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Symposium on Ivan Moscati’s “Measuring Utility. From the Marginal Revolution to Behavioural Economics”

Everything You Always Wanted to Know About Utility Measurement (But Were Afraid to Ask)

Jean-Sébastien Lenfant
p. 61-91
Référence(s) :

Ivan Moscati, Measuring Utility. From the Marginal Revolution to Behavioural Economics. Oxford: Oxford University Press, 2018, 352 pages, ISBN 978-019937277-5

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1A book on the history of utility measurement was sorely lacking but we have it now. Moscati’s achievement in Measuring Utility is undoubtedly both impressive and inspiring. Though it delves into topics partly well-known from historians interested in choice and decision theories, demand theory, utility theory, relationships between economics and psychology, I cannot imagine a single reader who would close the book without having harvested precious information and hindsight for his/her own research agenda.

2The book offers a history on how economists have dealt with utility as a concept likely to be quantified, either empirically or at least theoretically. It tells us the story starting from the marginal revolution of the 1870s—with occasional reference to earlier contributions, for instance by Bernouilli ([1738] 1971)—up to the advent of behavioural economics in the mid-1980s. In essence, the subject calls for an analytical method of investigation and a broad view on the economists’ agenda together with an interdisciplinary curiosity to grasp the trend of ideas about measurement. Moscati handles these three aspects throughout the book—though with varying weight and focus—and this is history of economic thought as I see it.

  • 1 Many interesting passages of Moscati’s book will be ignored in this review. I have chosen not to co (...)

3Before embarking on a critical assessment of certain parts of the book, I present a summary of the book and of its underlying narrative. Then, after a general evaluation of the book, I provide a critical assessment by discussing four aspects of Moscati’s narrative: the idea of a unit-based approach to measurement; the thesis that marginalists are not cardinalists; the treatment of ordinalism and rationality; and finally, the conception of measurement in relation to utility and psychology. Broadly, the idea I will uphold throughout is that Moscati’s story would have been more convincing had he put more weight on the meaning of utility in context and payed more attention to the issue of rationality as an essential aspect of the transformation of the views of economists regarding measurement. The result of my review, which owes much to Moscati’s insights, is to question the significance of certain ideas about measurement as a self-sufficient analytical tool to explain the fate of utility measurement in economics.1

1. The Story

4The main idea of the book is that the history of utility measurement was shaped partly by the evolution of ideas about measurement. It is articulated around four main parts. Part I deals with the first marginalists (circa 1870-1910). The first chapter deals specifically with the theory of measurement in philosophy, psychology and economics before and during the marginal revolution. The following chapters focus on the marginal revolution. Here, utility is at the heart of the reconstruction of economics as marginalists saw it. Moscati points out various views about utility measurement during that period, providing us with new arguments to de-homogenise the contributions of Jevons, Walras and Menger. In the second part, Moscati deals with the ordinalist revolution (starting with Fisher and Pareto) and describes its direct consequences on the debates about the status of utility in economics. The third part of the book is devoted to the rebirth of the Bernouillian expected utility model after von Neumann and Morgenstern’s restatement of it in Theory of Games and Economic Behavior (1944). It gives an account of the heated debates that ensued for a decade or so, leading to the renewal of utility as an instrumental concept for the study of behaviour under conditions of uncertainty. The last part is devoted to the experimental work of psychologists and economists fostered by the expected utility theory (EUT), in order to measure utility and test its predictive value on individual behaviour. Moscati highlights several phases in the use of experiments on utility up to the advent of behavioural economics. Each part of the book ends with a “Summing up” section, organized according to several methodological headings, the reading of which I recommend before reading the main text.

5One key idea in the book, which is precisely documented and argued, is that measurement does not mean the same thing at different periods of time. The main changes in this respect occurred relatively late, broadly between 1930 and 1950, when economists and psychologists freed themselves from the strict conceptions of measurement held in physics. In the prologue and in the opening chapter, Moscati introduces the reader to the notion of measurement in a historical perspective, borrowing mainly from the philosophy, physics, psychology and economics of the 18th and 19th centuries (Kant, Newton, Fechner, Wundt, Du Bois-Reymond, Helmoltz, Poincaré, Bernouilli, Bentham, Dupuit).

  • 2 What becomes important then is that measurement is part of a scientific process towards elaborating (...)

6Moscati’s main message here is that the prevailing representation of measurement during the marginal revolution, and for a long time after that, is a “unit-based” representation. This means that measuring consists in finding how many times a property or a quality attached to an object is represented in the same property or quality contained in another object that serves as a unit of measurement. This is the condition imposed on “real” or “fundamental” measurement of physical magnitudes, as conceived by physicists and philosophers of science. Early marginalists, as we understand Moscati, aligned their views on the measurement of utility with those of psychologists (rather psychophysicists) and physicists. This is not too surprising in a context of “physics envy” and given the inclination of certain economists to understand utility (pain and pleasure) as a subfield of the psychology of sensation and feeling. During the ‘ordinalist evolution’ (to use Wade Hands’ terminology), the escape from psychology would gradually be followed by an escape from a unit-based conception of measurement in favour of a broader view. According to this new view, measurement is a general practice that consists in assigning numbers to various qualities and identifying the set of operations that can be performed with those numbers so as to be able to express something that is still relevant about these qualities. Later on, in the 1960s, this view would continue to evolve towards a representational conception of utility.2

7Moscati argues that identifying those transformations leads to “revise in many important aspects the canonical history of utility analysis” (3). More specifically, he upholds that a careful analysis of the historical steps implies rejecting the traditional opposition between cardinal and ordinal utility as too simple. Instead, one should distinguish between three forms of quantification of utility: the unit-based form (also called the ratio-scale form) associated with early marginalists, the ordinal form associated with consistent Paretians, and the modern linear-scale form associated with expected utility theorists. Actually, the reader is given more information about these scales later on in the first part (45).

  • 3 Stevens’ contribution is important to help us confront the epistemology of psychology and of econom (...)
  • 4 I have not mentioned here the simplest kind of scale, the nominal scale, which is simply a way of l (...)

8The common typology since Stanley Stevens (1946) distinguishes various scales (or degrees) of measurement.3 The ordinal scale attributes numbers to a magnitude according to the rule that the relationship between two measurements of magnitude is reflected in the order of the numbers (if A is preferred to B, then U(A) > U(B)), hence any positive monotonic transformation of U(.) will do as well as U(.). The interval-scale (or linear-scale) approach assumes that the evaluation processes used by agents are arbitrary only up to a linear transformation of a utility function, which means that if U(.) represents the preferences of an agent, then any other function V(.) can also represent those preferences if and only if V(.) = aU(.) +b, (a>0). This interval scale has interesting properties since it preserves the order of utility differences and the ratio of utility differences. It makes sense to say that going from A to B is twice as much preferred as going from B to C. The acme of measurement scales is the ratio-scale, the one for which the zero value is given and cannot change while only units are arbitrary. It says that if U(.) represents the preferences of an agent, then V(.) functions in such a way that V(.) = aU(.), (a>0) are the only other scales acceptable to represent the same preferences. Hence, the ratio of absolute values is independent of the choice of the unit. There is at least one other scale, curiously mentioned in passing only once and late in the book: the one for which the unit of measurement is not arbitrary whereas zero is. In this case, preferences represented with U(.) can also be represented with V(.) = U(.) + b.4

9The rest of the first part of the book offers a precise account of the status of utility for the main protagonists of the marginal revolution (of the first and second generations) besides the three main figures, i.e. Jevons, Menger and Walras. As expected, it deals with Edgeworth and Marshall, but also with von Wieser and Böhm-Bawerk. Throughout this part of the book (chapters 2 and 3), Moscati’s main message is that all the marginalists shared a unit-based view of measurement (a ratio scale) and that they sometimes considered developing the theory solely on the basis of preferential judgments (Jevons being the best example of this attitude). Thus, they should be seen as distinct from the modern notion of cardinality which is precisely adjusted to deal with linear transformations of the utility function and not specifically with ratio-scale transformations. Hence, we should no longer be allowed to say that Walras or Edgeworth are cardinalists.

  • 5 Moscati does a wonderful job tracing out the discussions about the ranking of utility differences e (...)

10Part II is devoted to the ‘ordinalist evolution’ and its consequences on utility measurement. As in the first part, it opens with a chapter focused on epistemological and methodological issues about measurement circa 1910-1940. Moscati documents the foray of psychologists, mathematicians, philosophers and economists into a more flexible conception of measurement. The main figures of this story are Norman Robert Campbell, William Brown, Louis Leon Thurstone, with a significant hotspot: the British controversy over psychological measurement in the 1930s during which psychologists consolidated their own views on measurement. The next chapters describe Pareto’s innovation of the index utility function as a pure method of representation of agents’ preferences. It underlines Pareto’s inconsistencies regarding the fundamental economic data, particularly in terms of an agent’s ability to associate utility with pleasure or to compare the strength of utility variations quantitatively (stating, for instance, that a transition from A to B is twice as preferable as a transition from B to C), identified as Pareto’s postulate 2. It then presents a number of works aiming at clarifying the specific properties of utility that would stem from this postulate. In Austria, debates revolved around Čuhel and Mises’ commentary on the theory of the comparability of pleasures put forward by Böhm-Bawerk (1889), who had obviously given an erroneous interpretation of marginal utility theory (115). It is overall rather poor mathematically compared with Pareto’s achievements in the Manual. The ordinal approach was nevertheless adopted in Austria, but in a form that accepted the ranking of utility differences. The fundamental point here is that ranking utility differences is fundamentally not compatible with pure ordinalism since it goes beyond the needs of a theory of economic equilibrium, while accommodating at the same time a preferential judgment over transitions (transitions from one basket to the next) and eventually leading to the identification of a new meaning for the measurability of utility.5 These chapters are particularly interesting: they present various analytical comments on postulate 2 (involving Čuhel, Lange, Allen, Phelps-Brown and Alt) and the need for it to be based on a new preference relationship and to consider the potential uses of this postulate for welfare analysis. The last chapter of part II deals with the beginnings of empirical or experimental attempts at measuring utility (Frisch, Fisher and Thurstone), including a rather unsuccessful collaboration between Frisch and Fisher. In this part of the story, Franz Alt’s underestimated contribution (Alt, [1936] 1971) is particularly important in that it established a set of axioms in terms of preferences necessary and sufficient for the use of utility functions defined up to a positive linear transformation.

11Part III deals with the advent of the Von Neumann and Morgenstern rephrasing and axiomatization of the expected utility model (Von Neumann and Morgenstern, [1944] 1953) and its stabilization qua the dominant approach to choice under uncertainty in economics. Here Moscati is at his best, providing us with a lively story of the debates and reversals that occurred during the decade 1944-1954. This story has already been told partly in books or articles but we have here the most up-to-date and detailed presentation, based on several archival sources. Before embarking on the presentation of the axiomatics of EUT in Theory of Games and Economic Behaviour, Moscati shows how the notion of measurement evolved during those years in the field of psychology, bringing to the fore the contribution of psychophysicist Stanley Stevens. Mainly, the idea is that around 1941-1946, Stevens introduced a formal theory of measurement that supports the practice of social scientists in using various scales to represent and deal with various psychological phenomena or properties (or what is assumed to be a psychological quantifiable phenomenon). Stevens was inspired from Campbell’s distinction between a strict view of measurement in a fundamental way (for physical magnitudes) and a more general understanding of measurement as a set of rules to organise the values attributed to any magnitude (through a quantification process). Hence, Stevens would lead the way to all coming reflections and rationalizations about the practices of economists and psychologists in order to organize and think about the meaning of operations leading to the quantification of phenomena: “If we can point to a consistent set of rules, we are obviously concerned with measurement of some sort, and we can then proceed to the more interesting question as to the kind of measurement it is” (144, my emphasis).

12The rest of Part III deals with EUT. In 1944, Von Neumann and Morgenstern proposed a model of choice under risk. Instead of choosing between bundles of goods with certainty, individuals are now in a situation of choosing between bundles of goods associated with various outcomes (x,y) based on the realization of states of nature described by a set of probabilities, Li(x, pi; y, 1-pi), Lj(x, pj; y, 1-pj). On the one hand, the Von Neumann and Morgenstern model is based on the ordinalist idea of entrusting the individual with the Paretian capacity of ordering those bundles and of representing this order through an ordinal utility function U(.). On the other hand, Von Neumann and Morgenstern’s model is also oriented towards providing a manageable model, and therefore reactivate the Bernouillian idea (Bernouilli, [1738] 1954) of implementing a linear structure for probabilities. It is thus assumed that any U(.)can be represented by an algebraic operation involving a simple function of the outcomes, a “choice-generating function” as Friedman would later call it, labelled u(.), such that U(Li) = piu(x)+(1-pi)u(y) and Li is preferred to Lj if U(Li) > U(Lj). Along the way, because of an axiom—later called the Independence Axiom—u(.) gained a special property: it is not as arbitrary as U(.). If a function u(.) is an expected utility function used to assess the value of lotteries, then any other choice generating function v(.) that would be used instead of u(.) to represent U(.) would be linearly related to u(.) (i.e. v(x) = au(x) +b).

  • 6 Von Neumann, Morgenstern, Allais, Samuelson, Friedman, Savage, Strotz, Baumol, Marschak, Alchian, M (...)

13The book gives a detailed and lively account of the way a dozen of first class economists would be involved in stabilizing the understanding of this model and its underpinnings.6 This is in my view the heart of Moscati’s book and I venture to think that it is from episodes of this part of the book that he drew the main intuitions about its broader narrative. We can do no better here than to mention briefly the main steps of this story.

  • 7 If a subject is indifferent between L1(500, 0.4; 1000, 0.6) and L3 (600,1), L3 being an outcome for (...)

14The first step deals with the enthusiastic appreciation by certain authors (Wallis, Friedman, Savage) and the frankly unfavourable attitude of others (Baumol, Samuelson), a situation that proved fruitful to help further the understanding of the axioms, to clarify ideas about cardinality and to question the use of associated concepts such as risk aversion measures. Along the way, we see how Friedman and Savage (1948) inaugurated the operational use of the model.7

15We are then told how the restatement of von-Neumann–Morgenstern (VNM) axiomatics into a subjective probability model by Savage (1954) was a key moment of reversal, and how the Sure-Thing principle was the missing stone to convert naysayers to the fact that Expected Utility offered both a convincing and simple representation of individuals’ rationality in the face of risky situations. In the end, Moscati successfully shows how the conventionalist view on the choice generating function u(.) and its use explained the “peaceful cohabitation of cardinal and ordinal utility within utility analysis” (222)

16Now, the most pressing issue, as far as measurement of utility is concerned, is the meaning of the u(.) function. Is it a purely instrumental function justified by its manageability and the possibility of expressing preferences over lotteries through a parametric model? Or, more surreptitiously, does it say something about the psychological ability of individuals to interpret risky environments and measure them, and even evaluate heterogeneous situations? These two ways of interpreting u(.) are based on the views of the instrumentalist vs the realist (or the conventionalist vs the mentalist) about the modelling of rational behaviour. To put it differently, does the ordinalist conception of U(.) in the expected utility model hide some underlying mental operations that could be in some way connected with Pareto’s difference-of-utility comparisons? Indeed, for Von Neuman and Morgenstern (1944), the expected utility model can satisfactorily account for Pareto’s second postulate, which seems poorly motivated in the framework of Paretian choice. This issue was actually present from the start, as Moscati documents by quoting passages from Theory of Games and Economic Behaviour: “The failure of one particular device [i.e. Pareto’s postulate on the comparison of utility transitions] need not exclude the possibility of achieving the same end by another device. Our contention is that the domain of utility contains a ‘natural’ operation which narrows the system of transformations to precisely the same extent as the other device would have done” (von Neumann and Morgenstern, 1944, in Moscati, 197).

17Moscati’s first merit is to have been able to disentangle the web of questions that the EUT raised. I think that in doing so, he offers a pleasant narrative of how economists, at first inclined to interpret the model as providing a simple way of expressing a form of measurement of attitudes towards risks and of measuring the utility of money, were then led to retreat and see it as a purely instrumental representation. As an instrumental model, EUT can simply be used to build specific models representing individual behaviour. According to this instrumental view, if the model allows the satisfactory prediction of choices thus far unobserved (under new circumstances), then individuals will be said to behave as if they were implementing the EU model to make decisions. In the process, the numbers used by experimental economists are to be interpreted as purely instrumental variables, the sole purpose of which is to provide a map of acceptable future forms of behaviour. The practice of measurement would then be understood only as the practice of quantification of human actions according to certain rules, thus making them instruments of prediction. Moscati identifies different debates and is able to reconstruct a coherent narrative from the various papers and exchanges of letters between protagonists. One key issue is the interpretation of one specific axiom, later coined the Independence Axiom by Samuelson. Its plausibility was a hotspot: is it a gratuitous, arbitrary assumption or a reasonable one that everyone should accept? After Savage recast it as the Sure-Thing principle, Samuelson evolved from the first to the second viewpoint, while Friedman saw the issue of plausibility as the advantage of simplicity and operational content of the theory. Thereafter, the first experiments held on EUT (Mosteller and Nogee, 1951) would comfort the latter approach.

18The acme of this story is the famous Paris 1952 conference during which Allais, opposed to EUT, advocates the need to find a more complex and realistic model of choice under risk (involving a complex interdependence between probability and outcome). This part is particularly insightful in showing how decision theorists converged toward a common view on the use of utility in this model and the purely conventionalist conception of measurement associated with it. In his final analysis, Moscati describes how the conventional view was eventually heralded in contributions by Friedman and Savage (1952), Strotz (1953) (“measurement is always invented and never discovered”, Strotz in Moscati, 266), Alchian (1953) (“to say simply that something is, or is not, measurable is to say nothing”, Alchian in Moscati, 270), Ellsberg (1954) (“A ‘thing’ is ‘what is measured by a particular operation’”, Ellsberg in Moscati, 274).

19Part IV of the book is entirely devoted to the history of experimental utility measurements, with a clear focus on the expected utility framework (works on utility under certainty are not dealt with extensively). It starts with the celebrated experiment by Mosteller and Nogee (1951), in which subjects are presented with series of lotteries Li(x, p; yi, 1-p). For a given value of p, Mosteller and Nogee experimentally obtain the value of yi such that Li is probabilistically indifferent with the status quo (expressed as a certainty equivalent $0). By choosing several values of p, always assuming an expected utility maximization behaviour, Mosteller and Nogee were able to derive a functional relationship between u(.), p, and y. The utility function was then implemented in a second experiment with different p values in order to check whether it allowed satisfactory prediction of the subjects’ behaviour, which it did according to Mosteller and Nogee.

20Mosteller and Nogee’s experiment was the starting point of heated debates involving economists and psychologists. It led to other experiments which served as opportunities to see how psychologists could adapt the model to their own agenda and/or experimental standards. This is the case or the Davidson-Suppes-Siegel experiment (Davidson, Suppes, and Siegel, 1957). Along the way, we see how reflections on measurement went hand in hand with the experiments, leading to the explicit search for interval scale measurements (Suppes and Zinnes, 1961).

  • 8 Moscati’s choice not to discuss measurement-based experiments in connection with measurement-free e (...)

21The 1960s mark the beginning of a new period, with a different view of EUT. After benefiting from a supportive environment, EUT was now scrutinized in all respects. In psychology, the mid-1960s mark the start of a move toward a more cognitivist analysis of decisions and choices, hence putting measurement on the research agenda as one among other goals. Psychologists would turn the EUT model into an instrumental model to identify subjects’ deviation from—or violation of—the model. In so doing, they could follow alternative ideas put forward by Allais (1953) or later by Ellsberg (1961). The Michigan school of psychology (George Katona, Clyde Coombs, Ward Edwards and their students Sarah Lichtenstein, Paul Slovic and Amos Tversky) would become central to this agenda by the end of the 1960s, laying the ground for research in what was going to be coined behavioural economics. Moscati rightly notes that the Michigan strategy of testing EUT did not rely on any measurement assumption. For that reason, Moscati chooses to focus instead on late attempts at experimenting with EUT involving utility measurements (in the 1970s and 1980s).8 In these experiments (carried out by Karmarkar, 1974; McCord and de Neufville, 1983; Hershey and Schoemaker, 1985), the main idea it to show that different means of measuring utility led to different utility measurements due to subjective distortion of objective probabilities. Clearly, the issue of utility measurement was on the downslope in those years. Hershey and Schoemaker’s experiment is important in this respect, in that having confronted the results obtained with the certainty equivalence method and those obtained with the probability equivalence method, the main result is that the probability equivalence method yields greater risk aversion than the certainty equivalence method.

2. General Appreciation

22As a whole, I would say that the part of the book on EUT is by far the most enjoyable to read; it is more lively and more unified around a common thread than the rest of the book, which lacks synthetic presentations to a certain extent. This is not surprising since all the authors involved in that part of the story know each other and discuss, sometimes passionately, various issues linked to the von Neumann and Morgenstern version of EUT. In contrast, the first two parts provide series of short descriptions of contributions by many authors. The downside of this wealth of information is that the reader is sometimes at pains to connect all the authors to an encompassing narrative and cannot learn much about each author’s personal agenda regarding utility. This rather uncomfortable feeling is explained by the fact that the main goal of the first two parts seems to be narrowly confined to establishing that marginal economists abide to a unit-based conception of measurement and that the label “cardinalist” should be reserved to describe those who refer to linear-scale models of utility. I believe that a broader discussion on the views about utility and its role in the theoretical framework of marginalist economists could have enlivened the reading.

23On various topics (scales and measurement, EUT, ordinalism), I think the reader might have appreciated a more authoritative initial presentation of the theoretical structure which is to be the object of historical investigations. For instance, Moscati presents EUT rather quickly as von Neumann and Morgenstern present it in their book, with too few theoretical and methodological comments to help us anticipate the debates to come.

24That said, I have very few points of disagreement with Moscati’s specific discussion or presentation of authors or concepts and I find his broad narrative quite convincing. My main concerns are rather with the intermediate theses that constitute the narrative or the methodological underpinnings of Moscati’s study. What follows is an essay to integrate more elements into Moscati’s narrative and to connect measurement aspects with other methodological issues in the history of utility. It is hoped that this will set the stage for further debates in the community of historians and methodologists of economic thought.

3. Measurement Issues: Units, Zero and the Needs for Valuation

25Moscati’s treatment of the history of measurement leads us from considering physicists and mathematicians to considering psychologists and economists. Implicitly, there is the idea that these representations of measurement could be connected and that, when thinking about measurement, economists would strive to abide with the standards of fundamental measurement. My view is that things went somewhat differently, and that economists, in their search for making economics more empirical, had no reason to restrict their practices of quantification to fundamental measurement. Indeed, I think that Moscati’s interpretation of the marginalists as being stuck to the strong measurement view—which he associates with the idea that they refer to a unit of utility—is misleading because he focuses exclusively on the question of the unit of measurement instead of also taking into account the zero issue. To economists and to psychologists, the question of the zero is everything but simple and far from being a pure matter of arbitrariness. Hence it cannot be gauged with what took place in physics. I would like to invite Moscati to consider taking the issue of the zero as an integral part of the history of the measurement of utility (but also as a pending question for psychologists).

26Moscati considers that the natural evolution toward a broader view on measurement consists in starting with a given zero and an arbitrary unit, then considering an arbitrary zero (the interval scale) and finally arriving at the ordinal scale. Thus, we are told that because they were not able to conceive of a satisfactory unit and measure it, economists were led to think directly in terms of more and less, jumping directly to arguments of an ordinal nature (Jevons is a good example of this storyline). My guess is that this is not the most general line of argument and that Moscati’s thesis would require that marginalists were unable to identify clearly the problems linked with the choice of a zero. One can find examples that help us understand that the specificity of the measurement of utility in economics (or any mental magnitude in psychology) starts with the simultaneous definition of a unit and of a zero variation of utility. In this respect, it would have been most useful to consider scales of the kind V(.) = b + U(.) in the story, as I will try to illustrate.

27In Mathematical investigations in the theory of value and prices, Fisher (1892) imagines an experiment which could allow marginal utility to be measured. Fisher starts with two arbitrary values for bread (100 loaves) and oil (B gallons) and assumes that the marginal utility of the 100th loaf of bread is equal to an increment of β gallons over B and further assumes that U(150th loaf) = U(β/2). Considering that β is small enough, the marginal utility is linearized around β, so that U(β/2) = U(β)/2. If U(β)/2 is taken as the unit of marginal utility, then U(150th loaf) = 1 and U(100th loaf) = 2. From this example, on can easily figure out that the values would have been different had the initial quantity of oil, bread or both been different, and that if the initial quantity was, for instance, C gallons (C<B), then maybe new values (in place of β) would be obtained (γ and γ/3 for instance). Hence, changing the initial quantity of a given commodity for the consumer (the zero) would change both the unit and the ratio of marginal utilities. Fisher explicitly discards this possibility (Fisher, 1892, 15), and that is the interesting point: to obtain a measurement of utility, he has to say something about the independence of the measurement on the choice of the zero (the initial quantities used to define a reference point). It is only once this is fixed that Fisher goes on defining a unit as the marginal utility of the 100th loaf of bread, or as any other arbitrary chosen commodity.

28Therefore my point is that what is important in the development of a measurement of utility is that the unit-based view does not mean focusing on the need for a unit per se. Instead, it expresses the need to find a unit that will be unchanged with the change in the initial position of individuals, for who there is no natural value. Thinking of a natural zero would mean to believe in some kind of Kelvin thermometer for utility, or, more simply, to assume that problems to be addressed can ignore such problems. I cannot tell if this way of thinking of utility measurement can be extended to all authors, I merely contend that Moscati would have been more convincing had he considered the interplay between the unit and the zero in his account. The consequence of this is that marginalists were much nearer to the use of interval scale than Moscati upholds. Indeed, once it is recognized that the value of the unit is dependent on the value of the zero, we open up to a specific sort of interval scale such that V(.) = b + f(b) U(.) (hence the unit is no longer independent of the choice of the zero and vice versa). If f(.) is a linear function of b, we have an interval scale. If not, we have an ordinal scale.

4. On the Thesis About Marginalists Not Being Cardinalists and Expected Utility Theorists Being True Cardinalists

29The foregoing remarks lead one to question one of Moscati’s main theses in the first two parts of the book regarding the 1870-1940 period, namely that one should carefully distinguish cardinalists as conscious interval-scale measurement practitioners in the 1930s and earlier marginalists who were stuck in their traditional views on measurement and could not conceive of interval-scale measurement:

In utility analysis, the discussion about utility differences was associated with the definition and stabilization, from the mid-1930s onward, of the notion of cardinal utility as utility up to positive linear transformations. (129)

  • 9 Moscati’s tracking of the “right” use of the term does not lead to a clear conclusion. Samuelson wo (...)

30Throughout the first half of the book, Moscati keeps repeating that marginalists were not cardinalists, in the sense that they did not abide with a linear-scale view of measurement and that we should therefore restrict the use of the term “cardinalism” to its true historical meaning, i.e. as a view characterizing the use of utility in the expected utility model.9 I must say that I do not understand why Moscati insists so much on this terminological discussion, mixing issues of terminology, issues about the analysis and modelling of utility, and issues of representations and practices. In what sense are we better, in the end, saying that Jevons or Edgeworth were not cardinalists? I would like to discuss this further both on technical and methodological grounds in the hope that Moscati might clarify the methodological meaning of his statement

31The question is: can we assert, on the basis of Moscati’s material, that marginalists were stuck in a strict “unit-based” view of measurement that prevented them from thinking about measurement as a specific practice adapted to their own needs for economics, unable of freeing themselves from the internal constraints imposed on them by physics and therefore conceiving of linear scales of measurement? The idea of an epistemological obstacle is alluring indeed, and may prove adequate to explain some thoughts and practices, but it must be approached carefully.

  • 10 On this, Moscati could have paid more attention to Marshall’s or Edgeworth’s analogies between util (...)
  • 11 This leads to further criticism of other uses of the utility theory, either for welfare analysis of (...)

32My first answer would be that the marginalists were not far from using interval scales—as I tried to show in the previous section—and they recognized the arbitrariness of the zero (or its variability according to the problem at hand).10 Hence, there was no fundamental obstacle for them to be cardinalists according to the technical meaning that Moscati has in mind for this term. In this respect, I do not share Moscati’s thesis. It is also well known that since marginal utilities and the ratio of marginal utilities will be left unchanged with or without “b” in the scale of measurement, analytical results will be the same with a linear scale and with a ratio scale, as long as the goal of the theory is restricted to the domain of economic equilibrium.11 Hence, should we not consider that the understanding of measurement is more a question of practice in context rather than an epistemological characteristic attached to the community of researchers? Moreover, if an economist discards the arbitrariness of the zero (in order to have a ratio-scale), it may be because of the specific use that is made of the utility in his theoretical framework.

33However, it seems to me that Moscati’s thesis is weak if one regards it merely as an analytical statement about the use of a function rather than another, so that he may have a broader idea in mind. The true versus false cardinalist thesis makes sense if it can at least be integrated in a methodological stance regarding the meaning of cardinalism, i.e. the meaning of utility measurement. If one agrees with this view, Moscati’s thesis could only make sense once economists had realized the full extent of the meaning of the use of linear scales in EUT, which of course, only happened later, when the conventionalist view about utility was well established in the 1950s as a synthesis between the positivist stance heralded in ordinalism and the operationalist stance embodied in the expected utility assumption. In that case, it goes without saying that the views of marginalists were quite at odds with this methodological underpinning. If this is what Moscati had in mind, then all marginalists before the ordinal revolution (and its positivist content) are clearly condemned to be just unit-based utility theorists or involuntary cardinalists. As for the debate that follows Pareto’s Manual regarding the meaning of postulate 2, it becomes of utmost importance. After Alt’s axiomatization of Pareto’s postulate 2 in 1936, and later on after VNM’s axiomatics of utility in a risky environment in 1944, what could have been the meaning of utility valuations to those tempted to consider only linear variations of their calculations? Moscati does not address these issues in depth and we are left with intuitions that, as Lange put it, it may be useful for welfare economics.

  • 12 Though Moscati usually details the attempts at measuring utility (or derivative concepts such as ma (...)

34In the final analysis, it may not be possible to answer the initial question in this section satisfactorily. Later, in the summary section of part II, Moscati eventually argues that “if a utility theorist wants to go beyond ordinal utility, which itself is sufficient for demand and equilibrium analysis, he or she need not go all the way to ratio-scale utility but can stop at the less demanding cardinal utility [interval-scale] station.” (130) Economists of the 1950s may have been able to systematize this way of thinking theoretically but this cannot be interpreted as the discovery of a new scale. It simply involves a new appreciation of the meanings of utility.12

35I don’t think it is reasonable to evaluate the use of a modelling practice without linking it to its interpretation as a tool. Hence, the question is not whether X used or not a linear scale but why he/she did not. The answer to this lies in the way each author interprets a utility and the kind of use he/she wants to infer from it. My view is that Moscati fails to tell us precisely the methodological consequences of his thesis. Part of the answer seems to lie somewhere in the reflections about preferential judgements between transitions from one basket to another in the 1930s, and I suppose that this would have to do more with utility as a basis for (social) welfare valuations. Since Moscati has chosen to eschew the issue of welfare, we are left with a feeling of incompletion of the thesis about cardinalism.

36As I indicated above, I think this has no consequences on the broad narrative of the book. It merely points to the need to evaluate the way Moscati deals with ordinalism. Ordinalism is more than just a mathematical recipe to develop a utility function that represents preferences; it is a slow epistemological evolution that occurred mainly between Pareto’s positivist oecumenical views as exposed in the Manual (1909) and modern behavioural standards of the 1940s. It may be that Moscati’s measure-oriented view of ordinalism explains his main thesis about the divide between unit-based marginalists and later true cardinalists.

5. On the Treatment of Ordinalism in the Book

37What has taken place smoothly from Pareto to Alt (1936) and VNM (1944) (including Allen and Hicks’s contributions) is a move from an understanding of utility as a concept based on loose psychological notions (wants, desires, interdependence in consumption) to an abstract category of outcome valuation. With Pareto, the traditional view on utility became confronted to another view where it becomes an instrument to think about rational behaviour. Both views are intermingled in Pareto’s work, and Pareto’s ideas about tastes and the shape of indifference curves are linked to his ideas about consumption: as income increases, some goods are now consumed while others are no longer consumed, and it is the task of microeconomic tools to reflect those behavioural characteristics. Having said that, indifference curves are only incidentally instrumental in thinking about rational behaviour. With Hicks, Allen, and Von Neumann and Morgenstern, on the other hand, the theory of utility aims to organize or rationalize observable data, and the theory of utility usually assumes non-satiation of underlying preferences and abstract categories of goods.

38In a book devoted to utility measurement, it is not surprising that the author tends to evaluate various episodes of the history of utility by the swiftness of their capacity to provide good case studies of theoretical or empirical measurement. From this point of view, the ordinalist revolution opens the way toward a conception of utility in which measurement issues become secondary, even if the principle of quantification remains meaningful. As we know, a greater utility index solely indicates a preferred state to the consumer, nothing else.

39Instead of focussing on the meaning of ordinalism and debates with authors who stuck to the concept of diminishing marginal utility, Moscati focuses on debates about Pareto’s postulate 2. I think this is a great idea and an opportunity to support Georgescu-Roegen’s thesis about ordinalism:

For historical, and also accidental, reasons, in the folds of the ordinalist description of consumer's choice there was couched much more than the ordinalists intended to accept. It is doubtful that they ever have been aware of this and, thus, their very own arguments became the chrysalis of the cardinalist doctrine (Georgescu-Roegen, 1954, 505).

40This is certainly an important issue for choice and decision theorists to derive the theoretical consequences of dealing with comparisons of transitions from one bundle to another. To that end, Moscati tends to present Pareto as a missed ordinalist and, to my mind, eschews important methodological changes associated with Pareto and ordinalism, which would have led him to a richer analysis of the ratio-scale/interval-scale divide.

41As we know, ordinalism was the starting point of a deep transformation of the representation of utility which raised issues about how it should be measured. This change should therefore be carefully accounted for in order to compare the attitudes of economists toward measurement. Pareto’s Manual and other materials allow a strict interpretation of ordinalism, which, I think, could help clarify his own twists and many other difficulties related to the history of cardinalism in utility theory. I think it is possible to underline that beyond Pareto’s ambiguities or deliberate intrusions into “cardinalist” or “pre-ordinalist” thought experiments, his own stance regarding the meaning of ordinalism provided a sound barrier between an ordinalist-positivist attitude toward individual behaviour and a non-ordinalist attitude. Pareto (1909) pointed out the need for economics to keep a certain distance with psychological foundations of choice. His idea was not to deny the connections between the two disciplines. He was merely aware of the difficulties for psychologists and psychophysicists to deal with complex sensations, thus providing too weak a foundation for the complex motives of human actions. Adding to this a positivist attitude toward scientific explanation, Pareto proposed taking preferences as a starting point and utility as a mere mathematical tool used to summarize preferences. As we know, any positive transformation of such a utility function would represent the preferences of an individual equally well. He even suggested, as Moscati notes, that once we think we have observed enough of a subject’s choices to know his/her field of preference, then the subject can “disappear”: he/she will no longer be needed. Hence, ordinalism is first of all a proposal for a methodological transformation of economics, with consequences not only for the meaning of utility but also for the very idea of measurement.

  • 13 For interested readers, the most accurate presentation of Pareto’s contribution on utility remains (...)

42Pareto’s inconsistent ordinalism is associated with his use of the concept of decreasing marginal utility and the old definitions of complementarity and decreasing marginal utility, which are not independent of the choice of utility function.13 A word is in order to clarify Pareto’s attitude regarding utility. Pareto’s reference to diminishing marginal utility is anchored in traditional views about utility as an explanatory concept for individual behaviour. In particular, Pareto sticks to the idea that consumer behaviour in the face of variations in prices or revenue must be explained by making reference to local satiation of wants that explain consumption patterns.

  • 14 Pareto himself is quite confused since he considers that an individual’s ability to compare transit (...)

43Pareto’s second mistake is to express formally the fact of preferring a transition over another by means of the utility index function. Not only does this assume that someone (the agent) performs some calculation using utility indices a posteriori (which is in contradiction with the principle of ordinalism), but it also leads one to attribute to the utility index properties alien to the index utility function (because of a ternary or quarternary order relationship). To rationalize Pareto’s theoretical presentation of this, one can say that to be consistent with the principle of the utility index function and the methodology of preferences, Pareto should have presented the comparison between transition as a new psychological ability of individuals, and a new kind of preference relationship. It took more than two decades to clarify the point and analyse the consequences of postulate 2 for utility theory.14

44Moscati’s depiction of Pareto is interesting, because it shows how Pareto, exacerbating internal hesitations of earlier marginalists (notably Jevons), unconsciously lays the ground for future developments on the measurement of utility, namely an interval-scale utility function (using postulate 2). Meanwhile, I think that this weakens Moscati’s thesis. Efforts to separate early marginalists (whether unit-based or ratio-scale marginalists) from later marginalists (linear-based or interval-scale marginalists) and to give the latter a form of self-sufficient existence based on new views about measurement is not fully satisfactory if the formal tool originates in Pareto’s attachment to the utility-first approach in parts of his theory. Again, I would uphold that, from a purely analytical viewpoint, this episode suggests more continuity than disruption when going from a unit-based to a linear-based approach. I would tend to stress instead that the methodological change brought about by debates on ordinalism was fundamental to explain the passage from a unit-based to a linear-based view on measurement and to evaluate its validity.

45My point here is that Moscati does not fully acknowledge the methodological change owed to Pareto, and consequently fails to get the full benefit of it for his thesis about the transformations of utility measurement. To make a story about the transformations of utility measurement, one needs a story about transformations in the way measurement in economics is conceived. One also needs a story about the conceptions of utility and the meanings attached to attempts at quantification. One story cannot go without the other, and regarding this matter, Pareto’s ordinalism and the debates that followed until von Neumann and Morgenstern (1944) are an essential part of the story.

46To make the point more precisely, one needs to look further at the debates about the comparison of transitions (Pareto postulate 2) in order to identify the exact stances held by the protagonists. Moscati does a great job here but I would like to add a few details and push the argument further. Before that, however, I need to mention various issues that Moscati has chosen to ignore in his story line.

  • 15 Moscati quickly deals with Slutsky ([1915] 1952) and is not interested in other less known articles (...)
  • 16 Giocoli (2003, 67-85) has provided a very detailed and careful discussion of Pareto’s role in the m (...)
  • 17 More specifically, the word “rational” appears twice in the main text, in the first half of the boo (...)

47One should not forget that Pareto’s contributions (notably the Appendix to the Manual and Pareto, 1911) contain all the seeds for an axiomatic theory of choice and a full reconstruction of the theory of value and demand (Slutsky, [1915] 1952; Frisch, 1926; Hicks and Allen, 1934). It also contains the seeds for a positivist theory of rational behaviour (suffice it to mention the initial discussion between logical actions and non-logical actions in the Manual).15 Pareto conceived of economics as an always perfectible science of models, which points to a conventional representation of science and an instrumental use of models. With Pareto, we have the beginning of a conception of rationality as something that can be defined in behavioural terms, independently of the existence of utility: Pareto’s indifference curves contain the idea that people strive to have well-ordered preferences. This entails an opening to experimental or empirical work not just to obtain the indifference map but also to check the rationality of individuals. Even though Pareto was not the most ardent Paretian in this respect, the state of consumer theory in the late 1930s owes much to the fundamental step taken in the Manual.16 In sharp contrast with the progressive transformation of the theory of choice into a theory of rational behaviour, it is striking that Moscati does not pay attention to the subject of rationality in his story line. Before von Neumann and Morgenstern, there is no mention of it.17

  • 18 Georgescu-Roegen (1936, 557-565) deals with saturation and this is where the issue of integrability (...)

48Pareto argued that indifference curves are all we need to develop a theory of economic equilibrium, and he simply evoked various ways of doing so (Lenfant, 2012), which points toward a behavioural definition of rationality.He also added that indifference curves are not mentalist states of mind (on this, I disagree with Moscati’s interpretation) because they are representations of tastes all-things-considered because the theoretician can obtain them assuming that the subject has experimented with the objects of choice. Only in a perfect long-term stationary state could we hope to obtain a mental representation of our preferences (a correspondence between the subjective representation of facts and objective facts) in a form that is meaningful to an economist. Moreover, he indicates that in general, it is possible to define a utility function generating preferences but he also discusses why such a function may just not exist (hence depriving utility even of a purely mathematical existence): this is the famous non-integrability case already mentioned by Fisher and addressed by various authors up to Samuelson. Moscati does not mention this episode (the word “integrability” does not appear in the text), which I think is fundamental to qualify the interpretation of utility for the rest of the account.18 This could help understand the ordinalists’ distance with measurement while not discarding the idea of accepting certain practices of quantification if they can be used in an operational way. In the same vein, Measuring Utility eschews an important episode in the history of utility: the revealed preference theory. Moscati argues that this story does not affect his narrative because revealed preference was not applied to develop a utility function, and therefore, to measure utility. Here, I think that we touch on a possible twist in the way Moscati connects his narrative with the history of utility and this is where I depart from Moscati’s method: measurement issues are promoted as the filtering device to decide which material should be included or excluded in the narrative.

49Now, we should not put too much emphasis on the fact that Moscati does not deal with the items mentioned above (revealed preference, the beginnings of rational choice, integrability). Indeed, they are not directly useful to Moscati’s story. However, they help get a general idea of the epistemological standards and debates around utility and preferences during that period, notably the ingrained idea of identifying behavioural properties attached to theoretical statements, an idea that runs through almost all the contributions studied by Moscati. If one wants to identify how Moscati could have given more importance than he did to methodological aspects at work in the 1930s and 1940s, it is worth looking at the few contributions that are seminal in enhancing the use of cardinality in economics, and particularly those of Phelps Brown (1934), Alt (1936) and von Neumann and Morgenstern (1944). Moscati’s handling of the analytics of those contributions is illuminating. However, I would like to put more emphasis on the methodological stances of the authors before looking at their potential consequences on the subject of measurement proper.

50From Pareto’s theory of economic equilibrium and his definition of utility, one might raise two questions: is strict ordinalism limited to a preference-first approach? The answer is clearly positive, and it is not to be doubted that to all economists after Pareto, this was the most salient feature of ordinalism as he saw it. Now, there were certainly various interpretations about how to gather preferences and their operational significance.

51The second question is: is ordinalism limited to assuming ranking of bundles or can it be extended to other kinds of preferential judgments, such as ranking of transitions?

52The answer to this question is by no means self-evident. If one sticks to the idea that ordinalism aims to provide a sufficient basis for a theory of economic equilibrium, then one might argue, according to the Occam’s razor principle, that nothing else is required. At the same time, if the generative principle of ordinalism is individuals’ motivation to perform comparisons and to abide by them one way or another when making choices, then there is space to introduce other preferential judgments. For instance, one could conceive that individuals have the ability to rank transitions, provided (1) assumptions about such ranking goes together with satisfactory empirical knowledge to test it, (2) one does not presume about the possibility of using the same language to deal with various preferential judgments. Actually, (1) and (2) are not unrelated questions since psychological experiments, if judged satisfying regarding (1) could conceivably clarify point (2). I believe this presentation sums up the methodological concerns surrounding the development of utility theory from Pareto to the 1940s.

53I think it is important to identify how Phelps Brown, Alt and von Neumann and Morgenstern deal with points (1) and (2) and to understand the consequences of their stances and the results for our understanding of utility measurement.

54If one accepts transition ranking, this could be expressed through a real value function G(.), as suggested by Phelps-Brown (1934), such that G(I->II) > G(II-III) if transition (I->II) is preferred over transition (II->III). On this basis, is it legitimate to use a utility index obtained from preferences over bundles (U) to express the properties of G? Clearly, Pareto assumed this, as did Lange, while Phelps-Brown refuted such an unwarranted consequence.

55As Phelps Brown (1934) remarked, the summation of G numbers is no more meaningful than the summation of U numbers, since the former, like the latter, can be replaced with any increasing function h(G). Furthermore, even the language used to think about the type of psychological ability (that of ranking bundles) should a priori be regarded as different from the language used to think about the ability to rank transitions. In addition, he draws attention to the need to provide empirical counterparts to new assumptions: “The initial assumptions upon which the analysis of utility depends are assumptions about the experience of the consumer, and must be expressed in the terms appropriate to the study of experience.” (Phelps Brown, 1934, 69)

56Alt’s (1936) contribution is halfway between those of Lange (1934) and Phelps Brown (1934). He assumes that transitions must be thought of in terms of preferences (and not directly as a difference of utility), and at the same time he assumes that the same language of preference applies to both transitions and simple rankings. He then provides an axiom by which a preference property expressed for bundles is translated into a preference property for transitions. From this fundamental axiom and others (which are more usual), we find that utility functions are defined up to a linear transformation. Ultimately, entrusting the individual with a new type of preferential judgment leads to restricting the class of functions that can adequately represent the preferences of this individual.

57Now, as far as point (2) is concerned, Alt was sceptical about the possibility of ranking transitions through introspection or more sophisticated experiments.

  • 19 Actually, the axiom of independence was concealed in another axiom (Malinvaud, 1952).

58Von Neumann and Morgenstern’s (1944) tour de force is to get rid of Alt’s axiom and to obtain similar properties for the utility function. This is done through the axiom of continuity in probabilities and through the axiom of independence.19 Then, under the “natural” assumption that agents evaluate risky outcomes through the criteria of expected utility and that they tend to select the lotteries with highest expected utility, then L1 preferred over L2 is equivalent to E(u(L1)) > E(u(L2)). Even if they do not refer to Alt, it is clear to the authors that the utility property is obtained at a much lower cost in terms of psychological abilities. Furthermore, the assumption of a natural process to deal with elements of choice—the expected utility criteria to deal with bundles and probabilities—is seen as more natural and accessible to human beings than the simple assumption of complete ranking of bundles.

59Now, the point I would like to make concerns the consequences of these methodological elements in terms of measurement in the arguments of Alt (1936) on the one hand and Von Neumann and Morgenstern (1944) on the other hand.

60Alt and VNM’s arguments are important steps in the development of the spirit of ordinalism, even though their contributions are associated with cardinalism. Indeed, they both take into account the idea that axioms should be tested with some kind of replicable experiments. In the case of Alt, he is optimistic that experiments on the ranking of transitions would eventually support the axiom:

With respect to II the main problem is still open, namely whether it is at all possible to make comparisons between transitions of commodities by empirical observations. But I have good hopes that within a short time this question will also be answered in the affirmative (Alt, [1936] 1971, 430).

61VNM’s results would ultimately be linked to experimentation.

  • 20 Allen and Hicks (1934), who pushed the ordinalist attitude toward linking the language of preferenc (...)

62In both cases (Alt and VNM), utility on sure outcomes is used by agents to think about their preferences over new objects (transitions or risky outcomes). In the case of Alt, the underlying assumption belongs to the realm of thought experimentation and does not seem to have any clear behavioural equivalent. Such an experimental equivalent would need at least an external system of measurement to establish the coherence between various evaluations of transitions and to connect those evaluations with simple rankings. In the case of VNM, the expected utility device leads directly to experimental treatment, based on a system of measurement which is provided by the model itself. As a result, the use of the model appears to be a necessary step to think of agents as rational subjects.20

63Hence, my point is that the difference between VNM and Alt regarding measurement has to do with the way it is embedded in the theoretical framework. In the case of VNM, a measurement procedure is a by-product of the model. In a sense, it does not need justification, it imposes itself as the unique measurement scale and measuring device associated with the criteria of expected utility—variants being only linked to the experimental device. On the contrary, following Alt’s achievement in the field of choice under certainty, measurement is still external to the model and has to be developed independently. Even though they formally identify the same measurement scales to describe individual preferences, the theoretical status of the measurements that can be performed with these scales is not the same. I wonder if Moscati would agree that such a methodological detour through ordinalism modifies the weight of arguments regarding the interpretation of cardinalism, putting more weight on internal transformations of the methodological basis of the theory and less on external explanations regarding the meaning of measurement per se.

64As an aside, as far as the preferential understanding of ordinalism is concerned, the very possibility of developing a version of ordinalism that would eventually be cardinal does not seem to have been examined with sufficient generality so far, and I would like to invite Moscati to make a stance on this. On the basis of current knowledge, Postulate 2, correctly rephrased (in preferential relationships) does not seem to lead to interval-scale utility functions. First, because nothing proves that G-preferences (preferences over transitions) can be expressed in the same language as preferences for bundles of goods. Second, even if the two were connected, one would still need to develop an experimental counterpart to deal with preferential judgments for transitions, and presumably an appropriate measurement scale to go with it. Only then could rationality principles about preferential judgments be discussed and potentially tested. This is precisely the kind of scales developed by Coombs and Siegel in the 1950s (Coombs, 1950; Siegel, 1959; see also Lenfant, 2016) and coined ordered metrics. Moscati (44) considers that these scales have played a minor role in the development of utility theory. However, one would like to investigate this further: has enough empirical and theoretical work been accumulated on preferences using these scales (not in a VNM environment) to support or discard a preference-based approach to choice under certainty that would be compatible with a specific form of cardinality?

65We are not told what remains of this issue of satiation in the 1930s. As long as the theory of choice can render the idea that a price or income change leads to a modification of the consumer basket, then it seems sufficient to carry out empirical work without having to explain that choice is the result of the satiation of wants.

66To complete my overall critical assessment of the book, I would like to focus on the way measurement is put on a pedestal in the book and the consequence of this on the treatment of psychology and utility.

6. Comments on Measurement, Utility, and Psychology

67I have already explained how Moscati chooses to develop his account through the lens of measurement. The transformation of the theories on measurement in the social sciences constitutes the backbone of the narrative, and Moscati analyses how various practical attempts at measuring utility reflect on the transformation. A word on the advantages and drawbacks of this method is in order. First of all, one may wonder about the importance of measurement in economics in general. Second, one may question the parallel development of economics and psychology regarding measurement issues. Third, one may want to know more about the meaning of utility in the various contexts of its measurement.

68Moscati could have perhaps enriched his narrative by looking at other attempts at measurement in economics. In this respect, I find it very puzzling that Moscati focuses on measurement outside economics but ignores views and practices on measurement in fields of economics other than choice and decision theory. Relevant work would probably have been rare during the marginalist revolution but certainly not during the first half of the 20th century. And this slow rise of interest in measurement in various fields of economics could have highlighted the specificity of utility measurement in decision theory. I am thinking for instance about the measurement of inequality (Pareto, 1896; Gini, 1912 and 1921; Dalton, 1921; Yntema, 1933). Furthermore, measurement came to be a watchword in the 1930s (the Cowles commission motto was “Science is measurement”) and was implemented in various fields of economics and other social sciences. There is no doubt that in many cases, the word measurement was given a loose meaning. Of course, we cannot expect a complete panorama but it would have been interesting to know what was done under the heading of measurement in other fields of economics in the first half of the 20th century, and how this could or could not support the main narrative about the 1870-1930 period. On the contrary, Moscati chooses to confront disciplines, mainly on a theoretical level.

69Regarding the confrontation between economics and psychology and their interplay, Moscati is an expert and has significantly contributed to the recent trend of analysing the relationship between economics and psychology from a historical perspective in the literature. In the book, the interplay between economics and psychology is not merely confined to the history of experimental work on utility by psychologists (alone or in collaboration with economists). Moscati also argues that psychologists have contributed to a theory of measurement that would be more suited to post WWII developments on utility. In particular, he puts much emphasis on Stevens for developing a modern theory of measuring scales. I would like to qualify somewhat Moscati’s presentation and interpretation. Again, I believe that the presentation of psychology is somewhat biased by measurement topics.

  • 21 Moscati could have mentioned other psychologists who made similar claims and categorization, such a (...)

70First, one must keep in mind that Stevens, important as he was, is a psychophysicist so that his views on measurement may not be shared by all psychologists and would be challenged by the cognitivist approach.21 Second, I think one should not give undue weight to the influence of psychologists, especially during the period 1944-1954. Stevens’ approach, presented at the beginning of part II, has obviously had no influence on economists, as Moscati acknowledges. This is not surprising at a time when the positivist approach to behaviourism was still dominant whereas the cognitive approach was still incipient. Thus, taking Stevens as the yardstick for the current practice in psychology is debatable at a time when behaviourism and its specific conception of behaviour prediction was flourishing. Third, even though psychophysicists were able to develop a general categorization of measurement scales and practices, they were not necessarily in line with economists regarding the main goal of their discipline.

71Most of the work done by psychophysicists until the 1930s consists in finding scales of measurement and comparing alternative experimental methods and protocols to test the reliability of a scale and to experiment on various kinds of psychological continuum. Hence, the epistemological status of measurement in psychology is different from its status in economics (Lenfant, 2016). In the 1940s, those working along the lines of psychophysics seem to have been using various kinds of measurement scales and were not necessarily in search of ratio scales. Stevens, for his part, was hoping to obtain more powerful scales than linear scales:

It is important to note that in asserting [the] possibility [that utility is a power function of the quantity of money] we are assuming that utility can be measured on better than an interval scale. The [Von Neumann-Morgenstern] version of utility, the measure of which is derived from risky choices, envisages interval measurement only, and the question arises: on what grounds can we hope to do better? … The strategy suggested by these psychophysical developments [experiments related to prosthetic perceptual continua] is that the utility theorist might profitably forget about scaling utility up to a linear transformation and try directly for the larger prize of scaling it up to a similarity transformation [ratio scale] (Stevens, 1959, 53).

72At the same time, other psychologists were already inclined to work with less stringent scales, especially when dealing with issues linked to preferences. Coombs (1950) launched an “ordered metric scale”, which is not based on a constant unit of measurement. This ordered metric scale seems to have been devised specifically to deal with preferential judgment (Siegel, 1959).

73A few years later, work done by the younger generation of psychologists at the University of Michigan (Slovic, Lichtenstein and Tversky) clearly walked away from measurement issues and approached decision theory differently. Hence, it seems that the field of psychology held evolving views about the status of measurement in psychology, and that Stevens’ views are rather representative of one particular view on measurement.

74Once the expected utility model had triggered the interest of psychologists and called for some collaborative work, it is interesting to inquire whether economists or psychologists would change their views on measurement as a central issue for psychology. I would like to invite Moscati to tell us more about this and to clarify his standpoint on the influence of the work of psychologists on measurement in economic thought.

  • 22 Another structuring opposition is about the understanding of utility as either a mental state of mi (...)

75Finally, I would like to say a few words about the way Moscati discusses utility. On many occasions, I think the reader would like to know more about the meaning of utility for the various authors and how it connects with each author’s specific agenda (particularly for Edgeworth, Marshall, Fisher, Frisch, Friedman and Savage). Most of the time (except in the short summaries), considerations on measurement per se are independent of the issue of what is actually being measured and why. On this topic, we must be content with the idea that the economists’ understanding of measurement influenced their theory of utility. At the same time, Moscati seems to uphold that the broadening of the meaning of utility (from Jevons’ hedonistic satisfaction of needs to the satisfaction of a broader set of wants or desires, and later, to the satisfaction of a general set of motivations for human action) led to a change in the very conception of its measurement.22 However, this idea is not developed further. From the presentation of the book, it seems that reflecting on the meaning of utility will be relegated to being a by-product of what is said about its measurement. It is therefore strange that Moscati does not discuss the personal agenda of certain authors in order to comment on their attempts at measuring utility. For instance, we know that Edgeworth’s initial views were strongly influenced by utilitarian ethics in which the ability for pleasure and pain would command a share of labour and commodities in society (Edgeworth, 1881; Chaigneau, 1997). For his part, Marshall linked the measurement of utility to that of temperature (Lallement, 1985). We also know that Fisher’s views on marginal utility were the foundation for a theory of taxation (Fisher, 1927) and that Friedman linked his analysis on risk taking with that of income distribution (Friedman, 1953). For some authors at least, an attempt at putting measurements of utility in context would have been welcome.

76As a conclusion to this review essay, I hope the reader has understood that Moscati’s achievement is innovative in that it provides us with news ways to assess the history of utility in economics. To me, it is an inspiring book that forces us to take into account issues about measurement in our overall appraisal of the development of the theory of rational choice in economics. I am confident that Moscati’s narrative will foster new studies on the development of utility theory in the future and that Measuring Utility will be for long a reference book on the topic.

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Bibliographie

Allais, Maurice. 1953. Le comportement de l’homme rationnel devant le risque : Critique des postulats et axiomes de l’école americaine. Econometrica, 21(4): 503-546.

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Notes

1 Many interesting passages of Moscati’s book will be ignored in this review. I have chosen not to comment on Moscati’s views about what is known as the representational theory of utility. Nor will I discuss Moscati’s historical account of the 1970s and 1980s.

2 What becomes important then is that measurement is part of a scientific process towards elaborating, testing, and selecting a satisfactory model of behaviour, to which certain welfare statements could be attached.

3 Stevens’ contribution is important to help us confront the epistemology of psychology and of economics. According to Stevens, influenced by the operationalist fame of the 1930s, one can distinguish the four scales of measurement mentioned at the beginning of this essay (nominal, ordinal, interval and ratio scales) and associate them with certain acceptable empirical operations. Each scale is more demanding than the previous one in terms of operations (more operations must be possible).

4 I have not mentioned here the simplest kind of scale, the nominal scale, which is simply a way of labelling variables, with no quantification or relationship attached to the labels.

5 Moscati does a wonderful job tracing out the discussions about the ranking of utility differences even though he sometimes leaves us with open questions along the way. We still wonder at the end of part II what difference does a linear transformation can make. If a given preference relationship can be represented through classes of linear transformations of a utility index, what difference does it make for observable demand behaviours or for welfare issues? Because Moscati seems reluctant to discuss demand theory or welfare issues, we cannot assess the consequences of those analytical advances. I have tried to deal further with this question in section 5 of this essay.

6 Von Neumann, Morgenstern, Allais, Samuelson, Friedman, Savage, Strotz, Baumol, Marschak, Alchian, Malinvaud, Wold, Ellsberg and Arrow.

7 If a subject is indifferent between L1(500, 0.4; 1000, 0.6) and L3 (600,1), L3 being an outcome for sure, then 0.4.u(500)+0.6u(1000)=u(600) and by arbitrarily fixing a unit of measurement (as we are allowed to do due to the linearity assumption over u(.)) e.g. u(500) = 0 and u(1000)=1, we obtain a measurement for u(L3)=0.6. Then, by obtaining additional measures for other certain outcomes and using them in turn to build lotteries, we can check if declared preferences or indifferences are in accordance with the predictions based on the calculation using the expected utility model. The point here is that some lotteries used as certainty equivalent are then used to build lotteries. The work of Friedman and Savage (1948) was the starting point for deeper reflections on the validity of experiments, on the use of the certainty equivalent and on the methods most appropriate for experimentation.

8 Moscati’s choice not to discuss measurement-based experiments in connection with measurement-free experiments (Slovic and Lichtenstein, 1971; Tversky, 1969) fails to make us aware of the internal validity of one strategy versus the other as psychologists of the time could see them, and this is certainly regrettable.

9 Moscati’s tracking of the “right” use of the term does not lead to a clear conclusion. Samuelson would certainly have considered that a ratio scale is a special case of linear scale. To argue that there is some specificity in the terminology, one would have to associate the use of “cardinal” with the idea that we need it for a special purpose and that this implies recognizing specific abilities on the part of individuals, taking into account in their behaviour not only their preference but also the strength of this preference, assuming that the preference relationship to utility differences behaves normally (i.e. is transitive). No one seems to have explicitly made that claim or discarded ratio scale for being too specific a case or being associated with an old view of measurement. We can find in the Foundations uses of cardinal utility that pertain to the ordinalist vs cardinalist opposition: “[M]any writers have ceased to believe in the existence of any introspective magnitude or quantity of a cardinal, numerical kind. With this scepticism has come the recognition that a cardinal measure of utility is in any case unnecessary; that only an ordinal preference, involving ‘more’ or ‘less’ but not ‘how much,’ is required for the analysis of consumer’s behavior.” (Samuelson, [1947] 1983, 91). Furthermore, Samuelson considered that welfare analysis could be handled without resorting to cardinal utility.

10 On this, Moscati could have paid more attention to Marshall’s or Edgeworth’s analogies between utility and temperature.

11 This leads to further criticism of other uses of the utility theory, either for welfare analysis of for taxation purposes, which I will address later in this review.

12 Though Moscati usually details the attempts at measuring utility (or derivative concepts such as marginal utility), he unfortunately fails to describe Frisch’s model in greater detail, which he could have done by relying on Chipman (1998) and Dupont-Kieffer (2013). Frisch’s theoretical measurement implies a ratio-scale between the marginal utility of money and the marginal utility of a particular commodity.

13 For interested readers, the most accurate presentation of Pareto’s contribution on utility remains Chipman (1976, 67-86). Giocoli (2003) provides a refined discussion of Pareto’s methodological stance.

14 Pareto himself is quite confused since he considers that an individual’s ability to compare transitions is at best approximate. While people may be able to assert when a transition is better or worse than another they are unable to tell precisely when it is indifferent. This echoes Fechner’s well-known results about the variability of responses to the same stimulus in psychology.

15 Moscati quickly deals with Slutsky ([1915] 1952) and is not interested in other less known articles by the same author on Böhm-Bawerk’s theory of value (Slutsky, [1927] 2004). Slutsky recognized that there are two concepts of utility in Pareto. The one still linked to hedonism, ophelimity, and the index function of utility, which is “completely strict and abstract”. Slutsky certainly expressed that his results were independent of the chosen utility index (Slutsky, [1915] 1952, 28-29 and 52-53), and he went a long way to discuss the consequences of this for the relationship between economics and psychology, even pointing to the possible use of experimental budgets to see if the properties of the utility function refer to psychologically conscious phenomena, thus opening the way to a serious shift in the very meaning of utility. There is therefore a scattered reflection as to the meaning of utility which is radical in its shift from previous thinking while laying the groundwork for thinking about the proper way to use data in order to understand behaviour and rationalize it. Slutsky even suggested that eventually, the preference-first approach clarifies demand theory (as long as we can recover preferences one way or the other) while it opens the way to formidable questions in psychology (what are the conscious phenomena that are likely to affect behaviour?). Thus he arrives at an expression of the problems associated with ordinalism which are very much in tune with later discussions in the 1930s.

16 Giocoli (2003, 67-85) has provided a very detailed and careful discussion of Pareto’s role in the methodological turn toward a “consistency view of rationality”. It is beyond the scope of this review essay to argue in detail about Pareto’s complex stance. I would claim that Pareto, though he was incomplete in his treatment of indifference curves and behaviourist account of rationality, made some moves toward constructing a view of rationality based on consistent behaviour. The simple fact that there are no intersecting indifference curves assumes that the agents are able to rationalise their preferences in some sense (or that observers strive to make agents comply with this criterion). This move, however, did not lead to a generic economic agent of a Samuelsonian type merely because Pareto, at the same time, conceived of microeconomics has a mere tool for dealing with the behaviour of groups of agents, used to model market behaviour, in relation to other socio-economic data (Lenfant, 2001). Hicks would echo this view in Value and Capital, rejecting the idea that individuals should abide strictly by the principles of rational choice.

17 More specifically, the word “rational” appears twice in the main text, in the first half of the book.

18 Georgescu-Roegen (1936, 557-565) deals with saturation and this is where the issue of integrability comes in.

19 Actually, the axiom of independence was concealed in another axiom (Malinvaud, 1952).

20 Allen and Hicks (1934), who pushed the ordinalist attitude toward linking the language of preference with individual choice, could not consider postulate 2 as useful and did not try to reflect on the behavioural meaning of a transition-preference relationship.

21 Moscati could have mentioned other psychologists who made similar claims and categorization, such as Gulliksen (1946) who was actually also involved in measuring the utility of money: “The important thing is that numbers can be assigned to objects in such a way that an operation (not necessarily addition) with two numbers will indicate the result of some experiment which can be performed with the two objects represented by these numbers. This experiment should be independent of the rest of the population of scaled objects.” (Gulliksen, 1946, 202)

22 Another structuring opposition is about the understanding of utility as either a mental state of mind (the mentalist view) or a convention (the instrumentalist view). While the former dominated during the marginalist revolution, it faded away and most economists would claim to be conventionalists in the 1950s.

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Jean-Sébastien Lenfant, « Everything You Always Wanted to Know About Utility Measurement (But Were Afraid to Ask) », Œconomia, 9-1 | 2019, 61-91.

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Jean-Sébastien Lenfant

Université de Lille 1, CLERSE

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