The internal inconsistency of Welfarism

The internal inconsistency of Welfarism Antoinette Baujard∗† February 13, 2012 PRELIMINARY VERSION PLEASE DO NOT CIRCULATE

Abstract Welfarism is the view according to which utility is the only relevant information to derive social welfare. This paper challenges this apparently simple definition to put forward the philosophical and mathematical approaches of welfarism. These distinctions are deduced by the study of the review of the appraisals of welfarism, and the analysis of defenses strategies developed by welfarist economists. Formal axioms of ethical welfarism and formal welfarism respectively are discussed and introduced. The inconsistency between these two approaches is then established and analyzed. JEL classification code: B12, B31, D63 Key-words: interest, individual utility, social welfare, welfarism, formal welfarism, ethical welfarism, philosophy and economics ∗

Antoinette Baujard, GATE L-SE, University Jean Monnet, F-42 000, [email protected] † Previous papers, intimately linked with this one, have been presented at the third JFFoS symposium (Shonan, 2009), and in the seminars of LAMETA (University of Montpellier, 2010), and GATE L-SE (University Jean Monnet, 2010). I wish to thank the participants of these meetings, as well as Fran¸coise Bastié and Muriel Gilardone for stimulating discussions. Needless to say, I should be held responsible for any remaining deficiency and views expressed in this paper.

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The internal inconsistency of Welfarism

1

Introduction

The word ”welfarism” was first defined and discussed in Sen’s articles published in 1979, one in The Journal of Philosophy, and one in The Economic Journal 1 . Here is how Sen (1979a) defines welfarism: “Welfarism. Social welfare is a function of personal utility levels, so that any two social states must be ranked entirely on the basis of personal utilities in the respective states (irrespective of the non-utility features of the states).” This word is now well-settled in the philosophical literature, in which it is defined more broadly as the doctrine according to which individual utilities are the only relevant information to deduce social welfare. Welfarism is mainly justified for three reasons, which together amount to guarantee that social welfare is just based on the concern of individual wellbeing and nothing else. First, it is based on the defense of actual individual interests. Second, it asserts the rejection of paternalism. Third, there are no other ethical foundations but these two first criteria. Previous appraisals of welfarism have already undermined the two last arguments as we shall recall. This paper aims at studying the robustness of the first one. A warning at this stage seems necessary. I do not here questions the right intentions of welfarist theoreticians —which I share openly. My argument consist in moving the debate in the economic model and, further, their implementation into prescriptions of welfarist policies. I claim that it is questionable that these models and these policies may be called welfarist in this very sense. I assert there in fact co-exist several definitions of welfarism either in the welfarist or in the anti-welfarist literature. In other works, I have distinguished an ethical definition at the philosophical level, a technical definition at the operational level2 , and a formal definition at the mathematical level. We here focus on the philosophical and the mathematical levels. Basically, ethical wel1

And it first appeared, in quotes, in his 1977 paper published in Econometrica. Technical welfarism is the method according to which the only relevant information which shall be used in the actual appraisal of social welfare are the concretely measured utilities in the actual contexts of gathering and computing such data. Technical welfarism and ethical welfarism have been shown to be likely to be inconsistent in the context of Bentham’s felicific calculus (Baujard 2009) and, even, in the context of modern public economics model relying on the revealed preferences theory (Baujard 2006). 2

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farism is the doctrine according to which individual utilities are the only relevant information to measure collective welfare. According to this view, welfarism is justified because its alternative, non-welfarism, mechanically implies to go against individuals’ interest. On the other side, formal welfarism is meant to capture this view in mathematical terms. To make sure no other information but utility is taken into account in assessing collective welfare when comparing two social states, formal welfarism rules out any other information but individual utilities over these two states. Roughly, philosophers defend ethical welfarism, while economists develops welfarist models which respect formal welfarism, which are interpreted and justified on the basis of the former philosophical works. As developed in a previous paper (Baujard 2010), the mathematical formulation actually corresponds to an ex-ante verification of the welfarist principle while the philosophical one rather coincides with an ex post view. Beyond such a conceptual distinction, this aim of this paper is to show the internal inconsistency of welfarism, i.e. the inconsistency between its formal and its ethical definition, hence the fact that the justification of welfarism in welfare economics may not rely on the three reasons invoked above. The stakes of this paper are threefold. In a methodological point of view, it formalizes and discusses some problems induced by transdisciplinary works, which eventually provides conclusions likely to be relevant in each domain. For political philosophy, it provides a strong argument to reject welfarism. For welfare economics, it calls for a re-assessment of the value judgments contained in the welfarist models, nay for renewing the formulations of the welfarist framework. This paper is organized as follows. We first recall some of the most established criticisms. A presentation of the tango of criticism help to identify the main tension which crosses welfarism, i.e. the distinction between the formal and the ethical definitions of welfarism. Section 3 provides some basic notations and definitions which will be used in the paper, as well as the conditions of formal and ethical welfarism in diverse frameworks. Section ?? establishes the inconsistency of these two forms of welfarism in the arrovian framework on the basis of the reinterpretation of existing results, and discusses the stakes of this results. Section 5 concludes.

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2

Against welfarism

We may today reconstruct Sen’s intention when he introduced this term. He aimed at distinguishing within utilitarianism or within welfare economics the problem of information and the issue of aggregation. Most criticisms of utilitarianism at the time focused on the aggregation stage, and Paretian welfare economics could feel free from any serious reluctant appraisals. The introduction of the concept of welfarism was necessary to focus on the former. From this point, Paretian welfare economics was to be re-assessed because of its exclusive reliability on utility information. Criticisms in this regard were soon profuse and devastating, even though poorly considered by the welfare economists themselves. This section aims at recalling them (2.1), and at explaining why they had such a weak influence upon welfarist economics (2.2). This analysis will justify the necessity to distinguish between distinct definitions of welfarism (3).

2.1

Welfarism, an appraisal

I shall here distinguish three families of criticism (For a more systematic review of the problem of welfarism, see among others Sen 2002). One concerns on the difficulty to provide a definition; another one focuses on the problem of ethical legitimacy, and, lastly, another kind of objection focuses on the issue of gathering information. One the one hand, welfarism has been attacked because of the difficulty to provide a suitable definition of utility. How can we account for individual welfare? This proves to be a difficult task because of the diversity of interpretations of preferences. In economics, preferences may stand for individual choice (in the realm of the revealed preference theory), subjective individual interest, well-being, long term fulfillment, first rank preferences or superior rank preferences, individual welfare considered for public evaluations and decisions... This diversity induces a quite strange view of the economic agent, which Sen called a ‘rational idiot’ (Sen 1977b, see also Sen 1985c). It is indeed hard to find any consistency within this syncretism without engaging into certain specific theories. As a matter of fact, utilitarianism accepts to consider that utility both stands for individual interests and choices. For other theories, this 4


statement soon become contentious, while syncretism becomes the synonym of an overall confusion between the positive and the normative analysis of utility, between philosophy of action, social philosophy or political philosophy. On the other hand, if the distinction between the possible interpretations of utility is to be taken seriously, it necessarily entails a selection of the kind of utility which will be used in the social welfare computation and a rejection of the others for this purpose. Two questions may then be asked in this regard: firstly, which interpretation of utility is selected in economics? And secondly, which one should be selected? Firstly, in welfarist economics, the retained notion of utility is subjective —may it be revealed by actual choices or by surveys. Sen even gave a specify definition of welfarism, including this additional condition: not only should welfarist social welfare be solely based on utility information, but also the latter is considered as subjective (Baujard, Gilardone and Salles 2010).That subjective utility is able to provide reliable measures of actual well-being in all cases is controversial. There is a distinction between choices and actual well-being because of constraints of different natures, or because the individual does not have access to all relevant information, or has untrue beliefs. He may also have preferences of different orders (Sen 1974, 1977; Igersheim 2007). For instance, a smoker wants to smoke even though he would like not to want to smoke. If we observe his actions, we may infer smoking is good for him; if we ask him, he may confess it is not; if we ask his physician, the latter would assert it is not. In many cases, he would himself not even identify his well-being with his first-order wants. Furthermore, some individual may rationalize the situation by considering it is satisfying. For instance, a women whose husband forbids her to drive appreciates and concurs the rule to remain happy (among others, see Nussbaum 2001). Utility information here ratifies a given situation, rather than testifies the high level of well-being induced by the situation. Hence subjective utility may not always be the better source of information for real well-being. Secondly, it is stating the obvious that the notion of individual welfare used in social welfare evaluations for the public sector, which are distinct from any other notions of individual utility, should be based on the information on individual states which is needed by the public sector. The latter is likely to be distinct from individual behavior, individual interests, or individual fulfillment, at least for some conception of justice. And there is no a priori reason why this should be subjective utility. In the smoker example above, we may wonder which of 5


the three notions of utility developed in the discussion should be retain by a government who would like to enhance social welfare. The relevance of individual ‘utility’ for assessing social welfare is debatable, even though such first order preferences, as revealed through choices, do have some relevance for the individual. Some appropriate notion of ‘welfare’ —for instance second order preferences or health indication—could also be some candidates for this (obviously among others). Further, the judgment an individual may have when thinking as a citizen may differ from the preference he may have as a mere individual (e.g. as a consumer). This position corresponds for instance to the usual distinction between subjective preferences and ethical preferences (see among others Harsanyi 1955) or the arrovian distinction between tastes and values (Arrow 1963) —which is actually due to Buchanan. Hence a public notion of individual welfare should be disentangled from the individual notion of one’s welfare. To make things clear here, we may reserve the word (individual) ‘utility’ for the individual interest in her eyes, and the word (individual) ‘welfare’ in the public eyes. In a nutshell, welfarist economics have essentially favored a subjective account of utility, while welfarism is questioned for the confusion between ‘utility’ and ‘welfare’ in these specific sense. This move from the syncretism of preferences to a reduction to a specific ethical notion of individual welfare directly raises a problem of justification and legitimacy. Gibbard (1986) discusses the selection of the proper notion of utility when interpersonal comparisons of utility should be made. He establishes the incompatibility between the two following criteria : the definition of true preferences and autonomy of preferences. From this result derives the fact that utilitarianism does not pass the test of anti-paternalism, and that it implies a ‘concept of a person’s good or the intrinsic reward of life’ (Gibbard 1986: 192; on a similar argument, see Scanlon 1991). Goodin (1986), among others, defends the requisite of laundering preferences—to go from real preferences to ethical preferences. But if so, what criteria should be retained? And who should conduct the work of laundering preferences? More generally in welfarism, who is legitimate to define or identify individual welfare? Sugden (1998) considers the necessity of an ethical observer to operate this task, which entails that welfarism is closely dependent on a substantive notion of the good. Baujard (2010) brought to the same conclusion considering the impact of interactions on Bentham’s welfarism, in which the latter though pretends to build a normative criterion exclusively on individual interests. In any 6


case, and whichever Bentham’s intentions are in this regard, the justification of welfarism at least requires some external elements. And indeed, welfarism has been questioned because of serious ethical limits. First, welfarism raises some moral paradox, among which the paradox of expensive tastes or offensive tastes (Rawls 1971; Cohen 1989, 1990) points out that welfarist evaluations induces counter-intuitive prescriptions. For instance, in the case of welfarist egalitarianism, more money should be attributed to the Champagne drinkers rather to the water drinkers, whereas this taste information intuitively seem irrelevant for distribution —at least many people do think so (so say experimentalists Yaari and Bar Hillel 1984). Or in the case of utilitarianism, a standard criticism (which is actually rejected by many utilitarians) consists in showing than the criterion of sum may justify the cruelty of circus games, or any repugnant policy based on the agreement of a sufficiently important number of persons. Second, welfarism voluntarily excludes some moral values which we could have good reasons to value. In particular, it is impossible to attribute an intrinsic value to fundamental rights (Sen 1970a). This is indeed one of the well-accepted feature of utilitarianism: Bentham called the French Declaration of the Rights of Man ‘a nonsense upon stilts’3 , because he would not see how this human creation would be at all legitimate. He rather claimed that the only acceptable source of ethical judgment is individual interests. Welfarism also precludes from valuing freedom (and indeed may not be valued meanwhile, as established in Gravel 1994 1998; Puppe 1998; Baujard 2007, 2011), liberty (Sen 1982a,c), equality (Sen 1979b), or the procedure for itself (Sen 1982a, 1986). Third, welfarism is a consequentialism. Henceforth, neither the source of utility, the intentions at the basis of actions which we should appraise utility, motivations, or procedures in general has any importance. This makes it difficult to be consistent with any deontological doctrines. Consequently, the least we can say is that welfarism is not value free: it is strongly committed to utility over any alternative ones, and it is likely to favor certain notions of the good over others. Further, the values at stake may eventually depend on those who will select the retained interpretation of utility, inducing some inevitable paternalist drifts. Last but not least, there is also a pragmatic problem connected with the 3

In his letter to Jacques Pierre Brissot De Warville (mid-August 1789).

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process of gathering information on individual welfare, as soon as we recognize that this issue as a different task from that of elicitation of mere preferences. It is expensive, tedious and even hardly possible to get the relevant information to operate the interpersonal comparisons of utility likely to be necessary in some welfarist models (as in the case of Harsanyi 1955), or more generally to gather the relevant information on utilities in any welfarist models (Sen 1979b). Besides, not only getting relevant and reliable data on individual utility is difficult in strategic context (Sen 1979, Baujard 2009), but also we can show that the concrete conditions of the process may affect considerably the quality of the eventual decision, possibly leading to violate the premiss of welfarism (Baujard 2006, 2009). To sum up, welfarism is notably accused of confusion between diverse notions of utility, of paternalist drift and for the thick veil covering its necessary external ethical criteria.

2.2

The tango of criticism

Just as tango goes back and forth, criticism goes at and from welfarism: as soon as the blame should affect it, the criticism and the alternative are disparaged. Rather than describing the tango for itself, we claim that studying its evolution will provide the evidences to identify the main tension which crosses welfarism. The concept of welfarism, as well as its alternative, now seems to be well accepted in the literature. What is not or is beyond welfarism may be called nonwelfarism (Kaplow and Shavell 2001, 2004), post-welfarism (Maguain 2002) or even extra-welfarism (especially within health economics; see Brouwer, Culyer, Exel and Rutten 2008; Tessier 2009). For some review of post-welfarism, see, among others, Pattanaik (1994); Pattanaik and Xu 2003 (2003); Clément, Le Clainche and Serra (2008). Post-welfarism is characterized by the following elements—notice welfarism is defined exactly by the converse of each of these elements. (i) It may consider other source of social welfare than individual welfare. The individual basis for justice might be something different than utility or a diversity of such source, including utility. Have been considered undefended, among others: primary goods (Rawls 1971), resources (Dworkin 1981a,b), capabilities (Sen 1985a, Nussbaum and Sen 1993), opportunities (Arneson 1990), advantages (Cohen 1990), rights (Gaertner 1993, Pattanaik and 8


Xu 2009). (ii) It allows multi-dimensional account of elementary information (d’Aspremont and Gevers 2002). This is a technical argument. Synthetic indexes, such as Human Development Index belong to this family of postwelfarist evaluations. As pointed out by many authors and often defended by Sen, the problem of multidimensionality induces cases of interdeminacy. (iii) Besides, there is a similar argument, yet now normative-wise. The value at stake is not just utility but may consider more values, or even different value(s). This includes the defense of pluralism in general (Sen 1985b, 2009). Another instance is the consideration of equity besides utility (Dworkin 1981a, 1981b; Fleurbaey and Maniquet 2011). Notice the existence of value pluralism is technically and philosophically not straightforward (Baujard 2011). (iv) The possibility of interpersonal comparisons of utility has a different status. Some welfarist, among which utilitarians of course (Ng 1997 among others), do accept them; some non-welfarist reject them (Fleurbaey, Tungodden and Chang 2003); and some other non-welfarist think they are necessary. Sen is a perfect instance of the latter case. He rehabilitated the role of interpersonal comparisons in welfare economics, in consideration of two conditions. First, these comparisons are interpreted exclusively on normative grounds. Second, this is considered as plausible if utility are reinterpreted as objective subjects (Baujard 2011), which clashes with the standard view of utility as subjective in welfarism. Neither these attacks nor the emergence of some alternative has disturbed welfarist economists. The latter have even been providing sound answers to their criticism. First, welfarists criticized very strongly non-welfarist answers, accusing them of paternalism. Being non-welfarist would amount to go and get information about what’s good for individuals outside them, even against their own will. Thinking an expert would know better than a given individual about what’s good for him is scandalous. Welfarism, in return, would be an answer to paternalism since the trust on individuals’ sovereignty, hence on subjective preferences, testify that individuals are in the best position to know what is good for them. Secondly, the blame according to which welfarism considers a way to restrictive view of utility though seems to ignore that, within utilitarianism, conceptions of well-being is incredibly diverse: utility as satisfaction, as accomplishment, as an indicator of an objectively good situation.... Griffin(1986) among others has provided a comprehensive view of well-being. As a matter of fact, in the modern utility theories, two main models are used: the 9


weak model of preferences and the strong model of preferences (Haslett 1990). The latter is specific to economists and basically corresponds to the revealed preference theory. This argument is often referred to when questions are asked to welfare economists to know how utility of their formal models should be operationalized. And it is also actually one of the most standard source of elicitation of preferences, whatever their interpretation. The strong model of preferences is one of the privileged target of the anti-welfarist attack. On the contrary, the former model has been developed by philosophers, who—as we have seen above— pay attention to the conditions for relevant utilities. This argument is often referred to when questions are asked to welfare economists to know what interpretation they retain of utility in their formal model. In these answers, the welfarist camp feels free from any criticism. Yet in the first case, the accusation of paternalism should exactly come back to welfarism when the definition of utility or relevant utility is tackled. And in the second case, the interpretation of utility in formal welfare economics model turn from on model to another model of preferences and rely, now on the economic domain, now on the philosophical justifications.

3

Individual utilities, social welfare and conditions of welfarism

To be able to tackle the distinction among the philosophical and the formal arguments, we shall now propose an axiomatic characterization of a welfarist social welfare function respecting one and the other idea. This requires us to introduce specify notations, some standard definitions, and the formulation of different versions of the two retained versions of welfarism, ethical welfarism at the philosophical level and formal welfarism at the mathematical level. In a second place (4), we will study the consistency of these axioms.

3.1

Basic notations

Let us introduce some notations. Let a set of alternatives X which contains at least three elements x, y, z, ... 10


Let a finite set of individuals N = {1, ...i, j, ...n}. Rankings of alternatives are represented by binary relations. A binary relation over X is a set of ordered pair. For two alternatives x and y, three situations may occur. Firstly, state x is at least as good as y, which writes: x y. Secondly, state x is better than y, which writes: x y. Thirdly, state x and state y are indifferent. This social preference is noted x ∼ y. All in all, may be derived from : x y ⇔ x y ∧ ¬(y x) (where : neg is the negation symbol). So may indifference relation ∼: x ∼ y ⇔ x y ∧ y x. The binary relation is reflexive if, for all x ∈ X, x x. It is complete if, for all x, y ∈ X, x y or y x . It is transitive if, for all x, y, z ∈ X, x y and y z ∧ x z A binary relation which is complete and transitive is called a complete preorder. Let P be the set of complete preorders over X.A preorder which is anti-symmetric is called a linear preorder. Let LO be the set of linear preorders over X. A preorder which is transitive and asymmetric relation over X. Let S the preorder for the society S ⊆ N , and let S and ∼S respectively be its asymmetric and its symmetric part. In welfarist framework, social welfare may be represented by social welfare function W : X → R, equivalent to the preorder RW defined over the elements of X. Hence xRW y reads: ‘x is socially preferred to y according to the utility profile at stake.’ According to the framework at stake, such social welfare rankings may be derived from individual preferences. Different formulations may be retained to capture individual welfare information. First, we may consider the profile Pi of individual rankings written i defined over X.. Let i the complete pre-order standing for individual i’s preferences. Let i and ∼i respectively be its asymmetric and its symmetric part. Second, we may consider the list of individual utilities U, written ui . Let ui be the individual utility function which maps the domain of alternatives to the set of real numbers, standing for the individual’s utility level: ui : X → R such that ui (x) ∈ R. Third, social states may be described as the resulting process of all individual choices, noted αi , i ∈ N . The set of all possible individual choices for individual i is noted Ai = {αi1 , αi2 , ...}. The set of social states is described by A = Ai × N , whose elements are noted a, where a is the vector of all individuals choices where the choice of individual i may be disentangled from others’: a = (αi , α−i ). The 11

The internal inconsistency of Welfarism profile P0 i of individual orderings written 0i is defined over Ai , whereas the profile P”i of individual orderings written ”i is defined over A.

3.2

Some definitions

Let us now introduce some Pareto conditions, which shall be central in the developments below. Definition 1 (Weak Pareto principle) ∀x, y, ∈ X, ∀i, x i y ⇒ x y Definition 2 (Strict Pareto principle) ∀x, y, ∈ X, ∀i, x i y ∧ ∃i : x i y⇒xy Definition 3 (Pareto indifference principle) ∀x, y, ∈ X, ∀i, x ∼i y ⇒ x ∼ y Strong Pareto corresponds to the union of Strict Pareto and Pareto indifference principles. Definition 4 (Strong Pareto principle) ∀x, y, ∈ X, ∀i, x i y ∧ ∃i : x i y ⇒ x y et ∀x, y, ∈ X, ∀i, x i y ∧ @i : x i y ⇒ x y Let us now introduce a domain condition, according to which the social welfare ranking is defined for any possible complete preorder. This condition writes as follows: Definition 5 (Universal domain) is defined on P.

3.3

Conditions of welfarism

Let us first consider a philosophical definition of welfarism. Ethical welfarism is the view according to which utility is the only relevant information for moral judgments. Being non-welfarist in this sense implies a 12


serious discussion on the interpretation of the informational basis for justice, and the clear exclusion of any value which is distinct from utility, such as fundamental rights, freedom per se, and so on (see Sen 1980, Mongin and D’Aspremont 1998). As an illustration, Jeremy Bentham is clearly welfarist in this sense (see Baujard 2009, 2010). We now discuss different formal conditions meant to capture this notion. We shall present the standard formal welfarism condition in the next subsection. Firstly, as ethical welfarism requires that individual utilities are the only relevant information to generate social welfare, indifferent utilities should induce indifferent social welfare. Hence Pareto indifference becomes a standard expression to capture a minimal version of ethical welfarism. Definition 6 (0-EW) A social order is [0]-ethically welfarist if: For all i ∈ N, ((x ∼i y)) then (x ∼S y). Further, a social state x shall be considered as better than y only if x generates higher utilities, or does not induce lowest utilities. AMong others, Samuelson (1947) has defended this version. He then talked about individualism rather than Welfarism – the concept was indeed not yet discussed. Hence a wider Pareto condition is strongly linked with ethical welfarism. The social order may not contradict any of the individual utility information. Is this condition overly strong or trivial? The problem is not about refusing any new situation which would decrease utility as compared with a status quo (this would be overly strong; it is not neither to require that unanimity should be obtained to change from the status quo( this would be overly weak and trivially the same as Pareto) what is at stake here is to compare the new situations among themselves. In other words, if a situation violates this condition, it cannot be considered as respecting ethical welfarism. Let us thus consider the strong Pareto condition. Definition 7 (1-EW) A social order is [1]-ethically welfarist if: For all i ∈ N, ((x i y)) then (x S y), ((y i x)) then (y S y), ((x ∼i y)) then (x ∼S y).

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Another way to consider the importance of individual interest in social welfare is to require that the social welfare function does depend on the individual preferences, or utility functions. This implies among others to preclude constant functions (the social welfare function would always pick the same best solution or the same ranking, whatever the individual preferences are), or any dictatorial positions. This strongly reminds a very similar discussion that has been led by Arrow (1963: chap.3). Let us then introduce the non-dictatorship aspect of ethical welfarism. Definition 8 (2-EW) A social order is [2]-ethically welfarist if it is not dictatorial, i.e. if there does not exist any i ∈ N such that (x i y) then (x S y). Let us now consider a mathematical definition of welfarism. According to this version of welfarism (See Sen 1977c), the social ranking of two options should only rely on the individual utilities over these two options. According to Sen (1979a), “Welfarism is a strong version of the condition of ’neutrality’ used in the collective choice literature (see Sen 1970; 1977b), and demands that the social ranking of any pair of states be neutral to the nonutility features of the states, i.e. the concentration must be exclusively on the utility information about the states.” Formal welfarism is a mathematical property of social welfare functions, and is characterized by the following conditions: unrestricted domain, Paretoindifference, independence of irrelevant alternatives (see D’Aspremont and Gevers 2002). Under these conditions, all relevant information for collective decision is captured by the utility levels only. More specifically, the social ranking of any pair of alternatives must depend on the utility levels at these two alternatives only, so that any change in the profile of the utility functions would not make any difference in the ranking—at least when it does not change the ranking of these two alternatives. The social ranking on a pair of alternatives should only depend on the populations’s ranking on theses two options, which induces the rejection of any cardinality and of interpersonal comparisons. This excludes any information linked with the identification of the persons, for instance weighting differently rich(er) and poor(er) people, talented or handicapped people. Non-welfarism, on the contrary, would notably accept to attribute different values to social states according to other information such as the position of one person of the ranking of wealth or talent. 14


As an illustration, most of welfare economics or the arrovian framework are welfarist in this sense. Imagine a society made of boys and girls. They wonder what activities they shall together tonight. All boys would like to go and watch box rather than dance in the first part of the evening; and they prefer drinking in a bar to singing karaoké for the second part of the night. All girls would like dance rather than box; and they prefer singing karaoké to drinking in a bar. All these information concern individual preferences. No social preference shall be merely derived from this information since no unanimity closes the matter. It should be out of the question of deciding whether to favor boys or girls, or to decide whether one activity is more intrinsically valuable than another one: this would imply to commit to a specific idea of goodness or fairness while utility should be all that counts. The most we could require from a social order is consistency in rankings, and especially consistency in the use of individual utility information in building social preferences. Then, imagine a social judgment is stated on how to socially rank a pair of alternatives, then any social rankings of other pair of alternatives should not contradict the underlying information on individual utilities which are conveyed by this primary judgment. Definition 9 (1-FW) A social order is 1-formally welfarist: For all i ∈ N1 ⊂ N, ((y i x) ⇒ (t i z)) and, for all j ∈ N2 ⊂ N \ N1 , ((x j y) ⇒ (z j t)) Then, [ If (y S x) ⇒ (t S z) and if (x S y) ⇒ (z S t)] Let us now modify the boys and girls example to disentangle the description of social states according to individual positions. The utility each of the boys and girls derive from watching boxing or dance obviously depend on whether they go together to the show or not, so does it from drinking and singing. The decision taken by each boy or each girl hence depends on the other’s. This little example illustrates the tension between two distinct definitions of utility, as we have discussed above. If utility was to stand for well-being, then we would just focus on experienced well-being and would be derive from individual preferences regarding boxing or dance, but also from what the other will eventually do. This notion of utility is captured by the preference ” defined over A. Ethical welfarism, as weak or strong Pareto, would capture 15


the idea that this notion of utility is all what counts. On the contrary, if utility was, as in the economic models, to stand for behavior, then welfarism should require a restriction on such individual utility, which here happen to be a different information: choices are based on ex ante situations, when other’s choices are yet not made, the experience requirement does not hold. Here this notion of utility is captured by the preference 0 defined over Ai . Any other source of information should be considered as irrelevant. First, the other’s choices should not be taken into account, as the person may not be able to act differently in a given situation. Second, the fact that the eventual level of well-being may be lower or higher for certain choices configurations is not relevant neither: this would not be a subjective individual position, but an evaluation which would appeal to external judgement, hence a contradiction with welfarism. These restrictions so define a new version of formal welfarism, in which utility is definitely subjective in the sense that it can exclusively relies on individual judgment. This notion may be captured by a condition which is based on the Sen’s liberalism condition (Sen 1970a). Definition 10 (FW3) A social order is 3-formally welfarist if there exists at least two i ⊂ N such that i h 0 0 If (αi , α−i ) i (βi , α−i ) ⇒ (αi , α−i ) S (βi , α−i ) h i 0 0 If (αi , α−i ) ≺i (βi , α−i ) ⇒ (αi , α−i ) ≺S (βi , α−i ) h i 0 0 If (αi , α−i ) ∼i (βi , α−i ) ⇒ (αi , α−i ) ∼S (βi , α−i )

4

Formal welfarism vs. ethical welfarism in the arrovian framework

On the basis of the formulation of the different versions of ethical and formal welfarism, let us now study the compatibility and the stakes of the inconsistency.

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4.1

Positive and negative results

Do social ordering always respect both ethical welfarism and formal welfarism? There is different way to tackle this question according to the retained definition of the concepts. Let us remind some well established results from the literature and provide some unconventional formulation and interpretations. Conjecture 1 For all U ∈ D, [1]-EW, [2]-FW and [3]-EW are incompatible. Proof 1 Sen (1979a: 539–543) recovers the arrovian result, i.e. dictatorship, considering with the 2FW formulation of welfarism and Strong Pareto. These are exactly the same conditions, even though with a different terminology. There is another way to recover such a result. From the welfarism lemma (d’Aspremont and Gevers 1977, Sen 1977c, D’aspremont and Gevers 2002), formal welfarism, as defined in the utility domain, is characterized by Universal domain, Independence of Irrelevant Alternatives (henceforth IIA, according to the arrovian formulation, see Arrow 1963) and Pareto Indifference. Formal welfarism implies IIA, hence the restriction from non-utility information and to binary information, but the converse is not true. Here, [1]-EW corresponds to the Strong Pareto condition, hence includes Weak Pareto. Arrow’s theorem establishes that a social welfare function respecting U, IIA, Weak Pareto is dictatorial. In other words, requirements here are even harder in our case than in Arrow’s conditions, from which the impossibility straightforwardly derives. Let us now consider the compatibility of formal welfarism with ethical welfarism when the structure of interaction is considered. Conjecture 2 For all possible individual preferences orderings (Universal Domain), for all structure of interactions, there does not exist a pre-order which always respects simultaneously [1]-EW and [3]-FW. Proof 2 There are strong arguments to believe this conjecture should be easy to prove. Just as Sen (1979a) could recover the arrovian settings from the previous conditions, we recognize these new formulation amounts to the Paretian liberal settings. [1]-EW corresponds to the Strong Pareto condition defined on P”i . 17


As social states defined on all possible elements A also covers the scope of X, each them have an exact correspondence and a preference over X. Hence we may also derive the preferences over Pi from the preferences over P”i , so that 1EW also applies on Pi . [3]-FW deserves a closer attention. The individual preferences describe the fact that, if i is in better shape choosing one action αi rather than another βi , given the actions of others, then the social welfare function should concur with the individual ordering regarding αi and βi . This condition captures formal welfarism because there are no other information but relevant individual utility which are at stake to induce a solution. As they consider the other’s states as given, informations coming from P0 i fully applies to Pi with no restrictions. Hence, just as the minimal liberalism condition, it isolates the individual preferences, generally defined over X, which may become decisive on his private sphere. Contagion to dictatorship may then operate the same way as in the arrovian context, which helps to get the intuition of the negative result. Another straightforward intuition of the proof is to consider the equivalence between the profile chosen by Sen to obtain the result and the typical profile of a prisoner’s dilemma. As we deduce from this theorem, universal domain, Pareto and minimal liberalism are inconsistent. This is enough to prove our result.

4.2

The inconsistency of welfarism?

The second result, establishes that, for unrestricted domain, ethical welfarism in the sense of Strong Pareto, ethical welfarism in the sense of non-dictatorship and formal welfarism are incompatible. It may be well illustrated from the previous example displayed while presenting formal welfarism. In the boys and girls example, we may observe that the rankings of boxing and dancing is exactly similar to that of drinking and singing, which means the information on utility profile of the society on the ranking of boxing and dancing reflects exactly the utility profile of the society. According to welfarism, the social preference over the first pair of options (boxing and dancing) should then be exactly the same as the social preference over the first pair of options (drinking and singing). Hence, if the primary judgment is that boxing is socially preferred to dancing, then drinking should be preferred to singing. If on the contrary, the primary judgment is that dancing is socially preferred to boxing,

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then singing should be preferred to drinking. This mere example noticeably illustrates why single-profile neutrality is closely related to contagion of decisiveness to dictatorship. As a matter of fact here, whatever the social ordering over a couple of options, either boys will become the dictators of the night, or the girls will. For an essential discussion of the formulations of the neutrality condition and its stakes, see Fleurbaey and Mongin (2005). This result may though be based on excessively demanding conditions, in the sense that not only IIA imposes a kind of welfarism —i.e. the exclusion from non-utility information—but also a restriction to binary comparisons of utility—i.e. a very poor information on utility. As was previously shown the restriction of information from non-utility and even within the space of utility entails the Arrovian result. Sen (1977c: 1562): ‘Arrow’s impossibility theorem has much to do with this informational famine.’First, it excludes the possibility for interpersonal comparisons of utility. This should rules out utilitarianism which is indeed welfarist. Hence 2EW—which entails IIA— seems to go beyond the welfarist requirements of restrictions. Second, it also rules out a part of ordinal information which could still be of interest to avoid the impossibility (see Fleurbaey 2000, Fleurbaey and Mongin 2005). It yet remains interesting to qualify a significant part of welfare economics, standing in the arrovian framework, which indeed is often faced with impossibilities. Another issue concern welfarist theories which are Pareto-inclusive, and yet exclude less utility information than with IIA. Let us now take into account a difference between ex ante situation (status quo) and ex post situation (in which the actual utility is experienced). For this, let us distinguish between the utility information which is available before the choices, hence before exchanges, externalities, interactions, raw influences of each other on one another. The definition of formal welfarism excludes any kind of information which would not be individual utility—they are the inputs. On the contrary, in ethical welfarism, individual utilities are the relevant outcomes to be taken into account —they constitute the output. Intuitively, the differences are such that it would be quite likely that there exist some apparently ethically speaking welfarist doctrine that would not respect entirely all the conditions of formal welfarism. In certain regard, this assertion can even seem trivial4 . We here tackle the converse issue: is there any welfarist theories which may 4

For other examples of ethical views that are not welfarist whereas they just refer to

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not guarantee ethical welfarism. Formal welfarism and ethical welfarism have been shown to be likely to be inconsistent in the context of Bentham’s felicific calculus (Baujard 2010). I propose to now consider Sen’s theorem of the impossibility of a Paretian liberal (Sen 1970a). It is often interpreted as a result questioning the compatibility between rights and utility. Though there are no other information but utility used in the description of the conditions of Sen’s theorem. The liberalism condition has a strong relevance for liberal theories indeed, for trying to restrict this condition would amount to coercion. It amounts to favor ex ante information on individual utilities, on the basis of individual full information and full rationality. A welfarist would certainly not reject the prescription, otherwise, he would need to incorporate external value judgements or external informations on the interactions among people. In the context of interactions and decentralized choices, and for unrestricted domain, we may derive from the theorem that ethical welfarism (in the sense of Pareto) and formal welfarism (in the sense of respect of individual utility as the inputs for rational choice) are incompatible. This result is quite interesting because it is more general than the previous one, as far as independence is not required. Just as in the case of the arrovian context, the only way to restore the possibility is to incorporate further value judgments likely to justify either a domain restriction or accepting to consider another source of relevant information but these subjective utilities. A further remark may also enrich our view of welfarism. Minimal liberalism has been shown to be internally inconsistent (Gibbard 1974[26]) when considering the wider information provided by preferences P0i defined over Ai . The problem eventually comes from the structure of interactions, as perceived through the set P0 . In other words, to consider the possibility that utility (as the relevant source of information for action) should be a relevant a consistent information for well-being, the structure of interaction should primarily be suitable. In other words, welfarism when considering ex ante utility may just be consistent with ethical welfarism if we live in a perfect world. utility information, see Fleurbaey, Tungodden and Chang (2003).

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5

Conclusion

I have defined “syncretism of preferences” as the fact that utility or preferences are often attributed a wide scope of different possible interpretations. It has often been defended in economics for the sake of Ockham’ razors. One of the main conclusions of the paper is that this parsimony is likely to entail some severe inconsistencies. Let me now pull together the threads of the argument developed throughout the paper. Welfarism has been attacked in economics because of the difficulty to define, identify or justify the selection of the utility concept used in social welfare evaluation. The attacks missed their target because many utilitarians, well aware of the definition problem, had already developed new philosophical theories of well-being to get round the difficulties. Welfarist economists could even be rightly shocked by the paternalist implications of post-welfarist theories, while they would boast their exclusive concern for individual interests, a criterion which is most assuredly difficult to challenge. Criticism was backfired so to speak. I have though claimed much of criticism applies to welfarism. It holds in the economic domain because of the formal confusion between diverse notions of utility, while the answer belonged to the philosophical domain, where one consistent conception may be chosen. The confusion between both may constitutes a trick to circumvent the difficulty, but does not necessarily asserts a convincing answer. Eventually a criticism holds if and only it holds continually within one (or each) of the two domains. To be able to study the actual robustness of welfarism towards the attacks, the distinction between the definition of the notions within philosophy or within economics should be taken seriously. I have thus introduced two distinct notions of welfarism: ethical welfarism at the philosophical level, and formal welfarism at the mathematical level. The former aims at capturing its main philosophical justification, while the latter corresponds to the property of formal welfare economics models. I have developed diverse axioms capturing these notions, and I could derived from some unconventional interpretations of Arrow and Sen’s theorems the analysis of their compatibilities. As the two definitions fail to be consistent, so we could conclude the last defense would come to naught. I have no problem with welfarism, at least in the sense it is defended by contemporary philosophers 21


or some theoretical economists: so do I want to favor individual interests and reduce paternalism. My conclusion does not challenge some views of utilitarianism (among others) in which external value judgments are explicitly incorporated, and which clearly distinguish the notions of utility and adapt it in distinct cases. I nevertheless concur with the great efforts devoted in the last four decades to appraise carefully the use of welfarism in economics. I dispute the welfarist defenses relying on the three justifications exposed above, for it as been shown they do not hold, at least not meanwhile. I assert that the need of external value judgment is unavoidable, that the paternalist criticism does hold for welfarism, and that we have no guarantee its formulation enforces in all cases the defense of individual interests. One more word on the stand of this paper. Axiomatics is standardly used to study the compatibility between diverse value judgments. Here we have used the usual characterization method to establish some inconsistency between one doctrine and its usual interpretation, i.e. some links between the way a concept is captured in philosophy and economics. This approach shows the limits of interdisciplinary discussions, a way to lead such discussion within one consistent framework, and is a praise for further works on the boundaries.

References [1] Arneson, R. J. Liberalism, distributive subjectivism, and equal opportunity for welfare. Philosophy and Public Affairs 19 (1990), 158–194. [2] Arrow, K. J. Social Choice and Individual Values, 2 ed. Yale University Press, New Haven and London, 1963. Corrected and completed from the first ed.: John Wiley & Sons, New York, 1951. [3] Baujard, A. L’estimation des préférences individuelles en vue de la ´ décision publique. Problèmes, paradoxes, enjeux. Economie & Prévision 4-5, 175-176 (2006), 51–63. [4] Baujard, A. Conceptions of freedom and ranking opportunity sets: A typology. Homo Oeconomicus 24, 2 (2007), 231–254.

22


[5] Baujard, A. A return to Bentham’s Felicific Calculus. From moral welfarism to technical non-welfarism. The European Journal of the History of Economic Thought 16, 3 (sept. 2009), 431–453. [6] Baujard, A. Collective interest vs. individual interest in Bentham’s felicific calculus. Questioning welfarism and fairness. The European Journal of the History of Economic Thought 17, 4 (oct. 2010), 607–634. [7] Baujard, A. L’économie du bien-être est morte. Vive l’économie du bien-être ! Working Papers CREM 2011-02, ‘Public Economics and Social Choice’ Series, june 2011. [8] Baujard, A. Utilité et liberté de choix dans les classements d’ensembles d’opportunités. Raisons Politiques (Aoˆ ut 2011). Forthcoming. [9] Baujard, A., Gilardone, M., and Salles, M. An interview of Amartya Sen. Social Choice and Welfare (Forthcoming). Interview in Harvard University, 2010. [10] Brouwer, W. B. F., Culyer, A. J., van Exel, N. J. A., and Rutten, F. F. H. Welfarism vs. extra-welfarism. Journal of Health Economics 27, 2 (March 2008), 325–38. ´ment, V., Le Clainche, C., and Serra, D. Economie de la [11] Cle justice et de l’équité. Economica, Paris, 2008. [12] Cohen, G. A. On the currency of egalitarian justice. Ethics 99 (1989), 906–944. [13] Cohen, G. A. Equality of what ? On welfare, goods and capabilities. Recherches Economiques de Louvain 56, 3/4 (1990), 357–382. [14] D’Aspremont, C., and Gevers, L. Equity and the informational basis of social choice. Review of Economic Studies 44 (1977), 199–209. [15] D’Aspremont, C., and Gevers, L. Social welfare functionals and interpersonal comparability. In Handbook of social choice and welfare, K. J. Arrow, A. K. Sen, and K. Suzumura, Eds., vol. 1. Elsevier Science B. V., 2002, ch. 10, pp. 459–541. 23


[16] Dworkin, R. What is equality? Part 1: Equality of welfare. Philosophy and Public Affairs 10 (1981), 185–246. [17] Dworkin, R. What is equality? Part 2: Equality of resources. Philosophy and Public Affairs 10 (1981), 283–345. [18] Elster, J., and Hylland, A. Foundations of Social Choice Theory. Cambridge University Press, Cambridge, 1986. [19] Elster, J., and Roemer, J. E. Interpersonal comparisons of wellbeing. Studies in Rationality and Social Change. Cambridge University Press, 1991. [20] Fleurbaey, M. Choix social : Une difficulté et de multiples possibilités. ´ Revue Economique 51 (2000), 1215–1232. [21] Fleurbaey, M., Gravel, N., Laslier, J.-F., and Trannoy, A. Freedom in Economics, New perspectives in normative analysis. Routledge Studies in Social and Political Thought, 1998. [22] Fleurbaey, M., and Maniquet, F. A theory of fairness and social welfare. Cambridge University Press, 2011. Econometric Society Monographs. [23] Fleurbaey, M., and Mongin, P. The new of the death of welfare economics is greatly exagerated. Social Choice and Welfare 25 (2005), 381–418. [24] Fleurbaey, M., Tungodden, B., and Chang, H. F. Any nonwelfarist method of policy assessment violates the Pareto-principle: A comment. Journal of Political Economy 111, 6 (2003), 1382–1385. [25] Gaertner, W. Rights and game forms, types of preferences orderings, and Pareto efficiency. In Mathematical Modeling in Economics, Essays in Honor of Wolfgang Eichhorn, W. E. Diewert, K. Spremann, and F. Stehling, Eds. Springer-Verlag, 1993, pp. 177–187. [26] Gibbard, A. A Pareto-consistent libertarian claim. Journal of Economic Theory 7 (1974), 388–410. 24


[27] Gibbard, A. Interpersonal comparisons: Preference, good, and the intrinsic reward of life. In Foundations of Social Choice Theory [18], pp. 165– 193. [28] Goodin, R. E. Laundering preferences. In Elster and Hylland [18], ch. 3, pp. 75–101. [29] Gravel, N. Can a ranking of opportunity sets attach intrinsic importance to freedom of choice? American Economic Review: Papers and Proceedings 84, 2 (1994), 454–458. [30] Gravel, N. Ranking opportunity sets on the basis of their freedom of choice and their ability to satisfy preferences: A difficulty. Social Choice and Welfare 15, 3 (1998), 371–382. [31] Griffin, J. Well-being: Its meaning, Measurement, and Moral Importance. Clarendon Press, Oxford, 1986. [32] Harsanyi, J. C. Cardinal welfare, individual ethics, and interpersonal comparisons of utility. Journal of Political Economy 63, 4 (1955), 309–321. [33] Haslett, D. What is utility ? Economics and Philosophy 6 (1990), 65–94. [34] Igersheim, H. Du paradoxe libéral-parétien à un concept de métaclassement des préférences. Recherches Economiques de Louvain 73 (2007), 173–92. [35] Kaplow, L., and Shavell, S. Any non-welfarist method of policy assessment violates the Pareto principle. Journal of Political Economy 109, 2 (2001), 281–286. [36] Kaplow, L., and Shavell, S. Any non-welfarist method of policy assessment violates the Pareto principle: Reply. Journal of Political Economy 112, 1 (2004), 249–251. [37] Maguain, D. Les théories de la justice distributive post-rawlsiennes. Une ´ revue de la littérature. Revue Economique 53, 2 (mars 2002), 165–199.

25


[38] Mongin, P., and D’Aspremont, C. Utility theory and ethics. In Handbook of Utility Theory, S. Barbera, P. Hammond, and C. Seidl, Eds., vol. 1. Kluwer, Dordrecht, 1998, ch. 10, pp. 371–481. [39] Ng, Y.-K. A case for happiness, cardinal utility, and interpersonal comparability. The Economic Journal 107, 445 (1997), 1848?1858. [40] Nussbaum, M. C. Adaptive preferences and women’s options. Economics and Philosophy 17 (2001), 67–88. [41] Nussbaum, M. C., and Sen, A. K. The Quality of Life. Clarendon Press, Oxford, 1993. Edition 2001. [42] Pattanaik, P. K. Some non-welfaristic issues in welfare economics. In Welfare Economics, B. Dutta, Ed. Oxford University Press, 1994, pp. 197– 248. [43] Pattanaik, P. K., and Xu, Y. Non-welfaristic policy assessment and the Pareto principle. Public Choice Conference, Nashville, march 2003. [44] Pattanaik, P. K., and Xu, Y. Conceptions of rights and freedom in welfare economics: a re-examination. In Against Injustice: Ethics, Economics and the Law, P. Dumouchel and R. Gotoh, Eds. Cambridge University Press, Cambridge, 2009, ch. 9. Previously published as Andrew Young School of Policy Studies Research Paper Series, Working Paper 0733, October 2007, http://aysps.gsu.edu/publications/2007/index.htm. [45] Puppe, C. Individual freedom and social choice. In Freedom in Economics, New perspectives in normative analysis [21], ch. 3, pp. 49–68. [46] Rawls, J. A Theory of Justice. The Belknap Press of Harvard university Press, 1971. Trad. fr. par C. Audard, Théorie de la justice, Points Seuil, 1997. [47] Samuelson, P. A. Foundations of Economic Analysis. Harvard University Press, Cambridge, 1947. [48] Scanlon, T. M. The moral basis of interpersonal comparisons. In Elster and Roemer [19], ch. 1, pp. 17–44. 26


[49] Sen, A. K. Collective Choice and Social Welfare. Holden-Day, Inc., San Fransicso, 1970. [50] Sen, A. K. The impossibility of a Paretian liberal. Journal of Political Economy 78, 1 (1970), 152–157. [51] Sen, A. K. Choice, orderings and morality. S. Körner, Ed. Blackwell, 1974, pp. 54–67.

In Practical Reason,

[52] Sen, A. K. On weights and measures: Informational constraints in social welfare analysis. Econometrica 45 (1977). rééd. in A. K. Sen, Choice, Welfare and Measurement, MIT Press, Cambridge, 1982. [53] Sen, A. K. Rational fools : A critique of the behavioral foundations of economic theory. Philosophy and Public Affairs 6, 4 (1977), 317–344. Réèd. in A. K. Sen, Choice, Welfare and Measurement, MIT Press, Cam´ bridge, 1982. Trad. fr. in Ethique et économie, et autres essais, PUF, pp. 84–106, 1993. [54] Sen, A. K. Personal utilities and public judgements : Or what’s wrong with welfare economics? The Economic Journal 89, 355 (septembre 1979), 537–558. [55] Sen, A. K. Utilitarianism and welfarism. The Journal of Philosophy 76, 9 (1979), 463–489. [56] Sen, A. K. Plural utilities. Proceedings of the Aristotelian Society 81 (1980-81), 193–215. [57] Sen, A. K. Liberty as control. Midwest Studies in Philosophy, Social and Political Philosophy 7 (1982), 207–221. [58] Sen, A. K. Rights and agency. Philosophy & Public Affairs 11, 1 (1982), 3–39. [59] Sen, A. K. Commodities and Capabilities. Oxford University Press, 1985. [60] Sen, A. K. Goals, commitment and identity. Journal of law, Economics and Organization 1 (1985), 341–355. 27


[61] Sen, A. K. Well-being, agency and freedom : The Dewey Lectures 1984. The Journal of Philosophy 72, 4 (1985), 169–221. [62] Sen, A. K. Foundations of social choice theory: An epilogue. In Elster and Hylland [18], ch. 8, pp. 213–248. [63] Sen, A. K. Rationality and Freedom. Harvard Belknap Presss, Cambridge (MA), 2002. [64] Sen, A. K. The idea of justice. Harvard University Press, Cambridge (MA), 2009. [65] Sugden, R. The metric of opportunity. Economics and Philosophy 14, 2 (1998), 307–337. [66] Tessier, P. Harsanyi, Sen ou Bentham. Quelle perspective adopter pour l’évaluation du bien-être en santé ? Revue économique 60, 6 (2009), 1309– 1333. [67] Yaari, M., and Bar-Hillel, M. On dividing justly. Social Choice and Welfare 1 (1984), 1–24.

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