Measuring Utility
Ivan Moscati
Reviewed by William Peden
Measuring Utility: From the Marginal Revolution to Behavioral Economics
Ivan Moscati
Oxford: Oxford University Press, 2019, £22.99
ISBN 9780199372775
In late-nineteenth-century economics, there was an epoch-defining shift from the labour theory of value to the marginal utility theory of value. According to the latter, the economic value of some circumstance (obtaining some good, some service, and so on) is its subjective utility at the margin. Thus, while there is an absolute sense in which I prefer having water to having diamonds, at the present moment I value one more unit of diamonds more than I value one more unit of water. That is why I am willing to pay a higher price for a bowl of diamonds than a bowl of water of the same size, even though water is ‘more valuable’ in a sense. While the marginalists resolved a large array of anomalies that had troubled the labour theory of value, they also believed that utility should be measurable if their theory was to be scientifically respectable. Taking this shift as his starting point, Ivan Moscati has provided a well-written, thorough, and insightful account of the history of utility measurement from 1870 to 1985.
Although his research goals are purely historical, Moscati’s investigations have plenty of philosophical interest. First, his wide-ranging survey of different economists’ positions reveals the great variety of alternative views that one might have about utility measurement—and their problems. Second, there are some fascinating and neglected events that invite philosophically oriented case studies. Third, for those of us interested in decision theory and Bayesianism, his book provides a comprehensive yet comprehensible account of the origins of some crucial problems for the use of utility theory in expected utility theory (EUT). For example, he describes the discovery in the 1970s of the sensitivity of measured expected utilities to apparently irrelevant changes in the probabilities of lotteries in an experiment. As Moscati notes, these measurement issues are not just problems for EUT as a descriptive theory but also for its normative interpretation, since the advice of EUT in a particular decision problem could vary arbitrarily with the measurement method chosen. By analogy, EUT’s normative usefulness would be damaged if it was hard to elicit subjective probabilities, because it would be unclear what the theory advised in particular decision problems.
In Part 1, Moscati discusses the early marginalists’ views on utility measurement. Against the standard narrative in the history of economics, he argues that Carl Menger, William Stanley Jevons, Léon Walras, and their fellow marginalist revolutionaries were not cardinalists. According to a cardinalist view of utility measurement, the choices of the measure’s unit and zero point are arbitrary. Consequently, the measurements are unique only up to a transformation from utility function U1 to utility function U2 fitting the form U2(x) = αU1(x) + β, where x is a particular circumstance, α is a positive number, and β is a positive or negative number. However, cardinalism does entail unique magnitudes of differences among the values of a particular person’s utility function.
Moscati argues that the early marginalists held to a similar but distinct theory of utility measurement, which he calls a ‘unit-based’ theory. According to this view, there is a non-arbitrary zero point for utility. Only the choice of unit is arbitrary. Analogously, it is not arbitrary that zero kilograms is equal to zero pounds, whereas choice of metric or Imperial units for weight is arbitrary. In utility’s case, this means that transformations are only allowed if U2(x) = αU1(x). Put differently, there is no β term, and therefore if U1(x) = 0, then U2(x) = 0, but it is permissible that U1(x) = 2 and U2(x) = 2U1(x) = 4. As Moscati notes, a recalcitrant problem for the early marginalists was to reconcile their theory of measurement with their actual utility theories. Most obviously, what was the zero point of utility, and how could one determine it empirically in real situations?
In Part 2, Moscati discusses the emergence of yet another theory of utility measurement. According to ordinalism, the utility measure is unique only up to the preservation of the ordering of circumstances’ utilities: for any circumstances x and y, it requires only that transformations satisfy the condition that if U1(x) ≥ U1(y), then U2(x) ≥ U2(y). Therefore, the unit of measurement, the zero point and the magnitude of differences are all arbitrary. An astounding logical discovery in this period was that the key results of utility theory were derivable using only ordinal utilities. These formal achievements, by economists such as Vilfredo Pareto, strongly encouraged economists to adopt ordinalism: it avoided the problem of determining the zero-point, yet ordinal utility could play the required theoretical roles for utility. The marginalist theory of value and its advantages proved to depend on more modest theses about utilities than economists had previously thought. Moscati describes how these formal achievements helped the ordinalist view to reach ascendency, especially from the 1930s onwards. He also challenges some earlier accounts of these developments: contrary to Friedrich Hayek and George Stigler, he argues that ordinalism did not begin with Menger, but rather emerged in the work of later economists like Pareto.
Part 3 describes the rapid and remarkable developments of the 1940s and 1950s that occurred after the seminal work of John von Neumann and Oskar Morgenstern in The Theory of Games and Economic Behavior (1944). They proved the shocking result that if an individual’s ordinal utilities satisfy a few formal axioms, then their utilities are measurable, under many circumstances of risk, via cardinal utility functions. To the shock (for some, the horror!) of many economists, cardinal utilities became respectable again. However, the subsequent conflicts of the mid-twentieth century altered the very questions at issue. Thus, in response to criticisms of this new approach, Milton Friedman argued for distinguishing the u of EUT, which measures utilities in decision problems featuring risk, from the U of traditional utility theory, which measures utilities in the special cases where the decision-maker knows with certainty what will happen. On Friedman’s instrumentalist theory of measurement, the role of u was to provide a simple and predictively powerful theory of choice, rather than to extend traditional utilities to risky decision-making. Consequently, u could be cardinal and yet U ordinal, because u would be simply a predictive instrument, rather than measuring the same mental states as U. Moscati usefully notes that Friedman’s analysis of the matter was not universal among the supporters of EUT. For example, Dennis Robertson was a cardinalist, yet he regarded the two functions as measuring the same thing. Friedman’s vigour and arguments, along with those of similarly persuasive allies like Jimmie Savage, won over most economists to descriptive and normative EUT in the 1950s. Moscati argues that Friedman’s instrumentalism enabled the cohabitation between cardinal and ordinal utilities in contemporary economics.
Finally, in Part 4, Moscati examines the experimental attempts to measure utility within the new paradigm of EUT. Despite some promising early results, anomalies began to proliferate. While the early problems (such as the Allais paradox and the Ellsberg paradox) did not particularly worry most expected utility theorists, it turned out that different methods for measuring expected utility produced widely different values. From the 1970s, this troubled situation provided fertile ground for the growth of behavioural economics, neuroeconomics, and other departures from orthodox EUT. By excluding the popular revealed preferences approach from the scope of his discussion, Moscati finishes on a note that is arguably unjustifiably sceptical: he defends this choice by saying that much of the debate post-dates his chosen scope of 1870–1985, but a little relevant venturing outside one’s chosen dates never hurt a historian.
My summary hides one of the greatest strengths of Moscati’s book: His attention to lesser-known thinkers and debates, as well as figures in psychology and philosophy. For example, the work of Patrick Suppes rightly receives an extended discussion, as do neglected economists like Franz Čuhel and Louis Leon Thurstone. This also reveals some very puzzling moments that a more conventional account would overlook. Thus, we learn that R. G. D. Allen argued that the zero point of length is arbitrary, raising the bizarre prospect of negative lengths (p. 107). Another strength is Moscati’s use of private correspondence, which provides an extremely revealing account of the dynamic epistolary debates in the early 1950s. He also unearths some gems: Paul Samuelson, in a letter to Friedman capitulating on the normative value of EUT, writes: ‘I hate to change my mind, but I hate worse to hold wrong views’ (p. 183). This quote exemplifies the period’s fascinating combination of strong emotion and intellectual flexibility. Moscati also avoids the bogs of excessive biographical detail: despite some colourful characters, he writes with a sharp sense of relevance.
Yet his focus on the ideas and debates relies on an implicit historiographical decision to always seek internalist rather than externalist explanations. Thus, he ignores questions like, ‘What was the Cold War’s impact on EUT’s ascendency?’, or ‘Was Friedman’s instrumentalism partly a product of his experience as a liberal and Jewish wartime statistician during a conflict against the Nazis, such that theoretical truth seemed insignificant to him in comparison to simplicity and predictive power?’. Moscati might be right that externalist explanations have little to offer his project, but he should at least argue that point. Another historiographical choice is that he aims to be purely descriptive in his treatment of the assessments of the evidential relations by economists and psychologists, rather than to evaluate their reasoning. As a result, Moscati (perhaps inadvertently) gives the impression that the debates involved were mostly rational. Even if that impression is mistaken, it is notable that one can give such an account of a major debate within economics, because this creates a greater burden of proof for those who believe that economic debates are dominated by ideology and caprice.
There are some frustrating omissions. Moscati could have helped philosophers and economists trying to follow the historical narrative by explaining in more depth the transition from the labour theory of value to the marginalist theory. This story is painfully familiar for most historians of economics, but Moscati is aiming at a wide audience. More significantly, he often fails to engage in detail with rival interpretations. For instance, as mentioned earlier, Hayek and Stigler interpreted Menger as an ordinalist, whereas Moscati interprets him as having a unit-based view. However, Moscati only briefly discusses the Hayek–Stigler interpretation (p. 35), and this issue deserved much more detailed argumentation. Moscati has published articles where he enters into some of these debates, but his book’s cursory treatment and its frequent lack of references to more detailed discussions gives a false sense of obviousness to these complex exegetical questions.
For a philosopher of science, the book’s treasures more than outweigh these problems. Moscati details many thought-provoking events that beg for a philosophical case study. For instance, Maurice Allais disagreed with Friedman, Savage, and other 1950s advocates of EUT about the value of EUT versus Allais’s own approach. Yet they essentially agreed on the two alternatives’ theoretical virtues: both camps thought that EUT did well on simplicity but relatively poorly on descriptive realism (p. 188). The salient point of disagreement was the weighting of the theoretical virtues, and therefore the incident provides a clear case of a subtle type of theory choice debate.
This book has much to offer philosophers of science and historians of economics. It provides a thorough yet simple account of a crucial and complex period. By covering such a wide range of thinkers and relating their views to each other, it also offers a powerful launching pad into the wider literature. Both the historical and philosophical study of utility theory will benefit from Moscati’s efforts for many years to come. There are many philosophers of science who can benefit from such a book, because expected utility pervades much of contemporary philosophy of science, from Bayesian confirmation theory to the ethics of science, and from the philosophy of cognitive science to the philosophy of economics. Many philosophers might be tempted to say that the experimental evidence against EUT (such as the Allais paradox) the end is irrelevant, because they view EUT as a purely normative theory of decision. However, insofar as utilities are not measurable, EUT would have no normative value, and therefore the issues that Moscati covers cannot be dismissed in this way. They deserve more attention by philosophers of science. This book is a great place to start.
William Peden
Durham University
Durham, UK
w.j.peden@durham.ac.uk