Welfarism and Ethical Neutrality

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Welfarism and Ethical Neutrality

Jean-Sébastien Gharbi^* and Yves Meinard^†

Draft. Please do not circulate.

This version: 03/12/2017

Abstract: “Welfare economics” is the branch of microeconomics dedicated to study collective (i.e. social) wellbeing. Sen (1977, 1979) famously argued that using the welfare economics tools of analysis available at the time he wrote implied endorsing a doctrinal tenet, which he termed “welfarism”. This claim amounted to present welfare economics as an ideological corpus. This claim prompted attempts, by some prominent specialists of welfare economics, and especially of social choice theory, to distinguish two kinds of welfarisms. The first one involves a specific moral content, and is accordingly sometimes called “philosophical welfarism”. The second one is termed

“formal welfarism” (d’Aspremont & Mongin, 1998; Fleurbaey 2003a), and is presented as being strictly neutral in terms of ethical values. This distinction is buttressed on a second conceptual distinction, between the “informational basis” of social choice and the

“aggregation rule” involved. The former refers to the information considered relevant in decision-making. The latter to how this information is aggregated to provide a collective decision. The present paper discusses the claim that formal welfarism is ethically neutral. To do so, we analyze the ethical content of each of the axioms characterizing formal welfarism and its impact on the distinction between informational basis and aggregation rule.

Keywords: Welfarism – Ethics – Welfare Economics – Normative Economics – Social Choice – Informational Basis – Aggregation Rule.

JEL Classification: B41 (Economic Methodology), D60 (Welfare Economics), D70 (Analysis of Collective Decision-Making).

Words count: environ 10545

* Assistant Professor in economics, REGARDS, University of Reims Champagne-Ardenne (France).

Contact : [email protected]

† Full Researcher in environmental decision analysis, CNRS and LAMSADE, Paris-Dauphine University

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Jean-Sébastien Gharbi & Yves Meinard Welfarism and Ethical Neutrality

1. Introduction

“Welfare economics” is so widespread a phrase in economics that it is very rarely considered worth discussing or questioning. One often talks about “welfare economics” but rarely about what this phrase refers to. As a preliminary (and hence possibly disputable) step, one can define welfare economics as the branch of microeconomics dedicated to study collective (i.e. social) wellbeing (understood in terms of welfare). Referring to the classical distinction coined by John Neville Keynes between “positive” and “normative economics” (Keynes, 1890), it is commonplace to say that “welfare economics” is the subfield of economics dedicated to normative issues (Boadway & Bruce, 1984; Feldman &

Serrano, 2005). This understanding of welfare economics has been so largely accepted that this expression has become in the literature a strict synonym of

“normative economics” (Graaff, 1957, p. 2). Accordingly, it is not uncommon, until nowadays, to find the phrase “welfare economics” used to mean “normative economics” (Hausman, 2013).

Sen (1977, 1979) made clear that an ethical tenet, which he called

“welfarism”, was lying at the core of welfare economics as his contemporaries developed it. In other words, he showed that using the then available welfare economic tools of analysis implied endorsing specific doctrinal tenets of moral philosophy. Sen thereby also showed that it was possible to tackle issues constituting the traditional subject matter of welfare economics in a non-welfarist way. In doing so, he first emphasized the fact that identifying “welfare economics” with all of “normative economics” is disputable. He also and above all pointed out the morals commitments lying at the core of welfare economic methodological choices. One easily understands that such a claim, contended by an author who contributed significantly to revive the interest in normative economics after a long lasting period of abandonment (Sen, 1970, 2017),³ aroused fears that welfare economics might end up being seen as an ideological corpus.

This certainly explains why some specialists of welfare economics, and especially of social choice theory, felt the need to clarify the meaning of

“welfarism” by distinguishing two kinds of welfarisms. The first one is called

“philosophical welfarism” or “real welfarism”, and is admitted to involve a specific moral content. The second one is called “formal welfarism” (Mongin &

d’Aspremont, 1998; d’Aspremont & Gevers, 2002; Fleurbaey 2003a) and is presented, unlike Sen’s welfarism, as strictly neutral in terms of ethical values.

The ethical neutrality of formal welfarism relies on the assumption that it is possible to set a clear-cut separation between the informational basis (the only part of social choice supposed to be ethically committed) and the aggregation rule of a collective decision. In this article, we discuss the relevance of such a claim.

The article is organized as follows. In sections 2 to 4, we inquire into the definitions of the various forms of welfarism and into the relations and differences between them. Section 2 presents Sen’s famous and authoritative definition of

3 Arrow’s impossibility theorem (Arrow, 1951) had been interpreted during decades as implying the death of welfare economics. On this topic, see Fleurbaey & Mongin (2005) and Baujard (2017).

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welfarism (Sen, 1977; 1979). The axioms characterizing welfarism are detailed.

Section 3 then explains and discusses the distinction between real and formal welfarism (Fleurbaey, 2003; Rechenauer, 2003; Mongin & d’Aspremont, 1998).

We emphasize that the difference between these two forms of welfarism does not lie in an axiomatic feature. Section 4 is dedicated to the diverse other mentions of weakened forms of welfarism in the literature. We pay a specific attention to establishing if and how these categories are akin to those previously mentioned.

Sections 5 to 8 discuss the possibility for formal welfarism to be ethically neutral.

Section 5 explains why a clear separation between informational basis and aggregation rule is needed to allow advocating such an ethical neutrality.

Sections 6 to 8 discuss the ethical meaning of each axiom characterizing formal welfarism: Universal Domain (UD), Pareto indifference (PI) and Indifference of Other Alternatives (IOA). Section 9 briefly concludes.

2. Sen’s seminal definition of welfarism

Hicks (1959) is considered to be the first author to have coined the word

“welfarism”. However, it is Sen who introduced this word into contemporary debates about social choice in the 1970s, and he did it without any explicit reference to Hicks. Sen defines welfarism as:

“the principle that the goodness of a state of affairs depends ultimately on the set of individual utilities in that state, and—more demandingly—can be seen as an increasing function of that set.” (Sen, 1979, p. 464).

Sen claims that welfarism lies at the core of all welfare economic studies. This means that, in his view, welfare economics is not only a thematic subfield of economics—contrary to what was accepted since Pigou (1920). It is also a very specific way of dealing with issues in terms of philosophical stances—and he makes clear that this specific way can be discussed and criticized. By using the

“-ism” suffix to build the word “welfarism”, he presented it as a worldview or, equivalently, as a doctrinal corpus—on a par with, for example, socialism or liberalism.

Even though Sen’s 1979 definition is frequently quoted in the literature on economic theories of social justice, it is not the first occurrence of the term

“welfarism” in his works. Indeed, Sen used it in an earlier article entitled “On weights and measures: informational constraints in social welfare analysis” (Sen, 1977). In this paper, Sen defines “welfarism” as the principle that one should take account only of the personal welfare generated by states of affairs to choose between two of them. In other words, welfarism is defined as limiting to individual welfare (excluding any other possible information) the informational basis considered relevant. This point is perfectly in line with the 1979 definition quoted above. And it allows clarifying what it means to claim that welfarism has a doctrinal content: this informational basis restriction, constitutive of welfarism, has important ethical consequences.

But in addition to this definition in terms of informational basis, Sen also provided an axiomatic characterization of welfarism: “any Social Welfare Functional (SWFL) satisfying independence with unrestricted domain and the Pareto indifference rule […] may be called "welfarism."” (Sen, 1977, p. 1559). A

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SWFL translates the evaluation of states of affairs at the level of individuals into a ranking of these states of affairs at the level of the society they compose.

These three axiomatic components of welfarism are worth detailing.

- The axiom of Unrestricted Domain (UD) specifies if there are constraints imposed on the individual evaluations of states of affairs. In this instance, all the logically possible individual evaluations are allowed. In other words, the SWFL must be defined for every conceivable profile of preferences.

- The Pareto Indifference axiom (PI) states that if all the individuals assess that x is indifferent to y, then x will be considered indifferent to y at the social level. Formally, PI states that:

∀ x, y and ∀ uN, [uN (x) = uN (y)] ⇒ [x ∼ y]

(where x and y are states of affairs, u is an evaluation vector, and N is the set of individuals (i = 1, 2, 3, ..., n)).

- Lastly, “independence” refers to the Indifference of Other Alternatives (IOA). When ranking two states of affairs, all information about any other state of affairs than these two ones is excluded, i.e. considered as irrelevant. However, IOA is more specific than that: it does not only sets the irrelevance of information about any non-compared state of affairs in the binary relationship of x and y. Indeed, IOA also sets that if the relative ranking of x and y in two different profiles of evaluation are the same, then the ranking of x and y has to be the same in the two given profiles of evaluation. More formally, IOA states that:

∀ x, y and ∀ uN, vN,

[uN (x) = vN (x) and uN (y) = vN (y)] ⇒ [x ≽u y ⟺ x ≽v y]

(where x and y are states of affairs, u and v are evaluation vectors, and N is the set of individuals (i = 1, 2, 3, ..., n))⁴.

In both his 1977 (more axiomatic) and his 1979 (more philosophical) articles, when defining welfarism, Sen clearly aims at criticizing it: in each case he explains that the informational basis of welfarism is exceedingly narrow. He writes: “I would like to argue that (i) welfarism as an approach to social decisions is restrictive, and (ii) when the information on personal welfare is itself limited, it can be positively obnoxious” (Sen, 1977, p. 1559). Interestingly, the 1977 article mentions Nozick’s libertarianism and Marx’s theory of exploitation as alternatives

4 In his 1977 paper, Sen terms it the “axiom of Independence of Irrelevant Alternatives” (p. 1552).

Following Fleurbaey (2003a, p. 355), we replace this name by “Indifference of Other Alternatives”

(IOA) to prevent any confusion with the independence axiom used by Arrow in his impossibility theorem. Indeed, Arrow also calls his own independence axiom “Independence of Irrelevant Alternatives” (IIA) (Arrow, 1951, p. 26). If one associates IIA, with PI and UD, one finds his impossibility result, namely that there is no non-dictatorial social ordering function that satisfies UD, IIA and PI (Arrow, 1951, p. 59). IOA is a substantial weakening of IIA, notably because IIA excludes all information but ordinal and non-interpersonally comparable utility, whereas IOA does not.

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to welfarism (p. 1560). In the 1979 article, Sen mentions Rawls’s primary goods approach as a case of non-utility (i.e. non-welfarist) information (p. 471).

3. Real and formal welfarisms

In the recent social choice literature, the word “welfarism” is sometimes used in ways that do not explicitly refer to Sen’s authoritative definition, and make it difficult to understand the relationship with this definition. Fleurbaey’s distinction between real and formal welfarism (2003a) is a case in point.

According to Fleurbaey’s definition, real welfarism consists in building a social ordering function satisfying the axioms of Unrestricted Domain (UD), Pareto Indifference (PI) and Indifference of Other Alternatives (IOA) (2003a, p. 375). In other words, this definition refers to the very same axioms as Sen’s definition of welfarism (1977). The only difference is that Fleurbaey talks about

“subjective utility” whereas Sen refers to “individual utility”. Hence, if these phrases are considered as synonymous, then the two notions are equivalent. One can notice that the example of real welfarism provided by Fleurbaey is utilitarianism, an emblematic case of Sen’s welfarism and that the lack of mention of the sum-ranking rule of aggregation guaranties that real welfarism includes, but is not reduced to, utilitarianism⁵.

Formal welfarism is defined as an approach that also satisfies UD, PI and IOA. The difference with real welfarism is that the individual evaluation functions

“may measure any objective or subjective notion of well-being” (Fleurbaey, 2003a, pp. 375). This second definition is surprising from several points of view:

- One might expect from a concept called “formal welfarism” that it should capture a specific (“formal”) kind of a more general concept (“welfarism”), which already has an accepted definition (Sen’s one). One therefore might expect that anything being “formally welfarist” should be

“welfarist” in Sen’s sense. This is, however, not the case.

- Fleurbaey presents Sen’s capability approach as an example of formal welfarism, while readers of Sen (1980, 1985) cannot doubt that the capability approach was precisely introduced in order to be an alternative to welfarism.

- Last, but not least, the differences between real and formal welfarism exclusively hinges upon whether the individual evaluation criteria are subjective or not.

5 Using the concept of “utility” does not necessarily means accepting the real welfarist idea that utility is the relevant criterion of evaluation of states of affairs. Very often in social choice literature, “utility” is used to mean a “utility index”. The phrase “utility index” refers to the fact that all informational bases from the perspective of welfare economics (in other words, not only individual preferences but also primary goods or capabilities, which were initially proposed as alternatives to welfarism) share some formal properties. An individual bundle of goods in microeconomics, an individual bundle of primary goods or an individual bundle of functionings are represented by multidimensional vectors. Thus, a utility index is just a formal tool representing individual evaluation information and does not imply that the information taken into account is necessarily subjective preference satisfaction—contrary to what the use of the word “utility” might suggest. In order to avoid some possible misunderstandings, in this paper we use the expressions

“evaluation” or “evaluation information” instead of “utility”. For a conceptual analysis of the various possible meanings of “utility”, see for example Meinard & Gharbi (2018).

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An illustrative example of the implications of this second definition is provided by Fleurbaey (2003b)’s demonstration that a Rawlsian primary goods index is possible and that such an index satisfies UD, PI and IOA. It seems to contradict Sen’s claim in his 1979 article that Rawls’s primary goods approach is a case of non-welfarism—and to make totally puzzling the fact that Fleurbaey (2003b)’s title claims that the Rawlsian index is neither perfectionist nor welfarist.

The seeming contradiction vanishes once one understands that Fleurbaey would have reformulated Sen’s claim by saying that the Rawlsian primary goods index is not real welfarist, but is formal welfarist. A similar reason explains why Fleurbaey mentions Sen’s capability approach as an example of formal welfarism:

considering that the capability approach is a case of formal welfarism still allows claiming that it is opposed to real welfarism.

Formal welfarism is formally characterized by the so-called “welfarism lemma” (d’Aspremont & Gevers, 1977, Sen 1977):

[UD, PI and IOA] ⟺ SN

where SN is the Strong Neutrality axiom stating that if the utilities of two states of affairs in a given evaluation profile are at the same level than in two other states of affairs in a different profile, then the collective ordering of these two pairs have to be the same. Or, in more formal terms, SN is defined by the fact that:

∀ x, y, x’, y’ and ∀ ui, vi,

[∀i, ui (x) = vi (x’) and ui (y) = vi (y’)] ⇒ [x ≽u y ⟺ x’ ≽v y’]

(where x, y, x’ and y’ are states of affairs, u and v are evaluation vectors and i is an individual). In a nutshell, SN means that the social ordering function neglects all non-utility information and consequently is equivalent with formal welfarism (since SN does not specify which information is taken into account in an evaluation).

Although real and formal welfarisms satisfy the same set of axioms, the former is a subset of the latter. In other words, if a theory is a case of real welfarism it is necessarily also a case of formal welfarism, but the reverse is not always true. Fleurbaey articulate this point by saying, in an admittedly vague phrase, that “an approach may be formally similar to [real] welfarism, but philosophically quite far away from it” (2003a, p. 375).

In the technical literature on social choice theory, Fleurbaey is neither the only author nor the first one to have developed a distinction between different versions of welfarism based on considerations that are presented as

“philosophical”. For instance, Mongin and d’Aspremont contrast “the philosophical notion of welfarism” with a “purely technical” one, i.e. a “purely mathematical” welfarism (1998, p. 411). In the same vein, Rechenauer (2003) distinguishes a “philosophical welfarism” from a “technical” one. D’Aspremont and Gevers (2002) dedicated about ten pages to “formal welfarism”—which suggests that a non-formal welfarism exists. Because of the axiomatic similarity between real and formal welfarisms, it is crucial to clearly identify the nature of the difference between them.

“Real” or “philosophical” welfarism is presented by all the authors mentioned above as a welfarism of content—a welfarism that implies a doctrinal

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stance in terms of moral philosophy. It sets the quality, that is, the nature of the relevant information at the normative level: the only relevant information is subjective utility. Any information beyond subjective utility is considered ethically irrelevant and is neglected when adjudicating the relative goodness of two states of affairs. When it comes to “formal”, “technical”, “mathematical” or

“axiomatic” welfarism, it is presented as a welfarism of form. It does not intend to set any normative limit in terms of content on the information that can be considered relevant. In other words formal welfarism is much more flexible than real welfarism because it is only about ranking states of affairs and does not intend to say anything about the content (i.e. the normative criteria) used to order them.

Because formal welfarism does not specify any content as being an ethically relevant informational basis, this methodological framework requires (at least) one additional axiom dedicated to specifying the informational basis. Such an axiom is called an “invariance axiom” because its point is to define which kind of information can modify a choice and which kind of information leaves it

“invariant”. An example of invariance axiom is the axiom of Non Comparable Ordinalism (denoted as INVΦONC by Fleurbaey, 2003a). This axiom states “that any transformation of utility functions which does not alter individual ordinal preferences leaves social preferences unchanged” (Fleurbaey, 2003a, p. 351). An important element is to notice that IOA associated with INVΦONC is equivalent with the IIA axiom mentioned above.⁶ Arrow’s impossibility theorem teaches us that it is not possible to associate formal welfarism (and, consequently, real welfarism) with INVΦONC: there does not exist any non-dictatorial social ordering function satisfying UD, PI, IOA and INVΦONC. In other words, formal welfarism is totally incompatible with non-comparable ordinalism.⁷

It is however possible to be welfarist if one accepts another invariance axiom. For instance, it is possible to take into account cardinal information on evaluation functions and to allow any kind of comparisons (in terms of levels, differences and ratios). Such an invariance axiom, which could be called Full Comparable Cardinalism, is compatible with formal welfarism. Of course there exist many intermediates between these two extreme cases of invariance axioms (see, for instance, Fleurbaey, 1996, pp. 64–67) and it is necessary to check for each of them if they are compatible with formal welfarism.

The difference between real and formal welfarism cannot be totally grasped by the axiomatic analysis available in the literature. Indeed, this difference only stems from the kind of evaluation information taken into account (“subjective utility” in real welfarism, “any objective or subjective notion of well-being” in formal welfarism). The axiomatic specification involved by an invariance axiom does not exhaust the philosophical specification of the evaluation information: it only specifies some of its formal characteristics, such as whether it is ordinal or cardinal and the kind of comparisons it allows. In other words, an invariance axiom can formally exclude some criteria of justice, but it does not suffice for

6 See note 4.

7 Sen (1970, chap. 8) shows that relaxing the ordinalist requirement of INVΦ_ONC while keeping its non-comparable component (i.e. shifting to a Non-Comparable Cardinalism) does not allow avoiding Arrow’s impossibility result: avoiding this conclusion requires the abandonment of non- comparability. See also Sen, 1977, section 3.

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precisely specifying a philosophical concept of justice and the corresponding evaluation standard. For instance, the monetary metric is excluded if the invariance axiom forbids interpersonal comparisons of any sort. Likewise, it is necessary to accept interpersonal comparison to endorse the Rawlsian primary goods index or the Sennian capability approach, but no invariance axiom can specify one of these two philosophical stances. Then, even if two different formal welfarist theories of social justice satisfy the same invariance axiom, it does not follow that they will rank two states of affairs similarly (because they will compare these two states of affairs with respect to different vectors of evaluation).

4. Weak and strong welfarisms

In addition to the distinction between real and formal welfarism, the literature contains a series of concepts associated with welfarism, whose definition and exploration are not immune from a certain amount of terminological confusion. It is therefore useful to sum up and clarify these debates.

A prominent dichotomy is between strong and weak welfarisms. In the lines immediately above the characterization of welfarism called “welfarism lemma”, Fleurbaey (1996) claims: “Pareto-indifference principle implies a weakened form of welfarism. The IOA axiom brings with it a substantial reinforcement of the welfarist content of the social preorder”(1996, p. 63)⁸.

We have seen that welfarism is axiomatically defined by the combination of UD, PI and IOA. Nevertheless, Fleurbaey seems to state here that PI is enough to define a less demanding form of welfarism. Fleurbaey claims there is a welfarism implied by PI alone and specify that this, so to speak, PI-welfarism “nevertheless goes less far than absolute welfarism, which allows to construct a ranking for all kinds of utility vectors for all kinds of underlying economic context. For instance, utilitarianism proposes to pay attention to the sum of utilities in a universal way”

(Fleurbaey, 1996, p. 41). The “welfarist” aspect of PI lies entirely in the importance that it grants to (individual) utilities in ordering social alternatives.

Fleurbaey distinguishes explicitly a weak welfarism involved by PI alone from a so-called “absolute welfarism”. By contrast, one can then use the phrase “strong welfarism” (e.g. Maniquet, 2011) to designate the approaches that are more

“strongly” defined from an axiomatic point of view, such as formal and real welfarism.

The very phrase “weak welfarism” might seem awkward, given that “weak welfarism” is not even a form of “formal welfarism”. The point of using the term

“welfarism” to refer to PI alone can be understood as a means to emphasize the importance of PI as an element within the structure of welfarism. But it should not be understood as meaning that PI is sufficient to reduce the relevant informational basis only to information on individual utilities. This is probably why Fleurbaey sometimes calls the combination of PI and INVΦONC “individualistic quasi- welfarism” (2003a, p. 376, italics are ours)—a phrase that would sound weird if satisfying PI were enough to be welfarist, not even “weakly”.

8 Personal translation. Italics are ours. We modified denotations used in this excerpt in order to

facilitate reading. These remarks are valid for all the following quotations of Fleurbaey (1996).

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At first glance, Fleurbaey’s mention of an “absolute welfarism” (Fleurbaey, 1996, p. 41) that goes beyond “weak welfarism” could refer either to formal or to real welfarism. However, Fleurbaey also claims that “absolute welfarism” is distinct from welfarism as characterized by the “welfarism lemma”: “The form of welfarism induced by [the welfarism lemma] is not identical with absolute welfarism, according to which the only information that is relevant for social ethics is individual subjective utility. The mathematical welfarism of this lemma is more modest” (1996, p. 63).

Since the “welfarism lemma” defines welfarism at an axiomatic level by the combination of UD, IOA and PI, this lemma specifies formal welfarism (which is confirmed by the phrase “mathematical welfarism”). As a consequence, it means that “absolute welfarism” is just another name of “real welfarism”—which is, moreover, consistent with the idea (expressed some lines after the previous excerpt) that absolute welfarism takes only account of individual subjective utilities (Fleurbaey, 1996, p. 63). This conclusion is moreover confirmed by the fact that, when he defines Individualistic Quasi-Welfarism, Fleurbaey explains that PI by itself cannot make a social ordering function welfarist: PI alone only implies a “tint of welfarism” (Fleurbaey, 2003a, p. 376).

In a similar vein, when Fleurbaey writes that “the kind of welfarism embodied in IOA is purely formal, and is compatible with any empirical content given to the notion of ‘utilities’ ” (2003a, p. 358), it does not mean that IOA alone is enough to be welfarist. The point here is, as it was previously for PI, to make clear that IOA is a constituent element of welfarism and that satisfying IOA alone gives to social ordering functions properties that are akin to welfarism. But, as it was for PI, IOA alone is equivalent neither with real welfarism, nor with formal welfarism.

Notice that what we call here, following Fleurbaey (1996), a “weakened form of welfarism” or, for short, “weak welfarism” is different from “weak welfarism” characterized by Roberts (1980). Roberts shows that it is possible to build a weakened kind of formal welfarism which does not require satisfying PI, but only Weak Pareto (WP), according to which if a state of affairs x is preferred by all individuals to a state of affairs y, then x is socially preferred to y. Formally, WP states that:

∀ x, y, and ∀ uN, [uN (x) > uN (y)] ⇒ [x ≻ y]

(where x and y are states of affairs, u is an evaluation vector, and N is the set of individuals (i = 1, 2, 3, ..., n)). Since WP associated with UD and Continuity implies PI⁹, Roberts uses only an axiom of Weak Continuity (WC) and demonstrates that a social ordering function satisfying UD, WP, IOA and WC necessarily satisfies Weak Neutrality (WN). Contrary to Strong Neutrality, WN allows taking into account non-utility information to choose between two states of affairs, but only when the corresponding evaluation vectors are indifferent in terms of utility (see Roberts, 1980; Hammond, 1999; d’Aspremont & Gevers, 2002).

9 That is why the fact that Arrow (1951) refers to WP (and not to PI) is unimportant, insofar as WP is combined in this case with UD and a Continuity condition.

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Fleurbaey’s “weak welfarism” is, so to speak, a weakened form of formal welfarism insofar as it does not satisfy IOA. It can, for instance, satisfy a weaker axiom called Independence of Non-Indifferent Alternatives (INIA) allowing comparisons of two states of affairs “not only [depending] on their utility levels but also on how they are ranked by individuals with respect to other alternatives.”

(Fleurbaey, 2003a, p. 357). For this reason, we propose to call it “PI Weak Welfarism”. Roberts’s “weak welfarism” is a weakened form of formal welfarism insofar as it does not satisfy PI, but WP. In order to clearly distinguish it from the previous kind of weak welfarism, we propose to call it “IOA Weak Welfarism”.

Consequently, when Fleurbaey and Maniquet (2011) claim that their approach is “welfarist” and that it satisfies ordinalism and non-comparability (i.e.

INVΦONC) and WP (2011, p. 13), one should conclude that they use the word

“welfarism”, in this occasion, in a very broad sense and that their approach should, strictly speaking, be branded as a case of Non-Individualistic Quasi- Welfarism, in other words as a specific case of IOA Weak Welfarism.

Surprisingly, given what we just explained, Kaplow & Shavell (2001) intend to show that any non-welfarist method of policy assessment violates PI—which amounts to claim that PI is a sufficient condition to obtain formal welfarism.

Nevertheless, this result does not invalidate what we said previously. Indeed Kaplov & Shavell’s demonstration is done in single-profile, and in such a context there is no point to use an independence axiom like IOA. Then, in such a formal framework UD and PI are enough to set Strong Neutrality. In multiple-profile, however, it requires adding IOA (Fleurbaey, Tungodden & Chang, 2003;

Weymark, 1998; Blackorby, Bossert & Donaldson, 2005).

The Venn diagram below summarizes the relations between the different forms of welfarism and quasi-welfarism mentioned in the previous sections.

Figure 1: Relations between the various kinds of welfarism and quasi-welfarism¹⁰

10 We use and enrich a diagram from Gharbi & Meinard (2015). This diagram does not intend to be a representation of the relative importance of each set in regard with others, but only to represent their inclusion and exclusion relations.

Individualistic

quasi-welfarism Non-individualistic

quasi-welfarism Real

welfarism Formal, i.e. strong

welfarism PI weak welfarism

(Fleurbaey, 1996)

PI IOA

INVΦONC

IOA weak welfarism (Roberts, 1980)

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5. Informational Basis, Aggregation Rules and, Ethical Neutrality The distinction between real and formal welfarism consists in claiming that it is possible to identify a kind of welfarism that embraces a doctrinal content in terms of moral philosophy, namely real welfarism, and another one, formal welfarism, that does not. Clarifying what it means to claim that formal welfarism is ethically neutral requires reminding a classical distinction in social choice theory: the one between informational basis and aggregation rule.

The phrase “informational basis” is used to designate the space of relevant information in decision-making. In normative economics and, more specifically, in social choice theory, it refers to the set of characteristics taken into account.

Indeed, any decision requires paying attention only to a limited set of information and, as a consequence, to neglect others (Sen, 2011; 2017). The importance of informational basis in economic theories of justice and consequently in social choice theory has been strongly pointed out by the “equality of what?”

controversy. This controversy, initiated by Sen (1980), addresses the question of what a theory of justice has to take into account in order to play its role. Sen (1980) discusses three of the most influential informational bases in contemporary debates on social justice: individual preferences associated with (real) welfarism, Rawlsian primary goods and his own approach in terms of capability.¹¹

An “aggregation rule” specifies how the information taken into account is put together to provide a collective decision. In other words, an aggregation rule sets the constraints on how individual evaluations will translate into a social choice. Since a list of individual evaluation (for instance, preferences) is called a

“profile”, an aggregation rule is a function that maps each profile of individual evaluations into a collective information set, which can be understood as the social assessment of states of affairs (List, 2013). Majority voting, unanimity rule, dictatorship, summation and maximin (i.e. the rule maximizing the situation of the worst-off individuals) are examples of aggregation rules. It is well known that aggregating individual evaluations can be impossible (that it can be impossible to achieve a social assessment of states of affairs based on an aggregation rule depending on the properties that we want this rule to satisfy). Arrow’s impossibility theorem (Arrow, 1951) is one of these impossibility results.

In the definitions of real and formal welfarism stated above, the axioms UD, PI and IOA characterize the aggregation rule, while the informational basis is partly defined by the individual evaluation functions and is supposed to be constrained at the axiomatic level only by the invariance axiom. In other words, the alleged plasticity of formal welfarism (i.e. the fact that formal welfarism is able to deal with a very large scale of informational bases) and its correlated ethical neutrality both stem from the fact that formal welfarism is only an aggregation rule, that it does not endorse any ethical content.

Based on these concepts, Fleurbaey’s distinction between real and formal

11 Sen (2017) uses sometimes the phrase “informational basis” in a slightly different way by distinguishing between the “basal space” of the informational basis (corresponding exactly to what we call here “informational basis”) and its “aggregation system” (our “aggregation rule”) (p. 340).

However, Sen (2017) also at times uses the phrase “informational basis” in the sense we use (e.g.

p. 360).

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welfarism actually amounts to making two embedded claims, which are usually not explicitly distinguished: (i) the aggregation rules are independent of the informational basis; (ii) the aggregation rules captured by the axioms of formal welfarism are ethically neutral. If successful, the impermeable separation between informational basis and aggregation rule specified by these two claims guarantees that formal welfarism is ethically neutral—in other words, that the normative content with which formal welfarism deals remains totally exogenous.

Because its role consists in defining the nature of the goodness of state of affairs (i.e. to define evaluation criteria) in order to evaluate them, it is clear that any informational basis has (and cannot avoid to have) an ethical content.¹² Accordingly, our discussion of the ethical neutrality of formal welfarism does not target the (elusive) neutrality of the ethical content of informational basis. We rather target the possibility to set a clear distinction between informational basis and aggregation rule. In other words, we enquire into the possible influence of the (ethically committed) informational basis on the aggregation rule or, on the other hand, about the possible constraints stemming from the aggregation rule and modifying the informational basis (and consequently taking an ethical dimension).

Indeed, the only point to set a distinction between real welfarism and formal welfarism (while the two positions share exactly the same axiomatic features) is to emphasize the possibility of such an ethically neutral position—and consequently discussing this alleged ethical neutrality of formal welfarism amounts to enquire about the possibility of such a clear-cut separation. In a nutshell, asking if formal welfarism can be ethically neutral amounts to wonder if it is possible, in formal welfarism, to keep informational basis and aggregation rule independent of each other.

Formal welfarism especially emphasizes that there is a priori no reason to limit the informational basis, for instance, to individual preferences: its alleged neutrality precisely relies on this ability to embrace different informational bases.

Other kinds of evaluation criteria, such as Rawlsian primary goods (Rawls, 1971) or Sennian capability (Sen, 1985) and actually any other candidate, may be aggregated in a similar way.¹³ What specifies the informational basis at the axiomatic level, and consequently what sets a limit to the nature of the informational basis of a collective choice, is the invariance axiom and only the invariance axiom. The aggregation rules is only about how individual evaluations are compiled: it does not and should not modify the nature of the individual evaluation.

It is worth emphasizing that the ethical neutrality at issue here is not equivalent to the neutrality mentioned in the concepts of Strong Neutrality (SN) and of Weak Neutrality (WN). SN states that the only information taken into account to choose between two states of affairs is the individual evaluations U,

12 Such a statement does not imply that all aspects of the informational basis are ethically committed; it only implies that an informational basis with no ethical content would be a contradictio in terminis.

13 One crucial difference between preferences, on the one hand, and Rawlsian primary goods and Sennian capabilities, on the other hand, is that the former informational basis is strictly subjective when the latter are partly inter-subjective—which forbids, for instance, using a Rawlsian primary goods index in real welfarism.

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which, according to the definition of formal welfarism, can encompass an important variety of indices. WN states that the only evaluation information taken into account is the real welfarist utility (i.e. subjective preference satisfaction), except if this utility leads to a strict indifference between the two states of affairs to order. In this specific situation, non-utility-information can be exceptionally taken into account in the collective decision process. In both cases, it is different from defining a relevant informational basis, which amounts to define what kind of information will be included in the individual evaluation. Because SN (respectively WN) does not specify an informational basis, but only the (formal) aggregation rule, it is possible to satisfy SN (respectively WN) and to be

“ethically non-neutral” in the sense that we are interested in here.

The issue of the ethical neutrality of formal welfarism echoes the larger and older debate about the status of economics as a strictly positive science and on the scientific status of its normative aspects (Friedman, 1953; Gul & Pesendorfer, 2008). Fleurbaey (1996) explains that the normative economic approach to ethical issues aims at clarifying the logical implications of ethical values grasped by axioms (considered as given without endorsing them from an ethical point of view) and collective decision rules. Though related in some respects, the problem that we are dealing with here is much more specific than the one on whether it is possible and desirable to keep normative economics freed from any moral judgment. It would be misleading to think that claiming that formal welfarism is ethically neutral is exactly equivalent to advocate the idea that it is possible to deal with normative issues in a strictly positive way—the latter issue is linked to the status of value judgments in economics in general (Mongin, 2006). In other words, from a strictly logical perspective, it is possible to endorse any of the four available combinations of these two claims:

- Formal welfarism is ethically neutral and economics cannot be freed from any value judgment. Such a position amounts to claim that economics is necessarily normative in some of its aspects, but that aggregation rule can be kept free of any ethical commitment.

- Formal welfarism is ethically neutral and economics can be freed from value judgments. By advocating that normative economics is a strictly positive discipline (without explicitly taking a stance on the larger issue to know if economics in general is a strictly positive science), Fleurbaey (1996) seems to articulate these two stances.

- Formal welfarism is not ethically neutral and economics as a science has to be a strictly positive science. Such a position might be akin with that of Friedman (1953), who encourages economists to stop dealing with any normative economics issues—even though, for obvious chronological reasons, Friedman never mentions formal welfarism.

- Formal welfarism is not ethically neutral and economics is not (and cannot be) a strictly positive science. A stance that can probably be identified with the strong non-neutrality thesis discussed by Mongin (2006).

Let us come back to our main topic: the question of the ethical neutrality of formal welfarism can be summed up as that of the possibility to set a clear-cut separation between the informational basis and the aggregation rule. In the

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remainder of this article, we discuss this possibility by analyzing the possible ethical dimensions of the three axioms defining formal welfarism (sections 6 to 8).

6. On the ethical meaning of UD

One possible interpretation of the Unrestricted Domain axiom (UD) as a constitutive component of formal welfarism is to say that formal welfarism does not allow a priori sorting out any element¹⁴. At first glance, it might look as though one could not be more ethically neutral than UD. Indeed, even minimal ethical ideas, such as for example the idea that one should eliminate psychopathic or deeply anti-social preferences, seem to be more ethically restrictive than UD.

Restricting the domain is indeed a prominent way to make ethical judgments.

Therefore, rejecting domain restriction seems to be the best way to be “ethically neutral”.

Nevertheless, on closer examination, it could seem possible to discuss this first stance by emphasizing that refusing such ethical points necessarily implies being ethically committed—perhaps “minimally” committed but still, ethically committed, and therefore not ethically “neutral”. Unfortunately this last argument is flawed, since one actually can endorse UD not only in order to refrain from making ethical judgments, but also in order to commit oneself to be unable to make some ethical judgments, namely, the ones that could naturally take the form of a restriction of the domain.

According to formal welfarism, there is no way to claim that a specific opinion is (or can be considered) intrinsically bad, and then should be discarded.

Such a discard would require to endorse a normative system of evaluation and to provide an ethical evaluation. As UD seems to be intuitive and is for this reason a commonly accepted requirement, it could seem to be ethically totally innocuous:

forbidding the exclusion of any profile of information accepted by the evaluation filter of the Invariance axiom would be considered as less prescriptive and more

“open-minded” than deciding to a priori exclude some. Actually it is not innocuous. Let us remind, in this regard, that Arrow (1951, chap. 7) escapes his impossibility theorem thanks to a weakening of UD. Arrow’s argument to claim that UD is unnecessary is that in societies worthy of the name, people share some system of values—what in formal terms means that they agree to a priori exclude some profiles of information.

It is possible to interpret any a priori ethical principle, for instance Rawls’s principle of freedom (1971), as (ethically) restraining the domain of social choice to the subset of states of affairs satisfying this principle, i.e. as weakening UD.

Nevertheless, and this point is crucial, presenting the axiom defining the domain in such a way amounts to reject from the outset the idea of independence between informational basis and aggregation rule—what would reduce to nothing the efforts to distinguish real welfarism from formal welfarism. If one tries to clearly distinguish informational basis from aggregation rule, it could be better to say that a priori principles constraint the shape of the informational basis, insofar as they contribute to define the nature of the ethical evaluation of states of affairs, while the domain axiom (UD or any restricted domain axiom) contributes to shape the

14 We propose an alternative version of this section 6 in an appendix, after the reference list.

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aggregation rule (i.e. the rule used to compile, in a second time, information about evaluations) and only the aggregation rule. It is possible to advocate such a separation by distinguishing between the definition of the ethical space, namely the space defined by the informational basis and in which individual evaluation vectors take place, and their gathering, which can lead to take account of some information of the individual evaluation vectors, and consequently to neglect some others, but cannot modify the nature of this space and consequently the nature of the evaluation vectors themselves.

Nevertheless, and it is the most important in our discussion on the ethical neutrality of formal welfarism, even if UD is not a posteriori negligible in terms of ethical assessment (as shown by the example of Arrow’s impossibility theorem), it is not possible to advocate a priori such a restriction of the domain without ethically specifying the choice itself (i.e. it is not possible to define which profile of information to exclude without referring, explicitly or implicitly, to an ethical content)—what classical social choice (in general) and formal welfarism (in particular) do not do. Thus, even though UD can be a posteriori strongly ethically committed (because the absence of domain restriction can take an ethical meaning), at the most abstract level, endorsing UD a priori does not threaten the ethical neutrality of formal welfarism.

7. On the ethical meaning of PI

The Pareto Indifference axiom (PI) is often called the Unanimity axiom (e.g. Arrow, 1951). Indeed, by stating that:

∀ x, y and ∀ uN, [uN (x) = uN (y)] ⇒ [x ∼ y]

(where x and y are states of affairs, u a evaluation vector, and N is the set of individuals (i = 1, 2, 3, ..., n)), PI means that unanimity to rank two of states of affairs exactly at the same level in terms of evaluation should imply a social indifference between these two states of affairs.

In its formal expression above, is appears that PI takes account of all evaluations information and only of this information. One might therefore be tempted to criticize it from an ethical point of view by saying that PI constraints the informational basis—which would amount to claim that PI breaks the clear-cut divide between informational basis and aggregation rule. This approach would be wrongheaded, though. Indeed, recall that whether or not the informational basis is limited to individual preferences is only determined at the axiomatic level by the data filter provided by the Invariance axiom.¹⁵ Depending on the chosen invariance axiom, the evaluation vector u in the above formula can refer to utility in the usual economic sense, based on individual preferences, but it can also refer to another informational basis, such as primary goods or capabilities.

The ethical meaning of PI actually hinges upon a seemingly innocuous underlying assumption. PI assumes that it is meaningful to talk about

15 As we already mentioned (section 3, last paragraph), the Invariance axiom cannot by itself specifies all the characteristics of an informational basis. It only sets some formal constraints on the informational basis but it does not totally define this basis.

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uN (x) and uN (y) independently of the state of affairs (x, y or z) in which individuals are. Depending on the informational basis captured by u, this assumption might have far-reaching implications. The case where u captures utility in the usual economic sense is illustrative. The fact that individual preferences are largely determined by the actual state in which an individual finds himself has been largely studied in the literature on “adaptive preferences”

(notably Sen, 1997; Teschl & Comin, 2005; Begon, 2015). An immediate implication of this fact is that uN (x) and uN (y) are, in all likelihood, different when looked at from x, from y and from any other possible state of affair. PI does not tell from which state of affairs x and y are observed, and therefore neglects the observer’s position and all the ethical issues explored by the literature on adaptive preference.

Why should the issue of “adaptive preference” lead us to question PI? As emphasized above, denying PI would mean claiming that, in some situations, a given state of affairs can be considered better than another at the social level, even though everyone agrees to take the two states to be indifferent. Adaptive preferences provide a very strong reason to make such seemingly counterintuitive claim. Indeed if, for at least one individual i, we have good reasons to think that his preferences as mentioned in PI are due to an adaptation mechanism, and if this mechanism M as an ethical dimension E, it makes clear sense to claim that his judgment that x and y are indifferent can be considered irrelevant. In such a case, admitting PI means claiming that E is unimportant. Because E is ethical, the claim that it is unimportant is an ethical claim. In such a case, admitting PI implies endorsing an ethical stance and therefore PI cannot be said ethically neutral.

Notice that the reasoning spelled out above in the case where u captures utility in the usual economic sense does not apply when u captures, for example, the judgment of an impartial observer from nowhere. This means that the ethical meaning of PI depends on the content of u. In other words, the ethical meaning of part of the aggregation rule depends on the choice of informational basis, which is precisely what that informational basis vs. aggregation rule divide was intended to render impossible.

In other words, accepting PI amounts to make quite a strong assumption (usually not explicitly mentioned), namely to set an Endowment Conservatism axiom. Such an axiom sets that, although preferences are sensitive to initial endowment, this is no reason to reform the current pattern of individual endowments. Another way to phrase Endowment Conservatism is to present it as stating a specific case of Context Independence.¹⁶ The fact that choice is sensitive to the context is totally obvious for any Revealed Preference Theory proponent. In other words, if the implicit axiom implied by PI can be called an independence axiom, it is not an independence axiom in the same sense that Indifference to Other Alternatives (IOA). The kind of independence implicitly implied by PI actually specifies how and how much using PI both requires taking the context

16 Using the word “independence” in order to describe how and how much the context impacts choices can sound a bit disturbing. However, this is how the classical Revealed Preference Theory uses the expression “Context Independence” (arguably puzzlingly), to designate the fact that the context of a choice is taken into account with, and so to speak “within”, the choice. “Context Independence” could be as well (and maybe better) termed as “Context Dependence”.

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into account and considering this context, let us say by hypothesis, as being mutatis mutandis neutral.

Therefore, PI can be considered ethically neutral only (i) under the assumption of an implicit axiom of Context Independence and (ii) under the assumption that this implicit axiom has in itself no ethical content.

If one refers to the distinction between informational basis and aggregation rule, it seems hardly possible to advocate that such an implication is totally neutral in terms of ethics. Indeed, denying any relevance to individual position in terms of collective decision-making amounts to set a constraint not only on the aggregation rule (as PI does by construction), but also on the informational basis (what PI should not do, unless withdrawing the claim that formal welfarism is ethically neutral).

8. On the ethical meaning of IOA

The classical way to present any Independence axiom is to use the example of an election with only two candidates x and y and to point out that individuals’

opinion about a third candidate z (who is not in competition) should not modify the collective choice between x and y. Although it provides an intuitive idea of what any Independence axiom is, it does not allow specifying which kind of independence we are talking about. This description fits IIA, IOA as well as INIA.

IOA, stating that

∀ x, y and ∀ uN, vN,

[uN (x) = vN (x) and uN (y) = vN (y)] ⇒ [x ≽u y ⟺ x≽v y]

(where x and y are states of affairs, u and v are utility vectors, and N is the set of individuals (i = 1, 2, 3, ..., n)), is more specific. Establishing whether IOA has an implicit ethical content requires focusing on the specificities of IOA.

In order to investigate the meaning of IOA, it is useful to compare it with Independence of Non-Indifferent Alternatives (INIA), which is weaker (as mentioned in section 4). The difference between these two axioms is that the latter takes into account only the evaluation levels of the compared states of affairs, whereas the former allows taking into account the indifference curves on which evaluation levels are located in addition to the evaluation levels themselves (Fleurbaey, 2003b). In other words, shifting from IOA to INIA does not intend modifying the nature of information taken into account (i.e. the informational basis), it only intend modifying which elements will be picked up in the set of information defined by the information filter of the invariance axiom. However, as IOA excludes to take account of the indifference curve on which evaluations states are located and as INIA allows it, shifting from IOA to INIA noticeably modifies the quantity of information taken into account in the aggregation rule.

The comparison between IOA and INIA highlights the fact that IOA is not supposed to be an element of the set of axioms defining the informational basis (i.e. it is not supposed to determine or to modify the nature of the information), which is what the Invariance axioms contribute to do. Excluding the information about states of affairs that are not directly involved in the individual evaluations represented by a binary relation (as any Independence axiom do) should only

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amount to set constraints on the way information is aggregated, and should not set constraints on the nature of the information taken into account by the individual and collective decision rule. In both cases (IOA and INIA), the relevant information is the individual evaluation of the two (and only these two) compared states of affairs. The fact that IOA takes account only of the evaluation level of the compared states of affairs themselves whereas INIA takes into account the evaluation level of these states of affairs and the indifference curves on which these two states of affairs are located precisely means that IOA and INIA are two different rules of aggregating individual information in order to reach a collective decision rule.

The difference between IOA and INIA has also another direct consequence which has not been emphasized so far: by excluding the indifference curves with which the evaluation of the compared states of affairs is associated, IOA constrains the consideration not only of non-compared states of affairs (as any Independence axiom), it also constrains the consideration of the individual evaluation functions, which are not fully taken into account. Besides, it is worth mentioning that any Independence axiom (for instance INIA) excludes, by construction, some elements stemming from the individual evaluation functions—

INIA is more permissive than IOA in this respect, but it is not innocuous.

IOA is not supposed to set any constraint on the informational basis and consequently it is supposed to be compatible with any kind of evaluation (subjective or objective). Then the question can be asked: does excluding some elements stemming from the individual evaluation functions amounts to set a constraint on the nature of information taken into account (which would break the clear distinction between informational basis and aggregation rule) or does it amounts only to set constraints on how information is aggregated?

In order to answer this question, one has to pay attention, on the one hand, to the association of IOA with INVΦONC and, on the other hand, to the association of INIA with INVΦONC. Indeed these two associations do not have the same consequences in terms of informational basis. It is well known that IOA associated with INVΦONC limits the informational basis only to subjective satisfaction. This is actually an element that explains Arrow’s impossibility result—and a way to escape this impossibility precisely consists in weakening IOA, by using INIA instead. Such a substitution allows avoiding Arrow’s result because the association of INIA with INVΦONC does not set such a strong constraint on the informational basis. To be more specific, the association of INIA and INVΦONC allows interpreting the individual evaluation information not in terms of satisfaction but in terms of resources¹⁷. The fact that in both cases (with the association of IOA and INVΦONC and with the association of INIA and INVΦONC) the Invariance axiom INVΦONC is involved ensures that this latter axiom is not the only element to shape the informational basis. This means that in formal welfarism IOA does not shape only the aggregation rule, and then that the

17 It is crucial to make explicit that INVΦ_ONC associated with INIA does not allow any comparison of individual evaluation, but still makes possible some kind of interpersonal comparisons (Fleurbaey, 2003a, p. 376). This point illustrates that contrary to what one could think INVΦ_ONC is not the only axiom determining the possibility of comparisons.

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hermetic separation between informational basis and aggregation rule necessary to claim the ethical neutrality of formal welfarism is not satisfied.

Consequently, one can hardly claim that IOA is ethically neutral in the sense defined in section 5: it is clear that in formal welfarism (and consequently also in real welfarism), in other words in association with PI, IOA contributes to shape the informational basis. We showed that that the ethical neutrality of formal welfarism is defensible only if informational basis and aggregation rule are strictly separated.

9. Concluding remarks

In his 1977 and 1979 papers, Sen defined from axiomatic and philosophical points of view an almost hegemonic approach in welfare economic, which he named “welfarism”. In these two articles, he clearly pointed out and criticized the ethical content of this stance. The more recent distinction between the philosophical way and the formal way to be welfarist (notably explored by Fleurbaey, 2003a) does not solve the problem identified by Sen. Remembering that Sen provided in his 1977 article an exact characterization of what Fleurbaey calls “formal welfarism” is enough to make it clear. The debate on the ethical content of welfarism, which should have follow Sen’s discussion, did not happen—even though the problem has neither been solved nor accepted as such.

In this paper, we detailed the most prominent uses of the word “welfarism”

in the literature, in order to clearly distinguish this concept from its theoretical close variants—which are akin to welfarism, but are not strictly speaking welfarist. We then showed that the ethical neutrality of formal welfarism relies on the assumption that it is possible to set a hermetic ethical separation between informational basis and aggregation rule. On this basis, we then explored the ethical meaning of the axioms of Unrestricted Domain, Pareto Indifference and Indifference of Other Alternatives, the three axioms defining welfarism according to the social choice literature.

The main conclusions of this exploration are the following:

- Unrestricted Domain does not threaten the ethical neutrality of formal welfarism.

- Pareto Indifference can be considered ethically neutral only under the assumption (i) of an implicit Context Independence axiom of Endowment Conservatism and (ii) under the assumption that this implicit axiom has in itself no ethical content.

- Indifference of Other Alternatives is not ethically neutral in formal welfarism because, in association with PI, if contributes to shape the informational basis.

We conclude that even if it could be judged to be a minimal commitment, it is not possible to claim that formal welfarism is ethically neutral. In other words, we claim that it is still crucial to ask the question first asked by Amartya Sen about the meaning and scope of welfarism.