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

More Light on Measuring Utility. A Response to Herfeld, Heilmann, and Lenfant

Ivan Moscati
p. 119-132
Référence(s) :

Ivan Moscati, Measuring Utility: From the Marginal Revolution to Behavioral Economics, Oxford: Oxford University Press, 2019, 352 pages, ISBN 978-019937277-5

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Crédits : Oxford University Press

1Let me begin by thanking Jean Baccelli for organizing this review symposium, and Catherine Herfeld, Conrad Heilmann, and Jean-Sébastien Lenfant for their thoughtful reflections and comments on the book. Herfeld’s comments focus on the historiographical methodology adopted in Measuring Utility, while Heilmann’s and Lenfant’s address specific topics related to the history of utility measurement discussed, or not discussed, in the book. I start by responding to Herfeld’s comments and then move to Heilmann’s and Lenfant’s.

1. Response to Herfeld

2In her first and third comments, Herfeld argues that I should have made my methodological position about the historiography of economic thought (HET) more explicit, and that I should have explained how that position informed the history of utility measurement presented in the book. In particular, I should have discussed whether or not, or to what extent, the history of utility measurement presented in the book is in agreement with the critique of the HET-as-science-studies program and the defense of the internal approach to the history of economic ideas that I advanced some years ago (Moscati, 2008). In effect, a first draft of the Prologue to the book contained some pages in which I attempted to make my historiographical position explicit, and even to explain how and why my views about the historiography of economics have evolved since 2008. However, diverse but concomitant considerations induced me to cut those pages from the Prologue.

3First, the book is intended for audiences that go beyond historians of economic thought, and include mainstream choice theorists, behavioral economists, and philosophers of science. I considered that these potential readers might be more interested in the history of utility measurement than the evolution of my views about the historiography of economics. For sure, these views, implicit or explicit as they may be, have informed my history of utility measurement. However, a monograph intended for a broader audience is different from an article contributing to a methodological debate internal to the HET discipline, and I came to think that for the monograph a “show, don’t tell” approach was preferable: rather than telling the reader how my historiographical views had informed my history of utility measurement, I wanted to show the reader what kind of history, when all was said and done, these views were able to produce.

  • 1 See Weintraub (1996).

4Secondly, thinking specifically of my fellow historians of economics, I was afraid that discussing my views about the historiography of economics in the Prologue of the book would have stimulated the “meta-historical” attention of some of them rather than their historical interest. I wanted to avoid that, and I also wanted to avoid that the book might be primarily read as another contribution to the Methodenstreit begun in HET more than twenty years ago.1

  • 2 For an introduction to the philosophy of historiography, see Tucker (2004), Tucker (2009), Kuukkane (...)

5Thirdly, in the last few years I have realized that there exists a rich discipline called the philosophy of historiography, in which issues concerning the ontological status of the past, the nature of historical evidence and historiographic concepts, and the epistemic character of historical knowledge are hotly debated, and in which different schools of thought, like historical realism or narrativism, fiercely oppose each other.2 Although my reading of the literature in the philosophy of historiography has been unsystematic, what I read made me suspect that the categories through which I and other historians of economics have framed our methodological discussions in the course of the HET Methodenstreit—that is, categories like thin vs thick history, or internal vs contextual history—are somehow problematic. Moreover, when I tried to define my current historiographical approach using those categories, the result was far from clear-cut.

6At any rate, if I have to characterize my historiographical approach with respect to the categories traditionally used in HET, I could adopt the characterization offered by Herfeld towards the end of her review:

[Moscati’s] account … cannot be classified as externalist. However, it is not a proper internalist history either. … He draws on correspondences, and points the reader to relevant conference settings; and he discusses disciplinary backgrounds, and institutional affiliations to increase our understanding of the changes of particular ideas or practices. In later chapters, Moscati … details the experimental research practices to show how utility was measured. … [He] attempts to place his history of utility measurement into the larger context of measurement practices in psychology and, while less so, physics as well as the changing understanding of measurement more generally.

7This is a fair characterization of my work. However, it is difficult to accommodate it with the historiographical categories used in the HET Methodenstreit. Is mine a thin or a thick history of utility measurement? Is it an internal or a contextual history? Is it a balanced synthesis of the two approaches, or just an inconsistent mixture of them? Maybe the answer to these questions is that we historians of economics should abandon the simplistic dichotomies we have often used, become more familiar with the richer set of categories adopted in the philosophy of historiography, and accept that there are more ways of constructing coherent and convincing narratives than are dreamt of by those who keep asking: “What defines a legitimate contribution to the history of economic thought?”

8Herfeld’s second comment concerns the explanations that would be missing from Measuring Utility. According to her, my historical analysis remains primarily descriptive, and it systematically fails to explain why economists held certain views about utility and utility measurement, or why they changed them.

9I do not believe that the narrative of Measuring Utility is primarily descriptive. In contrast, I deem that most passages of my narrative are just about how and why economists held certain views about utility and utility measurement, and about how and why they changed, or did not change them. When the book’s narrative is mainly descriptive and does not provide the kind of explanations Herfeld seems to look for, this is because I found no robust historical evidence supporting them, and I preferred avoiding offering the reader anachronistic explanations (that is, explanations of the past based on present ideas that did not exist at the time) or merely speculative explanations.

10Let me try to clarify this issue by referring to one of the explanations that, according to Herfeld, would be missing from the book. She raises the question of “why these marginalists [Jevons and the other early marginalists] were ultimately not as concerned about solving the measurement problem as they should have been. Indeed, if utility measurement was a key concern for them, why did they ultimately not dismiss … the unit-based understanding of utility?” In the book, I extensively argue that Jevons and the other marginalists did not dismiss the unit-based understanding of utility because, just like every other philosopher or scientist of the time, they wholly identified measurement with unit-based measurement. For sure, one may ask: “But why did marginalists stick to such a restrictive idea of measurement? As Stanley Smith Stevens showed in 1946, abandoning the unit-based understanding of measurement is easy. Why marginalists, psychologists, and scientists in other disciplines did not make that easy move well before 1946, and possibly even in the 1870s?”

11I think that the last of these is a debatable historiographical question, and that we should avoid the anachronism of considering simple and straightforward what is simple and straightforward only from the viewpoint of present-day ideas, or to speculate about reasons and motives about which we do not have any historical evidence. In the published texts and correspondence of Jevons and the other marginalists I did not find any evidence supporting an answer different to the one I argued for in the book: no monetary incentives, no institutional constrains, no political preoccupations prevented marginalists from dismissing the unit-based understanding of utility. What I found is only what John Maynard Keynes ([1936] 1973, xxiii) would have called a long and difficult “struggle of escape from habitual modes of thought;” in this specific case, a long and difficult struggle of escape from the habitual conception of measurement. In the book I have comprehensively accounted for how this struggle originated and developed; I have spelled out which conceptual resources were available to the parties involved in the struggle and how those resources were used; and I have analyzed in detail how and why, in the 1950s, the debate on Expected Utility Theory eventually modified the economists’ conception of utility measurement. In my view, and given the historical evidence I found, this narrative provides a non-anachronistic, non-speculative explanation of why utility theorists first stuck to the unit-based understanding of utility and eventually dismissed it.

  • 3 For a discussion of the nature of historiographical explanation, see Kosso (2009) and Macdonald and (...)

12Possibly, the general philosophical issues Herfeld and I disagree over are what makes a historiographical explanation satisfactory and, even more generally, what is the nature of explanation in historiography as contrasted, for instance, to the nature of explanation in physical science. I do not think this is the right place for addressing these complex philosophical questions.3 The single, and arguably acceptable, point I would like to make here is the following: since the evidence we have about the past is limited (for instance, the published texts, manuscripts, and letters of economists reveals only a small part of what they thought and believed), it is not always possible to find the sort of explanations Herfeld seems to look for. In these cases, providing an accurate account of what happened and of how it happened, without attempting to provide anachronistic or speculative answer to the question “Why it happened?” is a sound historiographical strategy.

2. Response to Heilmann

13In his first comment, Heilmann remarks that in the book little attention is given to the interpretation of the probability concept and, more specifically, to issues concerning the measurement of subjective probability. In effect, the measurement of utility and the measurement of subjective probability have much in common. Both utility and subjective probability cannot be observed and measured in a straightforward way. For both utility and subjective probability indirect measurement methods based on the observation of choice behavior have been proposed. Finally, both utility and subjective probability can be interpreted either as mental variables existing in the individual’s mind or as instrumental variables that appear in models that have proven useful for describing or predicting some important economic phenomena. In effect, a monograph entitled something like Measuring Subjective Probability would be a nice complement to Measuring Utility, and I am thinking of whether this could be my next long-term research project.

  • 4 Some key contributions to the debate on the measurement of subjective beliefs are: Ramsey ([1926] 1 (...)

14The reason why in Measuring Utility I did not deal with probability issues in detail is that questions concerning probability, or even only questions concerning the measurement of subjective probability, are too complex to be dealt to in a book focusing on a different topic like the history of utility measurement. As Heilmann rightly notices, the philosophically oriented debates about the interpretation of probability—that is, of whether probabilities should be seen as frequencies, degrees of subjective belief, logical relations, propensities, or something else—have been extremely rich. But also discussions in economics and psychology about the measurement of subjective beliefs have been very intense, and have addressed issues concerning whether choice data only, or also verbal self-reports, can be used to measure subjective beliefs; whether subjective beliefs are sufficiently consistent to be captured by the Bayesian concept of probability, or whether non-standard notions of probability, like Choquet capacities, are more suited to provide a numerical correlate of subjective beliefs; furthermore, the very possibility that subjective beliefs may be expressed in numerical form has been challenged.4 There was no room in the book to properly address these kinds of questions.

15In the book I have discussed issues related to probability and probability measurement only when, and only insofar, this was necessary to address issues related to utility measurement. This is the case of the experimental measurements of utility based on individuals’ choices among gambles with monetary payoffs that are discussed in Chapter 13. Researchers like Donald Davidson, Patrick Suppes, and Sidney Siegel (1957) explicitly discussed the possibility that experimental subjects may misunderstand or distort the objective probabilities of the outcomes of gambles. This, in turn, would undermine the significance of the utility measures obtained from the subjects’ choices among gambles. In the book I explain how Davidson, Suppes, and Siegel offered a possible solution to the problem by constructing a special die, and verifying that the experimental subjects did not misunderstand or distort the probabilities of events associated with the tossing of the die.

16In his second comment Heilmann argues that my historical reconstruction shows that there is a “conceptual blind spot” in the history of utility measurement, that is, that economists have made little effort to clarify the nature of utility and preferences. In particular, Heilmann claims that economists have failed to answer straightforward questions like: “To what extent are preferences and utility mental or behavioural concepts, and what precisely is the mental state of a preference referring to?”

17I largely agree with Heilmann’s point about the “conceptual blind spot” in the history of utility measurement. However, the fact that the practitioners of a scientific discipline rarely engage in the philosophical clarification of the concepts they use is not limited to economics but characterizes most scientific enterprises. I would even say that “conceptual blind spots” are pretty much the norm in science, not only in bad science but also in good science. And I think that the approach of most scientists can be justified in different ways, e.g. by stressing the advantages of the division of labor between scientists and philosophers of science (scientists investigate the world, often using non-transparent concepts; philosophers of science investigate how scientists investigate the world, and possibly clarify the scientists’ non-transparent concepts); or by stressing that when philosophers attempt to clarify the nature of scientific concepts, they rarely agree about what this nature might be.

  • 5 See e.g. Hausman (2012), Cozic and Hill (2015), Dietrich and List (2016), Okasha (2016), Engelen (2 (...)

18In particular, the latter is the case with the philosophers’ attempt to clarify the nature of preferences in economics. As Heilmann rightly notices, this has been a topic of heated debate in the recent philosophy of economics.5 It is fair to say, however, that philosophers of economics have not yet reached an agreement on whether preferences should be considered as mental concepts, behavioral concepts, or, as, Francesco Guala (forthcoming) has recently argued, neither mental nor behavioural constructs.

19More generally, I am in favor of a “naturalistic” approach to the history and philosophy of science: rather than reproaching economists or other scientists for being “conceptually blind” or committing some other methodological sin, in my view historians and philosophers of science should accept the practices of scientists for what they are, and acknowledge that disciplinary debates typically provide scientists with just the conceptual clarification they need to advance or apply their scientific theories. For instance, the economists’ debate on the nature of the von Neumann-Morgenstern utility function reconstructed in Chapters 9-12 of the book provides a good example of a disciplinary discussion that produced just the conceptual clarification economists needed to advance and apply utility analysis.

20A further and more complex level of the naturalistic approach to the history and philosophy of science consists in formulating a systematic epistemological theory that could account for the scientific practices adopted in a certain discipline including, possibly, the discipline’s tolerance towards conceptual blind spots. In past work (Moscati, 2006; 2007), I did something in this spirit, and argued that an epistemological theory of Neo-Kantian inspiration that I called the Marburg view, can account for the history of neoclassical consumer theory more persuasively than other epistemological theories like Popperian falsificationism or Lakatos’s methodology of scientific research programmes. However, I had to acknowledge that my Marburg epistemological theory was highly incomplete, and this is why in the book I did not venture to apply it to the history of utility measurement.

21Heilmann’s third point concerns the Representational Theory of Measurement (RTM) and its possible limitations when applied to actual utility measurement. If I understand Heilmann’s comments correctly, I agree with them: RTM allows researchers interested in utility measurement to answer some important questions about the structure of the concept they want to quantify, but certainly not all questions that are relevant for actual utility measurement. In particular, RTM is pretty silent about how to construct and calibrate a reliable device for measuring utility. For instance, as discussed in Part Four of the book, one of the main problems that researchers face when they attempt to measure utility experimentally is that different elicitation methods, which in principle should produce the same outcome, in fact generate different utility measures. RTM has little if anything to say about how to solve these kinds of problems.

3. Response to Lenfant

22In his first comment, Lenfant argues that my reconstruction of the early history of utility measurement focuses too much on issues concerning the unit of utility and neglects issues concerning the zero point of utility. In particular, according to Lenfant, Irving Fisher and possibly other early utility theorists took into consideration the possibility that the unit of utility a may depend on the point b chosen as the zero point of utility, that is, the possibility that a=f(b). In turn, the very consideration of this possibility would have made the early marginalists closer than I claim in the book to the cardinal understanding of utility that emerged in the 1930s.

23In Measuring Utility I focus on issues concerning the unit of utility because these were the issues that Jevons, Menger, Walras and the other early marginalists discussed. The quotations from their writings presented in the first two Parts of the book provide, I deem, sufficient textual evidence in support of the book’s focus on the utility unit. In contrast, the early marginalists rarely discussed issues related to the zero point of utility, may it be the zero point of total utility or marginal utility. It is more difficult to use quotations to show that discussions about the zero point of utility were very rare in the writings of the early utility theorists. As an indicator of such a rarity, however, we could take the limited number of times the word “zero” appears in their major works in contexts where it refers to the zero-utility point. Thus, a text search on Jevons’s Theory of Political Economy reveals that he used the word “zero” with reference to the zero level of utility only twice (1871, 62-63). In his Éléments d’économie politique pure, Walras used the word “zéro” with reference the zero level on utility only once (1874, 80). In his Mathematical Investigations in the Theory of Value and Prices (1892), Fisher never used the word “zero” in relation to the zero-utility point. A similar text-search exercise could be conducted on the other major works of the early utility theorists and would arguably give similar results.

24Even the claim that the early marginalists took into consideration the possibility that the utility unit a may depend on the zero-utility point b does not seem well supported by the available textual evidence. The passages from Fisher’s Mathematical Investigations (1892, 14-16) that Lenfant uses to support this claim appear problematic to me. First, in those passages Fisher does not even mention the zero-utility point. Second, as Ludwig von Mises ([1912] 1953, 43-44) later pointed out, Fisher’s method to measure utility crucially depends on the implausible assumption that the marginal utility of β is twice the marginal utility of β/2, that is, on the assumption that U(β/2)=U(β)/2 (for a discussion of Mises’s criticism of Fisher, see section 5.4.2 of Measuring Utility). Similarly implausible is the assumption that the marginal utility of γ is three times greater than the marginal utility of γ/3, that is, the assumption that U(γ/3)=U(γ)/3. If we remove these implausible assumptions, we only know that U(100th loaf)=U(β)=U(γ) and that U(150th loaf)=U(β/2)=U(γ/3) which, however, does not tell us anything about the utility ratio U(100th loaf)/U(150th loaf) or about how this ratio could depend on associating B gallons of oil or C gallons of oil with the zero-utility point. Third, in the case that we accept Fisher’s implausible assumptions, we should also accept his conclusions, namely that the utility ratio U(100th loaf)/U(150th loaf) is independent of whether the zero-utility point is associated with B gallons or C gallons of oil (see Fisher 1892, 16). In any scenario, the claim that Fisher was concerned by the possibility that the utility unit might depend on the zero-utility point appears problematic to me.

25Finally, and this addresses the final part of Lenfant’s first comment, if the claim that the early marginalists considered the possibility that the utility unit may depend on the zero-utility point is questionable, also the corollary of this claim, namely that the early marginalists’ understanding of utility measurement was close to the cardinal understanding that emerged in the 1930s, appears debatable. I agree with Lenfant that, from a measurement-theoretic viewpoint, exploring the conceptual relationships between possible transformations V[U(x)] of the utility function, that is, transformations such as V[U(x)]=b+f(b)U(x), V[U(x)]=b+aU(x), or V[U(x)]=b+U(x), is a useful exercise. My only point here is that the historical evidence we have does not suggest that the early utility theorists reasoned in such measurement-theoretic terms.

26In his second comment, among other things Lenfant questions the conceptual usefulness of the claim that Jevons and the other early utility theorists were not cardinalists in the current sense of the term: “In what sense are we better—he asks—[in] saying that Jevons or Edgeworth were not cardinalists?” My answer, I am afraid, will not satisfy Lenfant because it is very much a repetition of what I say in the book or of what I have said already in this response. However, let me try to present it in extremely schematic terms, in the hope that this might help clarification:

  1. Early utility theorists identified measurement with unit-based or ratio scale measurement;

  2. Following this conception of measurement, they judged utility to be measurable or unmeasurable according to whether a unit of utility was available or not;

  3. They were convinced that at least part of their theories relied on the measurability of utility and, accordingly, they believed that measuring utility would have made their economic theories scientifically sounder and more defensible against the attacks of their critics;

  4. Therefore, early utility theorists attempted to identify a unit of utility, so to be able to measure utility;

  5. However, they failed to identify a unit of utility;

  6. They concluded that the utility featured in their theories was not measurable and, therefore, that the part of their theories relying on the measurability of utility rested on shaky scientific foundations;

  7. This problematic situation has little to do with the interval-scale measurement that in current economic theory is associated with cardinal utility.

  8. Therefore, Jevons and the other early utility theorists were not cardinalists in the current sense of the term.

  9. But why did early utility theorists not dismiss the restrictive unit-based conception of measurement? Because, just like every other philosopher or scientist of the time, they wholly identified measurement with unit-based measurement and their struggle to escape from such a conception of measurement was longer and harder than it might appear from the viewpoint of present-day ideas about measurement.

  10. What do we gain by saying that the early utility theorists were not cardinalists? We avoid projecting the current notion of cardinal utility back onto the past, and in so doing we are in a better position to understand the conceptual problems the early utility theorists actually faced.

  11. Does the circumstance that Fisher and maybe other utility theorists considered the possibility that the utility unit may depend on the zero-utility point indicate that they were not that far from using interval scales, and therefore from being cardinalists in the current sense of the term? The available historical evidence does not support the claim that early utility theorists considered the possibility that the utility unit may depend on the zero-utility point.

27In his third comment Lenfant discusses how ordinalism, and utility measurement within ordinalism, are discussed in the book. As I read this comment, Lenfant basically suggests various ways and directions in which my reconstruction of ordinalism and utility measurement within ordinalism could have been enriched, for instance by discussing Pareto’s economic thought more thoroughly or by including revealed preference theory into the narrative. Most of the extensions suggested by Lenfant make a lot of sense and could in effect represent topics for future work. However, I submit, they would not have changed the narrative of Measuring Utility in any substantial way. Some passages of Lenfant’s comment (“Now, we should not put too much emphasis on the fact that Moscati does not deal with the items mentioned above … Indeed, they are not directly useful to Moscati’s story”) suggests that he agrees with this view.

28However, Lenfant makes one important critical comment that I need to address, namely that my narrative does not pay enough attention to the theme of rationality. Generally speaking, I think that the word “rationality” has so many meanings and connotations that, in order to avoid confusion, it should be used very carefully. In decision theory, an individual is called “rational” if her preferences satisfy certain properties such as completeness, transitivity, or independence (in the sense of the independence axiom), and if she chooses her most preferred option according to her preferences. However, the words “rationality” and “rational” carry with them a powerful and enduring normative connotation, according to which being rational is a good thing, while being irrational is a bad thing. Because of this normative connotation, saying that an individual has incomplete preferences sounds much less severe than saying that his preferences are irrational. In economic discourse the two dimensions of the word “rationality” are often confused, and assumptions about the properties of preferences are often made more palatable by calling them “rational.” To increase the confusion, in philosophy and other disciplines “rationality” does not mean having complete or transitive preferences. For instance, one meaning of rationality in philosophy is compliance with the rules of logical inferences such as the modus ponens or the modus tollens.

29In the book I attempted to avoid these possible confusions. Accordingly, I used the words “rationality” and “rational” with parsimony, and took care that their exact meaning was sufficiently clear from the context of use. If this terminological prudence is taken into account, I would say that my narrative does pay sufficient attention to the rationality theme, at least insofar it is relevant to issues related to utility measurement. In particular, Chapters 10 and 11 analyze how in the early 1950s Marschak, Samuelson, Savage and other utility theorists discussed issues concerning the normative validity of Expected Utility Theory (EUT) in terms of what it means to behave rationally in conditions of risk. Similarly, Chapters 13, 14, and 16 discuss to what extent the choice behavior of individuals, as recorded in the experiments that Mosteller, Suppes, and other researchers performed since the late 1940s, deviates from rational behavior as defined by EUT.

  • 6 Boumans (2015) provides some important insights on this topic.

30In his fourth comment, Lenfant argues that some parts of my narrative could have been framed in a different way or developed in different directions. In particular, Lenfant finds puzzling that I focus on the relationship between measurement in utility theory and measurement in psychology, while I say little about views and practices of measurement in other areas of economics. I agree that my enduring research interests in the relationship between economics and psychology, and the fact that, as I explain in the Prologue, the initial idea for the book derived from reading Joel Michell’s Measurement in Psychology (1999), may have led me to an over-concentration on the relationship between utility measurement and psychological measurement. I also agree that a more general analysis of how measurement issues are dealt with in different areas of economics is a very rich and interesting topic of research.6 However, it is also true that only very rarely did the economists who discussed issues related to utility measurement in the period 1870-1985 relate these issues to measurement problems in other areas of economics. A possible explanation for this fact is that measurement problems in other areas of economics, such as the measurement of national income, the general price level, inequality, or the quantity and velocity of money, can be well conceptualized within the unit-based conception of measurement and, therefore, do not require any fundamental re-discussion of that conception. In this sense, the economists’ struggle with issues of utility measurement is quite different from the problems they faced in measuring other economic variables, and in effect more similar to the psychologists’ struggle with issues related to the measurement of sensations and other mental variables. If considered from this viewpoint, the book’s strong focus on the relationship between utility measurement and psychological measurement may appear justified.

31Finally, Lenfant regrets that on many occasions I do not discuss in sufficient detail the economic thought of the economists I consider and, more importantly, I do not discuss how and why their engagement with utility measurement was related to their more general research agenda. This is a fair criticism. My defense is that I did not want to write another history of utility analysis, or another history of economic thought. I wanted to focus on the economists’ ideas and discussion about utility measurement but, I agree, this focus sometimes comes at the cost of losing a more general picture of the ideas of the economists I considered.

4. Conclusion

32My goal in Measuring Utility was certainly not that of offering the “final word” about the history of utility measurement. Few of us, I believe, think that there are final words in historiography. I attempted to provide a comprehensive and well-documented account of the history of utility measurement, that could engage historians and philosophers of economics as well as scholars in neighboring disciplines, and that could constitute a good starting point for further historical research or philosophical reflection on that history. Such a project involved a number of decisions about what to include in my account and what to exclude, about how to connect the different parts of the long and complex history of utility measurement in a consistent narrative, and about which dimensions of the story should be emphasized. The comments by Herfeld, Heilmann, and Lenfant questioned some of those decisions and invited me to explain or defend them. I hope that my responses have been somehow persuasive, and that our exchange has shed more light on the project of Measuring Utility.

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Notes

1 See Weintraub (1996).

2 For an introduction to the philosophy of historiography, see Tucker (2004), Tucker (2009), Kuukkanen (2012).

3 For a discussion of the nature of historiographical explanation, see Kosso (2009) and Macdonald and Macdonald (2009).

4 Some key contributions to the debate on the measurement of subjective beliefs are: Ramsey ([1926] 1931), de Finetti (1937), Savage (1954), Ellsberg (1961), Tversky and Kahneman (1974), Schmeidler (1989), Manski (2004).

5 See e.g. Hausman (2012), Cozic and Hill (2015), Dietrich and List (2016), Okasha (2016), Engelen (2017), Angner (2018).

6 Boumans (2015) provides some important insights on this topic.

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Ivan Moscati, « More Light on Measuring Utility. A Response to Herfeld, Heilmann, and Lenfant », Œconomia, 9-1 | 2019, 119-132.

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Ivan Moscati, « More Light on Measuring Utility. A Response to Herfeld, Heilmann, and Lenfant », Œconomia [En ligne], 9-1 | 2019, mis en ligne le 01 mars 2019, consulté le 26 juin 2019. URL : http://journals.openedition.org/oeconomia/5161

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Ivan Moscati

University of Insubria, Varese, and Bocconi, ivan.moscati@uninsubria.it

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Les contenus d’Œconomia sont mis à disposition selon les termes de la Licence Creative Commons Attribution - Pas d'Utilisation Commerciale - Pas de Modification 4.0 International.

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