-universal scope (“perfect proxy”), as would be req (...)
  • 99 This evaluation is conceptually linked to the so-called “strict proportionality” test. According (...)

103Now, for such cases − and irrespective of the additional requirement that the means be “necessary” − stricter levels of SuffCC could be formulated. Suppose that a difference of treatment requires a “very strong”97 justification and makes a positive causal contribution to its objective, but the instrumental relationship is not considered sufficiently close.98 In such a case, the distinction could be said to make some contribution to the achievement of the objective, but insufficient to meet the proportionality test corresponding to the grounds on which it is based. As such, it is unjustified and therefore discriminatory. This is a way of accounting for those cases where a difference of treatment makes a contribution to its objective but is nevertheless considered unjustified for normative reasons: because the sacrifice made in implementing it would only be justified if the contribution were greater (or because there is no contribution, however great, that would compensate for that sacrifice). Here, justification involves a balancing of the value of the contribution that the measure makes to its objective (recognising that the contribution may be gradual), on the one hand, and against the other disadvantage that its implementation entails, on the other.99

104As far as I can see, there are at least two ways of leaving the basic level of the justification requirement, which I will call D2a and D2b. For the sake of simplicity, I will formulate the definition of only one additional level – the high one.

D2a (high level). There is a SuffCC between a means (M) and an end (E) if the former makes a positive causal contribution to the latter that exceeds a previously defined threshold.

105This could be formalised as SuffCC(M, E) ≡ [Pr(E|M·Kj) − Pr(E|Kj)] > u, where “u” denotes a specific value between plus 0 and minus 1.

106As with D1, under D2a the statement “The action M is SuffCC to bring about a state of affairs E” consists exclusively in a description of reality, in the description that M makes a contribution that exceeds the applicable threshold.

107Although this seems to be a satisfactory alternative, setting the threshold for a sufficient contribution a priori has a drawback. It renders the strategy insensitive to the particular characteristics of the phenomena in question and to what is known about the factors that constitute the underlying causal context. This is problematic because a P-CC could be relatively small and still be the known alternative that contributes most to achieving an intended state of affairs. So, discarding it would lead to discarding any effort to achieve the objective. In other scenarios, given the relative importance of a particular objective in a given area, it could also be the case that small contributions are considered proportional to their “cost” to the principle of equity in any case.

108The following definition avoids such a problem, while restoring another:

D2b (high level). There is a SuffCC between a means (M) and an end (E) if the former makes a positive causal contribution to the latter that is positively evaluated by the interpreter.

109This could be formalised as SuffCC(M, E) ≡ PE[Pr(E|M·Kj) Pr(E|Kj)], where “PE[…]” denotes the positive evaluation, as sufficient, by the interpreter.

  • 100 For an overview of these type of concepts, see Väyrynen 2021.

110Under D2b, and in contrast to the previous two definitions (D1 and D2a), the statement “The action M is SuffCC to bring about a state of affairs E” has a mixed descriptive and evaluative function. It involves both a description, according to which M makes a causal contribution to E, and an evaluative judgement about its sufficiency. According to D2b, the idea of SuffCC consists of a so-called thick evaluative concept.100

  • 101 That is, it is an evaluation that is conceptually linked to the proportionality test in the stric (...)

111This alternative delegates the judgement of the sufficiency of the causal contribution of a means to an end to the interpreter. This gives it the flexibility that D2a lacks, but at the cost of making such an assessment on a case-by-case basis rather than at the general regulatory stage. The decision involves a balancing of the reasons, which in the kind of cases at issue here are typically between the harm or disadvantage associated with the difference of treatment in question (the exclusion of a particular group from access to certain goods) and the benefit associated with the contribution to the achievement of its aim.101

112Taking stock, the proposed categorical definitions presented here (D1, D2a, and D2b) overcome the indeterminacy that results from translating the required means-end “appropriateness” as a mere P-CC. However, in the definitions expressing higher (non-basic) levels of justificatory requirement, a dilemma arises: a choice must be made between prefixing a sufficiency threshold (D2a) or delegating it to the interpreter (D2b), with the consequence that each regulative choice involves: insensitivity to context or the inclusion of evaluative elements in the idea of SuffCC.

8 Conclusions

113In this paper, I have examined some aspects of the reasoning underlying the assessment of whether a difference of treatment is justified and therefore not covered by the prohibition of discrimination. Let me take stock of the results.

  • 102 See Giles 2023.

114It can be plausibly argued that102 to say that a difference of treatment is “discriminatory” means, conceptually, to say that:

it is comparatively harmful to one or more persons;

it is based on the possession by those persons of certain legally protected characteristics (such as sex, race, etc.); and

it lacks sufficient justification.

115Moreover, the assertion in this discursive context that a difference of treatment is “sufficiently justified” means that:

it has a “legitimate aim”;

it is “appropriate” to achieve it;

it is “necessary” to achieve it; and

  • 103 This is only a summary of the reconstruction made in §1. It omits many details, such as the fact (...)

it is “strictly proportionate”.103

116What does it mean in this discursive context to claim that a difference of treatment is “appropriate” to achieve its aim? That is the question I have tried to answer in this article.

117The first step was to present the following basic schema for instrumental justification, an argument for assessing whether a difference of treatment is justified and therefore not prohibited as discriminatory:

(a) It is intended to bring about a state of affairs, E.

(b) Action M is appropriate to bring about E.

Therefore:

(c) Performing action M is instrumentally justified.

118We have focused on the second premise of the argument: What does it mean to require, as a condition of justification, that a means be “appropriate” to an end?

119To answer this question, I adopted an argumentative strategy that can be summarised in three steps. The first step was to elucidate the vague requirement of “appropriateness” as a given causal contribution. The second step was to reconstruct the content assigned to the notion of causal contribution by two conceptions of causality: the regularistic and the probabilistic. Both were presented as the basis for two models of instrumental justification, a regularistic one and a probabilistic one.

120The third step was to argue for an understanding of the requirement of “appropriateness” as a probabilistic causal contribution, and thus for the adoption of the probabilistic model of instrumental justification for cases of discrimination where general norms or practices are at issue. Why? Because it fits better with some theses about what should be required to justify these factors, and what is actually required by courts for this effect.

121Such a translation offers some regulatory opportunities. As we saw, an event C makes a probabilistic causal contribution (P-CC) to another event E if it produces a difference in the probability of the occurrence of instances of E, without being fully screened off by the causal contributions of the events that are part of the causal context. As a concept, the P-CC has a quantitative and gradual character. If we translate the “appropriateness” of means and ends required to justify an action into a mere P-CC, one could always ask how much contribution should be required? So, anyone who has to decide whether a means-end relationship is “appropriate” will therefore inevitably have to assume some answer to this question. This decision would then involve two types of judgements: an empirical one about the degree of P-CC of a means in relation to an end, and an evaluative one about how much P-CC is sufficient for justification purposes.

122To avoid a case-by-case assessment, I have explored various categorical definitions of sufficient causal contribution (SuffCC) for justification purposes. These are alternative options that could be adopted at the stage of legal regulation and help to refine the common strategy in anti-discrimination law of requiring more robust justification “very weighty” reasons for certain kinds of cases.

123A dilemma arises with definitions that express a higher (non-basic) level of justificatory requirement. A choice must be made between prefixing a sufficiency threshold (D2a) or delegating it to the interpreter (D2b), along with the consequence that each regulative choice involves: insensitivity to context or the inclusion of evaluative elements in the idea of SuffCC.

124Given the range of alternatives put forward, the claim that a difference of treatment is “appropriate” to achieve its aim could have one of three meanings, depending on the level of justification requirement adopted for each class of case:

D1 (basic level). The difference of treatment makes any positive causal contribution to the achievement of its aim.

D2a (high level). The difference of treatment makes a causal contribution to the achievement of its aim that exceeds a predetermined threshold.

D2b (high level). The difference in treatment makes a causal contribution to the achievement of its aim that is evaluated as sufficient by the interpreter.

Acknowledgment.This work was supported by the University of Genoa and project PID2020-114765GB-I00 from the University of Girona, funded by MCIN/ AEI /10.13039/501100011033. It was enriched by comments from Giovanni Battista Ratti, Jordi Ferrer Beltrán, Jaime Oportus Maino, Carolina Fernández Blanco, Marianela Delgado Nieves, Sebastián Rebolledo, and Diego Dei Vecchi, to whom I am very grateful. I am also grateful to the Revus reviewers.

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Notes

1 See Giles 2023 for a more detailed analysis of the elements of the generic concept of discrimination.

2 This is a weak permission (a non-prohibition): if the conduct were considered justified, there would be no rule in the legal system requiring its omission on grounds of discrimination. On permissions in a weak sense, see Alchourrón & Bulygin 2012: 175-176 and von Wright 1963a: 86.

3 ECtHR, “Belgian Linguistic case”, 1968, p. 34, §10. The ECtHR has reiterated this interpretation on several occasions since this case. See, among many others, “Marckx v. Belgium”, 1979, §33; “Rasmussen v. Denmark”, 1984, §38; “Abdulaziz, Cabales and Balkandali v. The United Kingdom”, 1985, §72; “Karlheinz Schmidt v. Germany”, 1994, §24; “Salgueiro da Silva Mouta v. Portugal”, 2000, §29; “Vallianatos and Others v. Greece”, 2013, §76; “Lupeni Greek Catholic Parish and Others v. Romania”, 2016, §164; “Biao v. Denmark”, 2016, §90; “Molla Sali v. Greece”, 2018, §135; “Jurčić v. Croatia”, 2021, §62.

4 As in the following European Directives: 2000/43/EC (2.2.b; 4); 2000/78/EC (2.2.b.i; 4.1); 2004/113/EC (2.b; 3.5); y 2006/54/EC (2.1.b; 14.2).

5 As in “Bilka-Kaufhaus”, 1986, §37; “Johnston v Chief Constable of the Royal Ulster Constabulary”, 1986, §38; “Sirdar v. The Army Board y Secretary of State for Defence”, 1999, §26; “Kreil v Bundesrepublik Deutschland”, 2000, §23; “Kücükdeveci”, 2010, §33; “Vital Pérez v. Ayuntamiento de Oviedo”, 2014, §60; “CJ v. TGSS”, 2022”, §48.

6 The UK’s Equality Act (2010) is a clear example. The only cases of direct discrimination that allow for justification within its framework are those based on age and disability (Sections 13.2 y 15). See Hepple 2010: 15 and Fredman 2011: 198 y ss.

7 See “Schuler-Zgraggen v. Switzerland”, 1993, §67; “Abdulaziz, Cabales and Balkandali v. The United Kingdom”, 1985, §78; “Jurčić v. Croatia”, 2021, §65.

8 See “Karner v. Austria”, 2003, §37; “Vallianatos and Others v. Greece”, 2013, §77, and citations.

9 See “Karner v. Austria”, 2003, §41, “Vallianatos and Others v. Greece”, 2013, §85, and citations; “Jurčić v. Croatia”, 2021, §65.

10 ECtHR, “Vallianatos and Others v. Greece”, 2013, §85.

11 See 2000/43/EC (2.2.b); 2000/78/EC (2.2.b.i; 6.1); 2004/113/EC (2.b); 2006/54/EC (2.1.b).

12 See CJEU, “Johnston v Chief Constable of the Royal Ulster Constabulary”, 1986, §38.

13 Generally, see OC-4/84, §56; OC-17/02, §46-48; “Espinoza Gonzáles vs. Perú”, 2014, §219; “Flor Freire Vs. Ecuador”, 2016, §125; “Guevara Díaz vs. Costa Rica”, 2022, §80.

14 CorteIDH, “Pavez Pavez vs. Chile”, 2022, §69. The Court had already expressed the same idea in “Gonzales Lluy y otros vs. Ecuador”, 2015, §256; and “I.V. vs. Bolivia”, 2016, § 241.

15 As the CorteIDH states in the extract just quoted.

16 See CJEU, “‘CHEZ Razpredelenie Bulgaria AD’ v. Komisia za zashtita ot diskriminatsia”, Grand Chamber, 2015, §120, §122, §128.

17 This seems to be the common understanding of the term in the literature on proportionality. Two notable examples can be found in Barak 2012: 317 and Bernal Pulido 2014: 933.

18 On the concept of effectiveness, understood as “to lead to” given results, see Fernández Blanco 2019: 266-269, 2021: 14-17.

19 According to Barak (2012: 305, 320), what distinguishes the necessity and appropriateness criteria in the proportionality test is precisely this: the former requires, in addition to effectiveness, that the means be efficient. The idea of efficiency adopted by the author following Rivers 2006 is inspired by the view of W. Pareto, for whom a distribution is efficient if “no other distribution could make at least one person better off without making any one else worse off” (Rivers 2006: 198). Given the limitations of the research I am undertaking here, it is not worth elaborating on this notion. For a more precise understanding, one might turn to the Economic or Law & Economics literature. See, for example, Margolis 1987, Cooter & Ulen 2012: 12-14, 42-43, Tuzet 2016: §3, Chiassoni 2013: 231-259 and Acciarri 2019: 6-9.

20 Similar arguments can be found in CJEU, “Reinhard Prigge v. Lufthansa”, 2011, §64. This judgment has its counterpart in CJEU, “Gennaro Cafaro v. DQ”, 2019, §49-55.

21 What I will say does not apply to discrimination cases mentioned in a previous footnote where no justification is accepted, as is usually the case for direct discrimination based on certain protected grounds.

22 Or “suitable”, “proper”, “adequate”, and other terms used as synonyms.

23 See CJEU, “CJ v. TGSS”, 2022, §48, and citations.

24 The relevance of factual statements in constitutional argumentation, a phenomenon that emerges in the framework of the proportionality test, has been highlighted in several works. In the Anglo-Saxon field, see for example Rosen 1972, Davis 1973, Acker 1990, Erickson & Simon 1998, Faigman 2008 and Larsen 2012, 2014.

25 I will explain these limits in the final paragraphs of §2.

26 See pp. 3, 23-26, 32-35, 58-60. Carter’s distinction between “judicial facts” and “legislative facts”, which follows K. C. Davis (1942: 402 ff.), illustrates that the kind of facts we are interested in – the latter – are not those that have occurred in a particular case. However, it does not contribute to the understanding of the requirement that concerns us, at the cost of multiplying the categories of facts according to the institutional context in which they are relevant (individual trials, legislative debates, constitutional trials, etc.). Specifically, the work does not further clarify a key aspect: how the phenomena of interest are causally related.

27 I will deal here exclusively with means-ends relationships of an empirical nature. But these are not the only possible relationships. There are also cases, for example, where a means is connected to its end by a (non-empirical but) conventional relationship.

28 “To bring about a state of affairs” or “to perform an act” is understood here as producing an “event” in the sense given to the term by von Wright 1963a: 26-28.

29 In its full version, the schema looks like this:

(*) It is instrumentally justified to perform any action which is appropriate to bringing about a state of affairs which is intended to be brought about and which is deemed to be legitimate to bring about.

(a) It is intended to bring about a state of affairs, E.

(*) To bring about E is deemed to be legitimate.

(b) Action M is appropriate to bring about E.

Therefore:

(c) Performing action M is instrumentally justified.

30 For the causal language, see Hitchcock 2003: 2-3.

31 Similarly, von Wright (1963b) has pointed out that one of the premises of the argument he calls “practical inference”, linking a means to its end, “rests upon a causal relationship” (p. 160). N. Cartwright (1979: 420, 431) has argued something similar about the idea of effective (in our terms: “appropriate”) strategies for achieving something.

32 With regard to the proportionality test, this view is expressed, for example, in Bernal Pulido 2014: 920 and Vázquez 2016: 62.

33 For present purposes, we are leaving aside the meaning of “appropriate” that is sometimes used in colloquial language, according to which a means is appropriate to an end if it is best suited to achieve it in comparison with others (because it was designed for it, because it fulfils it better than others, etc.). In our discursive space, this meaning is usually captured by the requirement of “necessity” mentioned at the beginning (§1).

34 In the sense of Tarski 1994: 110.

35 As, for example, in Cartwright 2004: §6 and Hitchcock 2003: 1, 21-22.

36 This is emphasised, for example, by Cartwright 2004: §6 and Frosini 2006: 313. This choice leaves out, among others, counterfactual approaches to causality.

37 For the merits of adapting one model or the other, see the counterpoint between the position presented in Schauer 2003: 123-125 and that defended in Arena 2018: 571 ff, 2019: 27 ff.

38 E. Eells addresses this problem in Eells 1991: 6.

39 Below, I follow von Wright 1971: 38-41, 2001: 66-77.

40 Cf. von Wright 2001: 66-67. In the following, symbols expressing conditional (→) and biconditional (↔) relations will be used in the traditional sense.

41 This relationship can be expressed, perhaps more intuitively for the study of causal relationships, as follows: ~C → ~E. The inversion is logically correct following the law of contraposition, according to which there is a logical equivalence between a conditional statement (such as E → C) and its contraposition, that is, the inversion and negation of its antecedent and consequent (~C → ~E).

42 Cf. von Wright 1971: 38-39, 2001: 70-71.

43 Its logical form is as follows: (C1 · C2) → E.

44 Its logical form is as follows: (C1 ∨ C2) → E.

45 Its logical form is as follows: E → (C1 · C2).

46 Its logical form is as follows: E → (C1 ∨ C2 ).

47 The application of this model in discrimination cases will be illustrated by an example in section §6.

48 This imperfect character is commonplace among those who study the phenomenon of legislation, something already pointed out by Aristotle (Vega López 2017: 28, 31-32).

49 Behind this assertion lies an assumption that is worth revealing, according to which legislators are instrumentally rational agents. Legislative rationality could be thought of as a condition for the legitimacy of legislative activity, in the sense that our freedoms can only be legitimately restricted if there is a (good) reason for doing so.

50 Cf. Schauer 1991: 25-31.

51 Cf. Schauer 1991: 31-34. Tussman & tenBroek (1948: 347-353) already considered these alternatives in their study of justification in discrimination cases.

52 Cf. Schauer 1991: 27, 29, 31.

53 Cf. Schauer 2003: 117. Notwithstanding this point, it is important to note that when the challenged distinction is based on characteristics such as the sex or ethnic origin of persons, a more robust justification (“very weighty” reasons) is usually required, which may require among other alternatives a closer instrumental relationship to the pursued aim, which is universal or close to it. Schauer (2003: 128-130, 131-154) himself has illustrated this higher standard by referring, inter alia, to the Supreme Court’s 1996 decision against the Virginia Military Institute for sex discrimination (“United States v. Virginia”, 518 U.S. 515). For a detailed reading of this decision and a suggested interpretation in line with previous US Supreme Court precedents, see Case 2000. There appears to be a counterpoint between Schauer and Case in their interpretation of the reasoning of the decision. While Case interprets the Court as requiring a generalisation of a universal rather than merely frequentist nature (a “perfect proxy”), Schauer seems to understand that according to the Court generalisations based on sex are wrong, regardless of their scope, whether frequentist or universal.

54 I am referring to CJEU, “Wolf v. Stadt Frankfurt am Main”, 2010, decided by the Grand Chamber of the Court. For a detailed overview of the case law of the CJEU on this issue, see Horton 2018.

55 CJEU, “Wolf v. Stadt Frankfurt am Main”, §37-39.

56 CJEU, “Wolf v. Stadt Frankfurt am Main”, §44.

57 CJEU, “Wolf v. Stadt Frankfurt am Main”, §40.

58 CJEU, “Wolf v. Stadt Frankfurt am Main”, §41, emphasis mine.

59 CJEU, “Wolf v. Stadt Frankfurt am Main”, §43. The reasons for this can be read in the same paragraph.

60 I will return to this in section §6.

61 The case is ECtHR, “Abdulaziz, Cabales and Balkandali v. The United Kingdom”, 1985.

62 Quotations are from §74-75 of the judgment.

63 According to some information, 90 percent of the men and (only) 63 percent of the women qualify as such.

64 See §79 of the judgment. Being “economically active”, the Court emphasised, does not mean (only) seeking employment with someone else.

65 The ECtHR questioned the government’s failure to demonstrate that. This suggests that if the government had done so, the Court would have considered it relevant to the appropriateness test.

66 Cf. §79 of the judgment. I will return to this argument in section §7.

67 I am referring to the tobacco labelling case, 95 BVerfGE 173, 1997, cited by authors such as Alexy (2003a: 136, 2003b: 437) to illustrate part of the structure of the proportionality test.

68 See §55 of the judgment.

69 Cf. Doll et al. 1994: 901.

70 A probability function assigns a real number to an event that represents the probability of its occurrence. It has a range of possible values from 0 to 1.

71 I will deal mainly with the contributions of P. Suppes 1970, N. Cartwright 1979, and E. Eells 1991. According to Cartwright (2004: §6), these are the foundations of the more sophisticated approaches that currently characterise probabilistic conceptions of causality. For a more general overview of the history and development of conceptions of causality, see Frosini 2006.

72 The problem regularistic approaches have in explaining imperfect regularities (as in the example) is one of the reasons often given for probabilistic approaches. The introduction to A Probabilistic Theory of Causality by P. Suppes 1970: 5-10 is illustrative on this point.

73 See Eells 1991: 59, 62 and Suppes 1970: 21.

74 The use of the expression “screening off” in the statistical literature to refer to the mentioned relationships goes back to H. Reichenbach [1956] 1971: 189-190.

75 That is: Pr(E|C·T) = Pr(E|T).

76 There is an exception to this, pointed out by authors such as Eells 1991: 59, 167 ff. If there is a case of causal intermediation, that is, if E produces C through the production of T, it is permissible to qualify C as the cause of E, despite the fact that T screens it off.

77 See Eells 1991: 1.1.

78 See Cartwright 1979: 422 and Eells 1991: 72. According to Eells, “it is within the appropriate subpopulations that correlations coincide with causation” (1991, p. 3).

79 See Bickel et al. 1975. This study has been cited by Cartwright to illustrate the problem we are dealing with.

80 Cf. Cartwright 1979: 423. W. Salmon (1971: 42-43, 2006: 63) has employed the idea of homogeneity for similar purposes (to develop a model of statistical explanation).

81 Cartwright (1979: 423) makes a clear distinction between the set of properties that make a causal contribution to E, which can be denoted {Ci}, and the state description (in Carnapian terms) that determines for each of these properties whether it is present in a given reference class or not, denoted Kj.

82 This can be expressed as follows: Pr(E|T·Kj) = Pr(E|Kj), where “T” denotes any other property not included in Kj.

83 In this sense, see Eells 1991: 85-86. There is discussion regarding whether C must increase the probability of E in every background context, or at least in one, without decreasing it in the others. See Eells 1991: 94 and Hitchcock 2021: §2.6.

84 I simplify here the notation used in Eells 1991: 88.

85 In a similar but not identical sense, see Salmon 1971: 44, 2006: 63. A suggestion in this direction can also be found in Cartwright 1979: 433.

86 Assuming that this means is the only one that is used to achieve the purpose

87 Which can also be expressed (as we saw in §3) as E → C.

88 This can be read as follows: If people over 30 are hired (~LE), then not all new recruits will have the physical ability to perform their duties 15 years after the incorporation (~E).

89 CJEU, “Wolf v. Stadt Frankfurt am Main”, §41.

90 This premise about the systematic fallibility of the mechanism of decision making based on general rules underlies Schauer’s thesis summarised in §4(1).

91 See §4(5).

92 See §4(4).

93 If Pr(E|C·Kj) Pr(E|Kj) were equal to 0, we would say that C makes no causal contribution to E. At the other extreme, if it were equal to 1, we could say that C is the sufficient and necessary cause of E.

94 On the predictability of judicial decisions and their value in terms of autonomy and power distribution, see Laporta 2007: 127-149.

95 The picture is different, but only partially, in US jurisprudence. The US Supreme Court applies different levels of scrutiny depending on the type of unequal treatment at issue. In terms of means and ends, sometimes a mere “rational” relationship is sufficient, sometimes a “substantial” relationship is required, while at other times only a “narrow” relationship is accepted. See, among others, Tussman & tenBroek 1948, Tribe 1988: 1436-1454, Galloway 1989, Chemerinsky 2006: 677-709, Mathews & Sweet 2010 and Congressional Research Service 2012: 2048-2059. However, the problem of clarifying what degree of causal contribution is meant by each term (“rational”, “substantial”, “narrow”) remains, and could be addressed with the conceptual tools offered here.

96 Cf. “Abdulaziz, Cabales and Balkandali v. The United Kingdom”, 1985, §79.

97 A difference on grounds of gender, race, etc.

98 For example, by not having a universal or near-universal scope (“perfect proxy”), as would be required in US jurisprudence for gender-based distinctions, according to the reading of Case 2000 mentioned several notes above, at §4(1).

99 This evaluation is conceptually linked to the so-called “strict proportionality” test. According to the current understanding, for there to be proportionality in the strict sense, “the benefits of adopting the measure in question must clearly outweigh the restrictions it imposes on the conventional principles it affects” (CorteIDH, “Pavez Pavez v. Chile”, 2022, § 69).

100 For an overview of these type of concepts, see Väyrynen 2021.

101 That is, it is an evaluation that is conceptually linked to the proportionality test in the strict sense.

102 See Giles 2023.

103 This is only a summary of the reconstruction made in §1. It omits many details, such as the fact that case law does not usually require the presence of all these elements as a condition for justifying all unequal treatment.

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References

Electronic reference

Alejo Joaquín Giles, “From “appropriate” means to desired aims
Revus [Online], 50 | 2023, Online since 18 March 2024, connection on 14 April 2024. URL: http://journals.openedition.org/revus/9819; DOI: https://doi.org/10.4000/revus.9819

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About the author

Alejo Joaquín Giles

Istituto Tarello, Universidad de Genova (Italia). Catedra de cultura juridica, Universidad de Girona (España). E-mail: alejojoaquin.giles(at)edu.unige.it.


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