Economic subjects | Economic history » Antoinette Baujard - A Utility Reading for the History of Welfare Economics

Source: http://www.doksinet A utility reading for the history of welfare economics ∗ Antoinette Baujard† December 3, 2014 Abstract Welfare economics has evolved during the twentieth century and came, some say, to a fateful dead end, preventing any rigorous contribution to policy recommendations. This trend is standardly explained by the controversy over the possibility and the relevance of interpersonal comparisons of utility. This analysis does not provide any hope to go beyond the bad news. Moreover, it fails to explain the possibility of a new welfare economics without comparisons Against the interpersonal comparisons reading, I claim a reasonable assumption is that under the discussion on comparisons, lies a fundamental evolution in the properties of utility. This paper presents a historical overview of the evolution of welfare economics through the XXth century, and derives a challenging explanation, the “utility reading”. It shows the evolution of welfare economics is

related to the characteristics of utility, notably its operational ability and its normative content. The paper concludes that the revival of welfare economics needs a specific notion of welfare, distinct from the utility concept used in microeconomics. Keywords: Welfare economics, history, utility, interpersonal comparisons of utility, cardinality, ordinality, welfare ∗ Though substantially different, a previous and extended version of this paper has been presented at the Summer School in History of Economic Thought and Methodology organized by BETA, Strasbourg University and Charles Gide Association in September 2003, and published as a Crem working paper in 2011 under the title: ‘Welfare economics is dead. Long live welfare economics!” A previous version has also been presented at the ESHET conference that was hel in Lausanne in May 2014. I thank the participants for their constructive comments, especially R Sturn I remain fully responsible for the views and mistakes

remaining in the paper. † Université Jean Monnet, Université de Lyon. GATE L-SE (UMR 5824) AntoinetteBaujard@univ-st-etiennefr 1 Source: http://www.doksinet Welfare economics is the economic study of the definition and the measure of social welfare. Its assesses the consequences of individual actions and public decisions on social states. It offers the theoretical framework used in public economics to help collective decision making, to design public policies, and to make social evaluations. The now old news of the death of welfare economics implies some inability to make any policy recommendation.1 This paper aims to provide an historical explanation of the reasons why welfare economics has evolved towards an inability or difficulty to provide sound prescriptions. This analysis may therefore contribute to imagine or settle new ways to forgo this bad news. An historical review describes an evolution of welfare economics through successive steps, as well as its division in

schools, and the clear cut partionning between disciplines. According to a standard reading I shall call it the “comparisons reading”, the evolution of welfare economics is explained by changes in the status of the interpersonal comparisons of utility.2 Let us recall the definition of comparisons In the case of intra-personal comparisons of utility, individual utility is called cardinal if it helps to account for the intensity of utilities. In such case, intrapersonal comparisons are meaningful: for one individual, she can compare social states at different times or different levels of utility. Conversely, it is ordinal if such intensity cannot be taken into account. Utilities just conveys information on orderings of social states: intrapersonal comparisons are meaningful to merely order social states. Interpersonal comparisons concern comparisons between different individuals If I say individual i derives a higher utility of her receiving good x than individual j receiving the

same good x, I make comparisons of i and j’s utilities derived from x.Comparisons of the utilities of different individuals reveal nec1 J. R Hicks (1939: 697)[27] notably wrote “Economic positivism might easily become an excuse for the shirking of live issues, very conducive to the euthanasia of our science.” Chipman and Moore (1978: 548)[11] added: “Judged in relation to its basic objective of enabling economists to make welfare prescriptions without having to make value judgments and, in particular, interpersonal comparisons of utility, the New Welfare Economics must be considered a failure.” E J Mishan (1981)[36] considers welfare economics was stuck in a dead-end. D M Hausman et M S MacPherson (1996: 96)[23] regretted that “Welfare economics is in limbo.” Ph Mongin (2002: 165)[37] at least provisionally, concluded: “Welfare economics died, or rather disintegrated progressively.” 2 This debate is particularly illustrated by the exchanges between Robbins (1932,

1938) [46, 47] and Harrod (1938)[21]. See also Hammond (1991)[20] On the reading of the evolution of welfare economics through the status of interpersonal comparisons of utility, see among many others, Hicks (1975: 310)[28]. 2 Source: http://www.doksinet essary to justify redistributive devices: “it is better to give x to individual i than to j”. They are also necessary to assess public policies who impact differently different individuals, ie, in the general case: “even though policy x reduces j’s utility, it sufficiently increases i’s utility to consider that x’s overall impact is positive for the society”. If no comparisons can be made, welfare economics cannot formulate any policy recommendations of such kinds. As we shall see in further details, the controversy on the status of interpersonal comparisons of utility is marked by a pendulum: from possibility to impossibility, from impossible to possible comparisons. The first movement (1890-1950) describes the

transition from welfare economics of Marshall and Pigou, whose recommendations are based on interpersonal comparisons, to the new welfare economics, where they are mostly prohibited. Either because such comparisons are not meaningful, or because they are value-laden, or both, they should be banished out of economic science, hence of welfare economics in particular. The second movement (1950-nowadays) describe the evolution from the arrovian impossibility theorem where they are banned, to new theses where such interpersonal comparisons are deemed necessary to address the specific issues of welfare economics, such as endorsing normative collective views and a possibility for recommendations. Now, this explanation can just hold if the possibility for collective normative judgments requires comparisons. A corollary is that, conversely, if no comparisons are possible, no collective judgement could be made. Nevertheless, in the theory of fair allocation and equivalence approach, social

welfare functions in which interpersonal comparisons of utility are still forbidden may exist. They can be used for evaluations, even considering distributive devices or in the general case of tradeoffs of interests. These new results contradicts seriously the reading of the evolution of welfare economics based exclusively on the status of comparisons (Fleurbaey and Blanchet 2013: 138–141[17]). Beyond this recent evidence of the failure of the comparisons reading, I claim it does fully explain the evolution of the field since the very beginning. Moreover, it is unable to lift the difficulties lead with the death sentence I therefore suggest to scrutinize further the explanations of the driving forces of the evolution of welfare economics, and conduct this study since the first stages of welfare economics. Behind the status of comparisons indeed, it is necessary to consider the framework constraints, and the properties of the used tools, entailed by the different stages of welfare

economists to understand what fundamentally explains the successive judgments of comparisons. 3 Source: http://www.doksinet I do not contest the importance of comparisons in the evolution. Farther and more importantly, my claim is that the analyses of the status of comparisons cannot but be explained by the properties of utilities. This paper aims at showing that the evolution of the concept of utility in economics through the XXth century therefore appears to be the primary explanation to the historical evolution and the fate of welfare economics I shall call this alternative reading the “utility reading”. The history of welfare economics is hardly known and studied. Most textbooks on history of economic thought do not even develop a chapter on welfare economics (except maybe the still forthcoming Baujard 2010,2011,2012[5, 4, 6]). Even more, very few articles consider the history of welfare economics as a whole. A notable and important exception is Mongin (2002[37]), which

addresses the issue of its evolution yet does not question the driving force of such an evolution. A difficulty is indeed that welfare economics covers a wide scope of sub-disciplines, including theoretical foundations of microeconomics, public economics, cost-benefit analysis, social choice theory, theory of fair allocation. There exist historical links between all these knowledges, moved by common questions or solutions, whose divergences come from different solutions to similar questions. But they are hardly commented anywhere as a whole. The thesis according to which the properties of utility is the most fundamental issue for welfare economics is present in the philosophical and the formal analysis of Mongin and d’Aspremont (1998)[39]. The rejection of the comparisons reading is explicit in Mongin and Fleurbaey (2005[18]) as well as in Fleurbaey and Blanchet (2013[17]), but just concerns the last stage of welfare economics. The utility reading is implicit in both Moscati’s

(2013a,b[40, 41]) articles. He defends the idea that behind the actual formal definition of cardinal or ordinal utility, authors may have retained different properties of utility, in particular for the sake of measurement. Yet he does not tackle the specific normative context of welfare economics in which comparisons are central. To my knowledge, no papers have ever made an historical reconstruction of the evolution of welfare economics through the utility reading, let alone have eventually concluded on the importance of the interpretation and formal properties of utilities in this evolution. The interest of this paper primarily lie in the defense of the “utility reading” of the evolution of welfare economics which challenges the well estab- 4 Source: http://www.doksinet lished “comparisons reading”. A side product of this study is the provision of a presentation of the history of welfare economics, while this unfortunately appears to be a scarce resource. Another side

product is to establish a link between comparisons and properties of utility. I first present the historical overview on the basis of which this analysis shall be conducted, and I shall recall the status of comparisons at each stage of welfare economics (section 1). After this, I will consider each period and study what in the properties of utility, beyond comparisons, explain the evolution. I shall not come back to the utilitarian heritage, and I shall start the discussion with the old welfare economics. In the first described period, section 2 describes which interpretation of utilities was assumed for making comparisons. Section 3 describes what notion of utility entailed their banishment, well explicated in the literature since the thirties. Section 4 discusses the relevance of Arrow’s result of the early fifties for studying interpersonal comparisons of utility, and opposes a slightly but substantially alternative explanation, in terms of richness of information on utility.

Section 5 explains under which conditions on the properties of utility the impossibility verdict can be overcome, should interpersonal comparisons be reintegrated or not. 1 An historical overview of welfare economics Although storyboards in successive periods are always somewhat artificial, we can expect a better understanding of the studied dynamics to emerge from it. Let us keep in mind that there should be no fetishism of the dates and of the blocks of contributions here proposed: this presentation is only instrumental. I provide a presentation of the historical evolution of welfare economics and its different approaches. I distinguish four successive steps3 , the two last being the most important for our scrutiny: [1790–1890] Since Bentham’s works on the principle of utility, the utilitarian legacy shall weigh heavily on the future welfare economics. Social welfare is assessed on the basis of individual utilities. The utility principle 3 For lack of space, I shall not

recall extensively in this article the details of each of these steps. The division in successive periods I here retain is presented through Mongin (2002)[37], Baujard (2010,2011,2012)[5, 4, 6]. See also, yet only partial presentations, Samuelson (1947)[50], Hicks (1975)[28], Cooter and Rappoport (1984)[?]. 5 Source: http://www.doksinet says that an individual shall and should promote her utility. It also says that the collective aim is to promote social welfare. This duality of the utility principle, defined at the individual and the collective level, generates some tensions. Although the issue of interpersonal comparisons of utilities is not explicitly raised at the time, the problem of the sacrifice of some individuals’ utilities for others which is directly linked to it is already important. This may explain the evolution within the family of the utilitarian philosophical theories (Baujard 2013[?]). As it is not formally part of welfare economics, I shall not develop this

period further in this paper. [1890–1940] “The old welfare economics”, which foundations are found in A. Marshall (1890)[34], is well represented by A C Pigou (1920)[44] This work aims to study the conditions of well-being in terms of market Pareto optimality. It is historically first applying the utilitarian project within the economic framework although authors wanted to become more independent of these philosophical traces. Interpersonal comparisons of utilities are well accepted as far as distributive aspects are central in the project of the first welfare economics. [1940–1950] The “new welfare economics” emerged in the late thirties, early fourties. It establishes a clear separation between the study of optimality conditions of social situations the study of the functioning of the market. We can distinguish between two approaches which we choose to label ”American” or ”Bristish” for the sake of clarity4 . The British approach is well-represented by N. Kaldor

(1939), J Hicks (1941) and T. Scitovsky (1941) They developed a new concept of Pareto improvements, the ‘Pareto efficiency criterion’, which considers the possibility of hypothetical compensations among individuals, and then applies the test of unanimity. Because the compensations are just hypothetical, their consideration are supposed not to imply any actual interpersonal comparisons of utility. 4 What goes well without saying, goes even better when you say it. Although we have here labeled the schools by some of their representative countriesUS, GB, no fetishism of the label should hold. Each of these school is before all international For instance, the ”Critics of welfare economics” of the Englishman Ian Little could be considered as belonging primarily to the the american Approach (Little 1950[33]). Conversely, many people in the US and elsewhere shall ground their practice on the Kaldor-Hicks justification, notable the hypothetical (or equivalent variations) among others,

to justify cost-benefit analysis, is well established in American agencies. 6 Source: http://www.doksinet The American approach, represented by A. Bergson (Burk 1938)[10], O Lange (1942)[32] and P. Samuelson (1947)[50], considers that normative judgments are contained to a subset of acceptable value judgments The Pareto criterion is one of them. They shall try to conceive a framework based on strictly ordinal utilities. [1950–nowadays] K. Arrow (1951,1963)[1, 2] established the impossibility of deriving a social utility function on the basis of individual preferences without resorting to interpersonal comparisons, as he himself interpreted. A clear separation between disciplines has resulted from this bad news. The problem was to be able to say something about social welfare and public decision. Arrow’s theorem was saying something that could be interpreted as an impossibility to build a social welfare function, as developed in the American approach. The British approach

therefore had a much greater appeal. It could be considered as immune from the Arrow’s result and it actually allowed for public recommendations Contemporary welfare economics developed in the wake of what I have called ‘the British approach of welfare economics’. It is well-represented by public agencies and most economic theorists in international, geographical or industrial economics in their welfare analyses, Important names are for instance Tinbergen, Haberger or Marglin. Welfare is there analyzed through surplus computations or cost-benefit analysis. Important researches have been conducted to be able to understand the theoretical foundations of the welfare evaluations based on compensating variation (or equivalent variations), as well as develop new tools to compute shadow prices. Normative issues as such are excluded from the scope of these analyses. They are left for an independent political treatment of distributive issues. It can be shown that interpersonal comparisons

are made, but at least they are not made explicitly. Besides, the French school of public economics focuses on theoretical reflection on the economic role and the decisions of the public sector (Kolm (2010[31]) . New tools are designed to settle optimal pricing of public goods, regulation, contribute to evaluate projects of public investments. Some “normatively motivated agents having some power” are supposed to chose and use economic tools to enhance social welfare through the choice of public policies. Some instances of such civil servants may be, after Jules Dupuit, Pierre Massé, Marcel Boiteux, François Divisia, René Roy or Serge Kolm. There the problem of interpersonal comparisons of utilities is hardly raised because 7 Source: http://www.doksinet there is no need to consider individual utilities as such. What is at stake is the personal judgment of a benevolent and higher technically trained civil servant on what is the public interest, as captured through the

choice of a social welfare function. Interpersonal comparisons are hence made, but they are normatively defined and personally justified by the view of the public decision maker. On a totally different approach, a normative economics emerged again to go beyond Arrow’s impossibility. Social choice theory constitutes consistent answer to the arrovian challenge and try to go beyond an impossibility. They eventually focus on a strict problem of aggregation, and has more or less became a part of voting theories, often letting alone the actual welfare issues. The theory of fair allocation was born in the 1970ies. The technics they used were inspired by the arrovian framework but they deliberatly The question of normative criteria is the central stake. There interpersonal comparisons are perfectly identified, analyzed and justified when they exist. 2 The age of interpersonal comparisons of objective and normative utilities In the old welfare economics, I denote two domains, surplus and

Pigou-Dalton transfers, which criticisms have led to the evolution of welfare economics. It is common to summarize it by considering the implications of these criteria on interpersonal comparisons of utility. I shall defend that the interpretation of utilities is eventually at stake in both cases. The need, the computation and the intellectual origin of comparisons of utilities is well illustrated by the consumer’s surplus. The notion of surplus, or rent – which goes back to the similar ‘total relative utility’ of J. Dupuit (1844)[14] – became a standard tool in economics after A. Marshall (1890)[34] to assess the intensity of the happiness of each individual. Dupuit needed to answer this question to be able to assess whether it was worth spending money on building new public infrastructures, e.g concert hall, roads or navigation channels. Marshall used the surplus notably to study the impact of a modification of prices, for instance due to consumption taxes or subsidies, on

each individual’s utility, and from then on, on the society’s welfare. As we all know, consumer’s surplus is the area between the demand curve, and 8 Source: http://www.doksinet the price line; the producer’s surplus is the area between the price line and the supply curve. At the individual level, utility is objectified by a monetary measure 5 . By summing the willingness to pay at different quantities, it provides a metric of intensity of utilities, assesses cardinal individual utilities, and implies intrapersonal comparisons. At the collective level, when used to sum or weigh different individuals surpluses – as necessary to consider social welfare –, it assumes the possibility of interpersonal comparisons. Surplus computations are very much used in welfare economics – even nowadays. If we accept that intrapersonal comparisons are meaningful, do interpersonal comparisons make sense? First, assuming that the metric of cardinal utility provided by surpluses is

satisfying, whether we can use them as such to compare different individual’s utility depends. It depends on the heterogeneity of agents. They are homogeneous if each of their demand curve looks the same, and their ability to produce utility from the commodities or the policy at stakes are similar. Unfortunately, people in a society are not homogenous in this sense: it is difficult to consider producers and consumers on the same ground, or that winners or losers of a policy belongs to the same class of the society. Marshall is well aware of this restriction, so that, when elaborating on surplus, he assumes that most of the situations studied by political economy affect in approximately equal proportions the different classes of society, and consider the social utility, as the individual utility of an average man6 . This strong assumption allows to erase the problem of heterogeneity of agents, and thus that of difficulties in justifying interpersonal comparisons. Second, Walras raised

an objection at Dupuit’s ‘relative utility’. Even though the analysis of the latter is different (due to a different demand curve in both case: Dupuit plots it on a price-quantity axis, while Marshall considers a quantity-price axis), the criticism holds for both cases. Walras regrets that this construction is based on a confusion between the utility function and the demand function, whose interpretation, and properties may be different. He could have thought of the differences between interpreting a choice and a necessary positive utility, but focuses on a 5 “ The excess of the price which he would be willing to pay rather than go without the thing, over that which he actually does pay, is the economic measure of this surplus satisfaction. It may be called consumer’s surplus” It should be noted that this is a quote of the 9th edition. In the original text of 1890, Marshall speaks not of ‘consumer surplus’ but the‘rent consumer ’. (Marshall 1890: 124[34]) 6 For a

detailed presentation of the ‘average man’ or ‘normal’ and considerations on the “median man”, see Martinoia (1999: 322 ff.) [35] 9 Source: http://www.doksinet strict internal criticism, proper to the general equilibrium thesis against partial analyses. Prices variations indeed modifies the budget constraint, hence should entail a modification of the demand of other goods, and the prices of other goods. This has but an effect on utility which is unduely neglected by surplus analysis. Along the same line, Pareto (1892, 1896)[42] remarks that surplus analyses implicitly assume that marginal utility of money is constant. He shows that if this should hold, the price elasticity of all goods should equal to -1, which is highly impossible. Third, Samuelson (1942)[49] regrets the confusion between the assumption of constant marginal utility of money – which may be considered as reasonable, though it is not properly at stake in surplus analysis – and the assumption of

constant marginal utility of income – which is the relevant issue for surplus. In the latter case, Samuelson insists that is very unlikely that this assumption holds. It is fair not to consider the criticisms addressed at surplus just concern the mere comparisons of utility. These criticism are more substantially led to the interpretation of utility and the properties of the utility functions. First the meaningfulness of comparisons derives from that the possibility ot aggregate individual surpluses; and the latter relies on the heterogeneity or homogeneity of the ability of different individuals to derive utility from the same attributes, hence on the assumption of a plurality of utility functions in the society. Second, the confusion between demand curve and utility function relies on an interpretation of utility which would more or less directly led to individual demand behavior, and to the relevance of computing utility within an analysis of partial equilibrium rather than in of

general equilibrium. Third, assumptions on marginal utility of incomes have a direct consequence on the possibility and interpretation of comparisons. Let us now turn to the case of Pigou-Dalton transfers (Pigou 1920: chap. 8)[44] They consist in this judgment. Let us say you want to compare two incomes – or welfare, national dividend, or whatever – distributions. Consider the following happens. (1) Individual p is poorer in x than in y of the amount δ; (2) individual r is richer in x than in y of the amount δ; (3) individual r is richer than p in state x, and at least as much richer than p in state y; (4) all other individuals remain unaffected between x and y. This change may result of a regressive transfer from the rich guy of the amount δ to the poor guy from x to y. After such a transfer, called Pigou-Dalton transfers, distribution y shall be judged less unequal than x. Pigou considers that the economic welfare of the society shall be higher after transfers than before 10

Source: http://www.doksinet transfers if nobody’s welfare is decreased (Pigou 1920: 87-97)[44]. Of course, such transfers imply interpersonal comparisons of utilities. Because social welfare is higher when rich people are not so rich and poor people are not so poor, it is socially better to transfer income or utility from certain people to others: the latter shall produce more social welfare than the former. More fundamentally, committing to the principle of transfers entails two implicit and necessary assumptions on utilities: they imply value judgment hence they are normative utilities, and they are objective. First, utilities have an unavoidable normative status: any social welfare judgment imply some values judgments. Pigou, as an economists of the old welfare economics does not hesitate to explicitly recognize his a priori egalitarian position. Notice surplus may have a similar interpretation – although Marshall does not make a similar confession, and even pretends his

framework is free from any utilitarian traces7 –, aggregation of surpluses of different persons suppose a normative position8 . The assumption of homogeneity of agents should make the trick. Let us say each time the tool is used when the assumption does not hold, then the use of surpluses is value-loaded. Second, utilities should be objective. Utility is objective when it is interpreted as a state of the world such that it can then be computed equally by any observers. If utility is measured by the time to smile in a day, by the amount of calories consumed per week, by a monetary assessment of happiness, or any other uni-dimensional objective attributes of the same type, then they are quantifiable under a common metric, whoever the observer is. Comparisons of different utilities do not only make sense, they are possible and easily tractable. Furthermore, in each of such cases, the sum of utilities makes sense. Such computation are possible in Pigou’s framework since he defines

welfare economics as the study of a part of welfare which is quantifiable with the measuring rod of money9 . More generally, the objectivable nature of utility allows for this quantification and comparisons. Notice this 7 See Martinoia (1999)[35]. J. Schumpeter (1954: 415)[51] indeed considers that surplus is merely utilitarianThis is just one reference defending this position, among many others. 9 “The range of our inquiry becomes restricted to that part of social welfare that can be brought directly or indirectly into relation with the measuring-rod of money. This part of welfare may be called economic welfare.” (Pigou 1920: 11)[44] See also Hicks’s interpretation (Hicks 1975)[28]. Quantification, in Pigou’s framework, is notably possible thanks to the use of national dividend. 8 11 Source: http://www.doksinet analyses could also be applied to the surpluses analyses. Indeed surpluses are being objectivized thanks to the computation of monetary measures on the basis of

the demand curve. I do not intend to say that objective utility is a necessary nor a sufficient property to allow for any quantification and comparisons. Some scholars spent much effort to justify intra and interpersonal comparisons of subjective utilities; conversely, objective utilities do not imply the total absence of idiosyncrasy, and further work may be required before making comparisons with such objective utilities (Bentham 1789[7], Baujard 2009[3]). What I put forward here is that a metric is much easier to find in such context, such that inter-and intrapersonal comparisons are meaningful with less difficulties –and no need for primary work – for objective utilities10 . Let us conclude on the first welfare economics. What makes policy recommendations possible is the possibility of comparing utilities intra and interpersonally But such possibility is more fundamentally due to certain assumptions on the homogeneity of utilities, and the objective and normative properties of

utilities. 3 The age of questioning comparisons: Compensations between subjective utilities From the thirties onward, interpersonal comparisons of utilities have been strongly criticized. Most welfare economists then refrained from using any L. Robbins claims, in his famous essay of 1932, that any interpersonal comparisons of utility, and in particular the use of the (standard) assumption of decreasing individual marginal utility in an interpersonal context, are, subjective in the following sense: they cannot be the result of any scientific demonstration11 . The intensity of satisfactions of two different individuals 10 A similar argument is the essence of the controversy between R. Cooter and P Rappoport (1984)[12], Rappoport (1988)[45] one hand and P Hennipman (1988)[24] another 11 “They are in fact entirely unwarranted by any doctrine of scientific economics [.] The proposition we are examining begs the great metaphysical question of the scientific comparability of different

individual experiences. [An interpersonal comparison] is a comparison which is never needed in the theory of equilibrium and which is never implied by the assumptions of that theory. It is a comparison which necessarily falls outside the scope of any positive science. To state that A’s preference stands above B’s in order of importance is entirely different from stating that A prefers n to m in different order. It 12 Source: http://www.doksinet indeed cannot be measured nor compared, whichever by introspection or observation, i.e by any scientific method All assumptions about the equal or unequal ability of individuals to transform purchasing power, goods or attributes into utilities are inevitably based on value judgments or conventions. Now, whereas science studies observable facts and is aimed at some objectivity, the consideration of value judgments belongs to a normative discipline. It follows that they should be excluded from the scope of science If we rephrase, science

just tackles positive facts, interpersonal comparisons of utility are normative rather than positive; such normative issues can never be considered as scientific. If economics is a science, it cannot rely on interpersonal comparisons12 Here, the argument is clear: interpersonal comparisons should be ruled out per se. Let us consider what argument of intrinsic importance has contributed to provide Robbins’ essay such a large echo, not only in welfare economics but in economics in general, and which still rings today. The reason why Robbins rejected comparisons is based on the will to contain economics within the scientific method.13 Restoring the scientificity of economic study entails two implications for welfare economics: a positive interpretation of individual utility is required, and a neutral criterion of aggregation of these individual utilities is needed. The first implication becomes possible thanks to the emergence of the new demand theory. R G D Allen and J Hicks (1934)[26]

reconstructed the theory of demand on the basis of marginal rates of substitution between goods, and of elasticities of demand with respect to price and income. Utility functions are used to account for the complexity of income effects and involves an element of conventional valuation. Hence it is essentially normative It has no place in pure science.” (Robbins (1932: 130 ff )[46]) 12 Notice other critics, on operationality, or on moral stakes (including the justification of circus games, the number wins, and the question of separeteness of the person), have also considerably weakened the popularity of interpersonal comparisons in welfare economics, yet much later on. 13 Notice this is an old argument, which was already present in Pareto’s work. He presents his projects of creating a pure economics as strictly scientific in the sense that we can strictly on facts. This position entails his famous, yet too often forgotten distinction between (subjective) ophelimity and (objective)

utility (Pareto 1896)[42]. We even here touch the limits of chronological presentation: Pareto who wrote in the late XIXth or very early XXth century should be considered as the first author of this second period which we artificially stated it started in the thirties. 13 Source: http://www.doksinet substitution effects between goods. Utilities yet only convey ordinal interpretation related to each consumer’s behavior, and does not at all stand for any normative notion of welfare. There is no reason, in particular, to choose a common scale to capture individual’s i demand behavior in good x or y, and to capture individual’s j demand behavior in those goods. Limited to the theories of demand and exchange, such a concept of ordinal utility is not compatible with any interpersonal comparisons of utility: they would be meaningless. Without any comparisons, it may seem difficult to assess which the best policy is when the welfares of different individuals are concerned. As a

second consequence, finding another aggregation principle remains necessary L Robbins, and many others, suggests to keep up with an attitude of minimum attention to optimality criteria. Welfare economics should contend with finding the optimal means to achieve a consistent end14 : this may at least avoid inconsistent policies. Pareto criterion is a good candidate for this15 : if people are unanimous to order a pair of options, this ordering should be reflected in social preference, or, at least, the social preference should never contradict the unanimity of preferences. This criterion can be translated as a condition of effectiveness: a state is Pareto efficient if it is impossible to improve the status of any individual in the society without damaging the situation of at least one of them. The information used to apply this criterion is limited to individual utility comparisons between pairs of options, hence to strictly ordinal utilities. No other criterion would be able to avoid the

need for interpersonal comparisons, and these would not be meaningful As a conclusion, what explains the rejection of interpersonal comparisons is an evolution of the properties of utility used in economics – i.e ordinality –, which gathers the overall project of doing a science with economics. Let us go a step further in the historical overview. The Pareto criterion alone does not allow to decide when there is a conflict of interest. A ranking of social situation just based on the Pareto criterion in this case is incomplete: it merely cannot decide. Most of the time though, policies do entail winners and losers. A criterion which just concern improvements that may not affect negatively anybody is most likely mute to assess most policies. To achieve a more complete ranking of social situations and be able to make 14 See Robbins (1932: 134)[46]. See also E. Barone’s works See Samuelson (1947: 214-217 )[50] or Schumpeter (1954: 416)[51]. 15 14 Source: http://www.doksinet

policy recommendation, a trick consists in sticking to situations that are potentially better in the sense of the Pareto criterion, rather than just better in the sense of the Pareto criterion. Considering potential improvements considerably extends the scope of this criterion. The principle of compensation criteria was introduced by Kaldor in 1939 and developed by Hicks and Scitovsky, whose contributions are sometimes labelled as belonging to the British approach to the new welfare economics. Potential transfers permit to transform incomparable situations into comparable situations in the sense of Pareto. The argument is the following Going from a first situation x to y may create winners and losers, so that the two situations are not comparable. Yet, in the case where transfers from the winners to the losers would increase the situation of the latter until a point where they do not strictly prefer the status quo to the new situation, we can say the new situation is better in the

sense of Pareto.16 The actual decision of making transfers or not is fundamentally a distributive issue, involving normative questions, which are not in the scope of economic science. This decision is hence not the role of an economist, and belongs to the decision-maker. This separation of tasks guarantees that no normative issues are involved in the economist’ assessment of the situations. With such potential transfers, the situations are ordered according to the Pareto criterion, yet still considering strictly ordinal considerations, and a priori no interpersonal comparisons of utility. These transfers have been both widely used and strongly contested. First, they entail inconsistent rankings of social states. John Chipman and James Moore (1978) showed that: “The welfare criteria suggested by Kaldor and Hicks, even with the qualifications added by Scitovsky and Kuznets, could not escape the possibility of giving rise to an inconsistent sequence of policy recommendations, unless

either the distribution of income and wealth or the forms and degree of dissimilarity of consumers’ preferences were assumed to be suitably restricted.” 16 Let x, y, z be social states. According to Kaldor’s criterion (1939)[29], x is preferred to y, if, from x, it is possible to get to state z by transfers, and such that the potential state z is better than y, Pareto-wise. According to Hicks’s criterion (1939)[27], x is preferred to y if, from y, it is not possible that, by transfers, to obtain a state z that would be preferred Pareto-wise to x. According to Scitovsky’s criterion (1941)[13], x is preferred to y if both Kaldor and Hicks’s criteria are satisfied. 15 Source: http://www.doksinet In particular, there exist cases of intransitivities that cannot be eliminated but if individual preferences are all identical and quasi-homothetic. In other words, either the criteria entails inconsistency, either exaggeratedly restrictive assumptions on preferences or individual

states must hold.17 Furthermore, these criteria are not strictly equivalent to the Pareto principle A positive number of successive compensatory changes may not correspond to a Pareto improvement. According to Boadway paradox (1974), a move from of a Walrasian equilibrium to another may result from such compensatory changes even if there were no gain of efficiency. In short, the words ’Pareto criteria’ do not necessarily mean what they mean. Second, even though interpersonal comparisons of utility are avoided, the normative criticism linked to these comparisons still holds. On the one hand, if transfers are eventually made, it is enough to observe ex post that the new situation is better, Pareto-wise, than status-quo, so that these criteria are redundant (Sen 1979:25). On the other hand, if transfers (hypothetical compensation) are not done, it is trivial to say that losers do loose. The mere idea that compensations could have been possible is little consolation. As Marc Fleurbaey

(2008: 3.1) said: “Such criteria are then typically biased in favor of the rich whose willingness to pay is generally high (i.e, they are willing to give a lot in order to obtain whatever they want, and therefore they can easily compensate the losers; when they do not actually pay the compensation, they can have the cake and eat it too).” Persons with the highest willingness to pay are the most advantaged, which we can but recognize is a partial view. Last but not least, when you throw interpersonal comparisons by the door, they may well come back by the windows. Considering that compensations may be realized logically implies that compensations are meaningful. Transfers allows to compare losses and wins on monetary terms, which advantage is to be interpersonally comparable. To devise the application of compensation tests, comparisons are basically possible and necessary, implying that utilities are now reduced to their mere proxy, i.e, willingness to pay (or to accept) These

normative criticisms basically entails a standard assessment of the test of compensatory transfers: 17 Notice these restrictions are similar to those described above for Marshall surplus to hold. 16 Source: http://www.doksinet it is utilitarian without saying his name, and pretending to be neutral and scientific (Worland, 2005). Chipman et Moore (1978: 581, 584) conclude: “When all is said and done, the New Welfare Economics has succeeded in replacing the utilitarian smoke-screen by a still thicker and more terrifying smoke-screen of its own.’ [] After 35 years of technical discussions, we are forced to come back to Robbins’ 1932 position. We cannot make policy recommendations except on the basis of value judgments, and these value judgments should be made explicit. [] Judged in relation to its basic objective of enabling economists to make welfare prescriptions without having to make value judgments and, in particular, interpersonal comparisons of utility, the New Welfare

Economics must be considered a failure.” In a nutshell, the actual banishment of interpersonal comparisons, fundamentally linked to the evolution of the concept of utility used in micreconomics in order to make economics a science, comes with the impossibility of welfare economics to make policy recommendations. The British approach to the new welfare economics has developed an successful attempt to reestablish the possibility of recommendations –successful in the sense that it soon became widely used and inspiring for cost-benefit analysis. Yet we have shown it supposes a silent reincorporation of comparisons, implying again a reassessment of the interpretation and the properties of utilities. 4 Arrow’s theorem without comparisons The history of welfare economics has been widely disrupted by the Arrovian impossibility result. At the very beginning of the fifties (1951[1]), Arrow explored whether a rational social preference relation can be derived from the ordinal rational

individual preferences. Four conditions should hold18 The condition of universal domain allowing for any profiles of individual preferences captures the 18 We here just briefly recall the theorem. See, eg, Arrow 1963[2] or Gaertner 2006[19] for a more detailed presentation and some proofs. 17 Source: http://www.doksinet sovereignty of individuals, who may have any preference without any restriction. Pareto condition guarantees that the society should not contend with an option that would be Pareto dominated by another; and if everyone prefers one option to another, then the society prefers the former option to the latter. The condition of independence to irrelevant alternatives (now denoted IIA) requires that, if everything keeps the same except, the ranking between two alternatives for two individuals, the social ranking of these two alternatives does not depend on other alternative neither on the preference of the others, neither of the names of these two individuals. Finally,

a non-dictatorship condition requires that there does not exist any decisive individual on every options, i.e, an individual whose preference on any pairs of options always replicates into the social preference. Arrow’s theorem establishes that there does not exist any rational social preference relation that satisfies these four conditions simultaneously. The mathematical framework used by Arrow to tackle the problem of aggregation is based on binary relations, unlike the analysis of continuous functions standardly used in microeconomics. Within this framework, the condition IIA imposes that the information on individual preferences is restricted to binary information only, i.e, on pairwise comparisons over social states only. This allows Arrow to remain faithful to ordinalism, not only standard in the field of consumer’s demand theory but also in the analysis of social welfare after Bergson. The main reason for attributing such an importance to ordinalism is that the intensity of

utilities cannot be observed experimentally (at least easily), hence there is no way why such information may seriously be considered as scientifically relevant for the computation of social welfare. This change shall have dramatic consequences. Let us say, for instance xPi yPi z and yPj x hold.19 The only relevant information for the arrovian 19 For all i, Ri is the preference relation of individual i between two social states, such that xRi y reads: “individuals i weakly prefers option x to y”, or, “according to individual i, x is at least as good an option than y”. This individual preference Ri is a complete preorder, i.e, it satisfies properties of reflexivity, transitivity and completeness Relation Ri is reflexive if and only if: ∀x ∈ X, xRi x. Relation Ri is transitive if and only if: ∀x, y, z ∈ X, xRi y and yRi z ⇒ xRi z. Relation Ri is complete if and only if: ∀x, y ∈ X, xRi y or yRi x. Individual preference Ri is defined by: ∀x, y ∈ X, xPi y ⇔ xRi

y and no-yRi x. It is asymmetric if: xPi y ⇒ no-yPi x, which corresponds to strict individual preference. It is symmetric if : ∀x, y ∈ X, xIi y ⇒ xRi y and yRi x The symmetric part of the individual preference corresponds to indifference. Respectively the asymmetric and 18 Source: http://www.doksinet framework is: xPi y, xPi z, yPi z and yPj x. If we say beside that individual i prefers more x to y than j does prefer y to x, it seems possible to compensate the loss of utility of individual j by the increase of utility of individual i. By comparing gains and losses, we could reach a social agreement, and deduce that x is better than y for the {i, j} population, as in the analyses of surpluses or potential transfers. IIA condition prevents any such conclusion since no information on interpersonal comparisons is contained in the pairwise comparisons. IIA does not though require unanimity to infer a social preference. There may well be disagreement between individuals and still

a solution. IIA does not exclude all kinds of interpersonal comparisons In case of disagreement between i and j over x and y, the social preference should remain still when the names of the concerned persons i and j, and/or of the options x and y, are permuted. Beside, the observation such that individual i prefers more x to z than he does prefer x to y – as implicit in the first description of i’s preference – cannot be taken into account because of IIA. Rather than an interpersonal information, IIA has here excluded an intrapersonal information from of the consideration of social welfare, the characteristics of individual trade-off between three social states, as fully described in the usual indifference curves. “The social welfare function was to depend only on indifference maps; in other words, welfare judgments were to be based only on interpersonally observable behavior. The Condition of Independence of Irrelevant Alternatives extends the requirement of observability one

step farther.” (Arrow 1963[2]: 109-110) In other words, there is here a sort of confusion between two sorts of properties: comparability in the one hand, ordinality in the other hand. Let us make a retrospective analysis of Arrow’s justification of IIA. According to the principle “if you can move mountains you can move molehills”, the focus on binary information was indeed a sufficient condition to rule out interpersonal comparisons of utilities (Arrow 1963: 32). It is though not necessary to rule out all but binary information to contend with ordinal preferences. Although the restriction to binary information allows the exclusion of interpersonal comparisons of utility but is not necessary to exclude them, it is one possible explanation for Arrow’s negative result. Let us develop this conclusion. With the sole information available in the binary framework imposed by IIA, the comparison of any two options y and x is just based on individual preferences over x and y, and no

other options, i.e, the preference symmetrical part of Ri are written Pi and Ii . 19 Source: http://www.doksinet profile is such that i prefers x to y and j prefers y to j. By the unrestricted domain condition, this could be compatible with any preference profiles, including xPi y or yPi x, yPi z or zPi y, and xPi z or zPi x. Knowing that xPi y, imagine we had the following profile: yPi z and zPi x. Individual i’s preference is hence intransitive (or inconsistent since we get xPi y and yPi x) Saari (1998)[48]’s interpretation is that the arrovian framework imposes no objection to the consideration of irrational individual preferences, so that the transitivity of the social preference is a plausible risk. In general words, the arrovian framework induces the exclusion of some relevant description of the individual ordinal preferences, from which the impossibility is derived. An explanation for the impossibility was the poverty of information on preferences, strictly reduced to

binary comparisons. It aimed at avoiding the computation on intensities of utilities or comparisons of utilities, but it went much further. It totally prevented to use information on ternary comparisons for instance. Whereas Arrow interprets the choice of IIA as necessary to avoid comparisons, we see it as responsible for much further and unnecessary20 restrictions. Although a common reading of Arrow’s impossibility is that the ban of interpersonal comparisons is responsible for the impossibility of social choice, my demonstration shows that another property of preferences may be held responsible for the impossibility, namely, the access to more than binary information on ordinal preferences. I claim this is historically due to the influence of revealed preference theory in Arrow’s vision of what a good intepretation for preferences should be. The Arrovian result may be considered as the death knell of social choice. Some also derived another reason for the death of welfare

economics in general. 5 The need for enriching information on utility Two obvious distinct moves have resulted of the schock induced by Arrow’s theorem. On the one hand, social choice theory, faithful to the arrovian framework, developed in the area of binary relations to thrive to go be20 Unnecessary to be consistent with the reasons developed by Arrow. 20 Source: http://www.doksinet yond the impossibility. On the other hand and totally independently – and indifferently–, welfare economics developed in a totally different framework: the British approach, pretending not doing any interpersonal comparisons of utility was at least succeeding in providing collective recommendations. These two trends constitute important sub-disciplines of economics. I shall however focus on two other evolutions, that took some time to establish as relevant solutions for welfare economics. The first evolution is based on the considerable influence of A. K Sen (1979)[54] in social choice

theory and in normative economics in general. He considers that the problem of social choice can be overcome by allowing comparisons interpersonal utility, and by enriching the information contained in the utility that is to say, using post-welfarist evaluations of social states. An assessment is welfarist if it is based exclusively on information on individual subjective utilities; it is post-welfarist if it takes into account information of other kinds (See, e.g, Sen 1970, 1979, 1985, 1991, 1999[52][53][54][56][57][58], and Pattanaik 1994[43] or Sugden 1993[59]). The possibility of comparisons critically depends on a renewal of interpretation of utilities (See Baujard 2003). This obvious link is not explicitely put forward by Sen to my knowledge, but essential to understand the solution here provided When utilities are subjective, comparisons are not meaningful. A condition for restoring the possibility of comparisons is to change in the intepretation of utilities. In his essential

role in the existence and the development of the debate against welfarism, Sen indeed defended the use of more objective information on individual welfare. This evolution has further consequences The focus on objective utilities may suppose multidimensional accounts for the quality of life, it is necessary to identify these dimensions. All this process may be best conducted by a team of multidisciplinary workers. In a nutshell, the use of objective utilities (with comparisons indeed) is a solution for welfare economics. The second evolution is meanwhile older and more recent. Older because it is inspired by ‘the American approach’ to welfare economics since Samuelson and Bergson. Social welfare should there be interpreted as the view of the whole society (Bergson 1954: 242[8]; Arrow 1963: 107[2]). A problem is hence raised to identify which view should be retained by welfare economists. At least should it respect three distinct conditions First, social welfare is based on

individual preferences only this condi- 21 Source: http://www.doksinet tion corresponds to what Samuelson calls individualism in his 1947 book and Sen later called ‘welfarism’. Second, welfare economics does not pretend to exclude interpersonal comparisons of utility, but it should contend with a minimum number of normative criteria21 : the Pareto criterion and a restricted number of redistributive criteria (typically the Pigou-Dalton principle of transfers). Third, such criteria are transparently captured trough a social welfare function. An important question is whether Arrow’s result concerned or not the existence of any social welfare function. The debate really was born in the 70s. Certain theorists defended this view: it is impossible to find a “reasonable Bergson-Samuelson [function] based on individual orderings” (Kemp and Ng 1976: 59). The explanation they provided was that “the Bergson function must make interpersonal comparisons [of utility] or be

dictatorial” (Parks 1976: 450) Others, namely Samuelson, considered the result had nothing to do with welfare economics. We talk of a more recent than Sen’s rehabilitation of comparisons of utilities, because the evolution I want to put forward here is mainly conducted by Marc Fleurbaey since the 1990ies. Firstly, they reinterpret Arrow’s impossibility Rather than a restriction to ordinal information, Arrow restricts information to binary comparisons. He went further than needed As soon as a possibility of social choice could be derived with non-binary yet ordinal preferences, we will have shown that this over-zealous restriction of information is alone responsible for the impossibility. That is what these economists do. The restriction in Arrow’s theorem is not linked to the rejection of interpersonal comparisons of utilities (see Mongin and Fleurbaey 2005, Fleurbaey and Blanchet 2013). It rather derives from the negation of a substantial amount of non-binary ordinal

information on individual utilities, the kind of information that would still be acceptable in the Hicksian view of utilities, and basically consistent with the demand theory. Secondly, if restoring a possibility of social choice does not in itself require to reintroduce interpersonal comparisons of utility, the reintroduction of normative criteria could not be avoided for this purpose. They propose clear and transparent normative criteria in their use of utilities in welfare models, which make use of all advances of social choice theory. As a result, they propose an microeconomic solution to welfare economics, in which comparisons of utilities are not required, utilities are subjective, and they are embedded in a normative framework. 21 Mongin (2006)[38] qualifies this approach ‘the containment claim’. 22 Source: http://www.doksinet 6 Conclusion By studying the waltz status of interpersonal comparisons, it appeared that their relevance for welfare economics and help for

public-decision making greatly depends on the normative interpretation and the operational status of utility. Both normativiy and operationality are necessary to ensure the fertility of welfare economics. The problem has therefore been moved from the debate on the possibility of interpersonal comparisons of utilities, to the normative and operational properties of utilities as such. The properties of utilities may alone explain the evolution of the concept of utility and, from then on, the evolution of welfare economics. In particular, if utilities are objective, they can be compared; if they are subjective, there are few solutions to make meaningful comparisons. As utilities were supposed to be fundamentally subjective, especially under the dominance of the revealed preference theory, it is impossible to imagine to compute any arithmetics on their values. If there were objective, adding them would rather makes sense. Under the mere possibility or impossibility of comparisons, the main

differences in these two positions lies in the differences of the acceptable interpretations of utilities and their resulting properties of the utility. Ultimately, this paper intended to prove from an historical perspective that the debate on comparisons is hiding a more profound debate on utilities. It highlight that the evolution of welfare economics over time is mainly explained by a quite yet powerful evolution of the interpretations of utilities. In the old welfare economics, the fundamental reason why comparisons of utilities are possible is that utilities are homogeneous, objective and have an accepted normative status. In the new welfare economics, comparisons were banned for two reasons linked to the scientific move of the period. Utilities’ normative meaning could not be accepted any more; if utilities are indeed subjective, comparisons have no operational meaning. A common interpretation of Arrow’s theorem is that it is due to the impossibility of comparisons, while it

may merely be due to further restriction of ordinal preferences to binary information. The historical influence of revealed preference theory certainly played a role in the Arrovian over-restriction. The impossibility of social choice, which may precipitate the death of welfare economics, is shown to be also due to information on intra-personal comparisons rather than just inter-personal comparisons. In the last stage we described, we describe how 23 Source: http://www.doksinet to overcome the news of the death of welfare economics. There are basically two distinct paths. A first path has been strongly influenced by Amartya Sen’s works. It defends an objective version of utilities and we accept interpersonal comparisons Normative criteria are clearly established This move basically implies to move away from any theoretical grounds of microeconomics, and accept that welfare economics is now the job of pluridisciplinary researches. A second path is being defended by Marc Fleurbaey

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