Conventions, Operations, Predictions

Chapter 12 analyzes the third phase of the debate on expected utility theory, from the end of 1952 to 1955. The issues concerning the nature of utility measurement gained an autonomous status in this phase. Milton Friedman, Leonard J. Savage, Robert Strotz, Armen Alchian, and Daniel Ellsberg argued that measuring utility consists of assigning numbers to objects by following a definite set of operations. While the particular way of assigning utility numbers to objects is largely arbitrary and conventional, the assigned numbers should allow economists to predict individuals’ choice behavior. This is similar to the operational conception advanced by psychologist Stanley Smith Stevens and definitively liberates utility measurement from its remaining ties with units and ratios. The novel view of measurement quickly became standard among mainstream utility theorists, and its success helps explain the peaceful cohabitation of cardinal and ordinal utility within utility analysis that began in the mid-1950s.

Measuring Utility, Destabilizing EUT

Chapter 16 shows how the validity of expected utility theory (EUT) was increasingly called into question between the mid-1960s and the mid-1970s and discusses how a series of experiments performed from 1974 to 1985 undermined the earlier confidence that EUT makes it possible to measure utility. Beginning in the mid-1960s, in a series of experiments seminal to the field later called behavioral economics, Sarah Lichtenstein, Paul Slovic, Amos Tversky, and others showed that decision patterns violating EUT are systematic. The new experimenters who engaged with the EUT-based measurement of utility from the mid-1970s, namely Uday Karmarkar, Richard de Neufville, Paul Schoemaker, and coauthors, showed that different elicitation methods to measure utility, which according to EUT should produce the same outcome, generate different measures. These findings contributed to destabilizing EUT, undermined the confidence in EUT-based utility measurement, and helped foster a blossoming of novel behavioral models of decision-making under risk.

Marschak and Utility Measurement at Yale

Chapter 14 continues the history of the experimental attempts to measure utility by discussing two further experiments performed at Yale University in the early 1960s, one by Trenery Dolbear and the other by Jacob Marschak in association with Gordon Becker and Morris DeGroot. Like the experiments conducted in the 1950s, these were also based on expected utility theory (EUT) and aimed at measuring the utility of money of individuals on the basis of their preferences between gambles where small amounts of money were at stake. There are some differences in the designs of the experiments of the 1950s and those of the 1960s. Like the experimenters of the 1950s, however, Dolbear, Marschak, Becker, and DeGroot also confidently assessed their experimental findings as validating EUT: the theory was not 100 percent correct, but in an approximate sense, it appeared to be an acceptable descriptive theory of decision-making under risk.

From Chicago to Paris

Chapter 11 studies the second phase of the debate on expected utility theory (EUT), which commenced in May 1950, when Paul Samuelson, Leonard J. Savage, Jacob Marschak, Milton Friedman, and William Baumol initiated an intense exchange of letters. These economists argued about the exact assumptions underlying EUT, quarreled over whether these assumptions are compelling requisites for rational behavior under risk, and debated the nature of the cardinal utility function u featured in EUT. This correspondence modified the views of all five economists and transformed Samuelson into a supporter of EUT. In a prominent conference in Paris in May 1952, Friedman, Savage, Marschak, and Samuelson advocated EUT in the face of attacks from Maurice Allais and other opponents of the theory. The Paris conference and the publication of an Econometrica symposium on EUT in October 1952 marked the emergence of EUT as the mainstream economic model of decision-making under risk.

Stevens and the Operational Definition of Measurement in Psychology, 1935–1950

Chapter 8 broadens the narrative beyond utility measurement and discusses an important outcome of the 1930s British controversy over psychological measurement, namely the operational definition of measurement put forward by American psychologist Stanley Smith Stevens in 1946. For Stevens, measurement consists of the assignment of numbers to objects according to certain rules. Since there are various rules for assigning numbers to objects, there are various forms, or scales, of measurement. Each scale is identified by the empirical operations used to create it and by the class of mathematical transformations the numbers in each scale can be subjected to. From this operational viewpoint, unit-based measurement is just a particular, and quite restrictive, form of measurement. Stevens’s definition of measurement was broad enough to include the psychologists’ quantification practices as measurement and quickly became canonical in psychology. The final section of the chapter discusses drawbacks to Stevens’s operational theory of measurement.

Cardinal Utility

Chapter 6 reconstructs the progressive definition and stabilization of the current notion of cardinal utility as utility unique up to positive linear transformations. This notion was the eventual outcome of a long-lasting discussion, inaugurated by Vilfredo Pareto, regarding an individual’s capacity to rank transitions among different combinations of goods. This discussion continued through the 1920s and early 1930s and underwent a decisive acceleration from 1934 to 1938, that is, during the conclusive phase of the ordinal revolution. In this latter period, the main protagonists of the debate were Oskar Lange, Henry Phelps Brown, Roy Allen, Franz Alt, and Paul Samuelson. In the discussions that led to the definition of cardinal utility, some of these utility theorists began to envisage a broader notion of measurement according to which utility can be measurable even if no utility unit is available. Until the mid-1940s, however, cardinal utility remained peripheral in utility analysis.

Prologue

The prologue outlines the main passages in the history of utility measurement in economics and presents the four main goals of the book. First, the book reconstructs in detail economists’ ideas and discussions about utility measurement from 1870 to 1985. Second, it brings into focus the interplay between the evolution of utility analysis, economists’ ideas about utility measurement, and their conception of what measurement in general means. Third, it explores the relationships between the history of utility measurement in economics, the history of the measurement of sensations in psychology, and the history of measurement theory in general. Finally, it discusses some epistemological problems related to utility measurement. Not discussed in the book are the measurement of social welfare, revealed preference theory, the post-1950 econometric approach to demand analysis, and the analysis of discrete choices initiated in the 1970s.

From Utility Measurement to the Representational Theory of Measurement

Chapter 15 offers a conclusion to the history of measurement theory by reconstructing the origins of the representational theory of measurement in the early work of Patrick Suppes. In particular, the chapter shows that Suppes’s superseding of the unit-based understanding of measurement that he had embraced in the early 1950s, his endorsement of a liberal definition of measurement à la Stanley Smith Stevens in the mid-1950s, his conceiving of the project of an axiomatic underpinning of this notion of measurement in the late 1950s, and the realization of this project during the 1960s all have their origins in the utility analysis research he conducted from 1953 to 1957 within the Stanford Value Theory Project. The representational theory of measurement received full-fledged expression in Foundations of Measurement (1971), a book coauthored by Suppes, Duncan Luce, David Krantz, and Amos Tversky, which quickly became the dominant theory of measurement.

The Expected Utility Theory and Measurement Theory of von Neumann and Morgenstern, 1944–1947

Chapter 9 discusses the axiomatic version of expected utility theory (EUT), a theory of decision-making under risk, put forward by John von Neumann and Oskar Morgenstern in their book Theory of Games and Economic Behavior (1944). EUT was a changing factor in the history of utility measurement. In fact, while discussions of the measurability of utility before 1944 focused on the utility used to analyze decision-making between risk-free alternatives, after that year, discussions centered on the utility used to analyze decision-making between risky alternatives. In Theory of Games, the nature of the cardinal utility function u featured in von Neumann and Morgenstern’s EUT, and its relationship with the riskless utility function U of previous utility analysis remained ambiguous. Von Neumann and Morgenstern also put forward an axiomatic theory of measurement, which presents some similarities with Stanley Smith Stevens’s measurement theory but had no immediate impact on utility analysis.

Ordinal Utility

Chapter 5 deals with the ordinal revolution in utility analysis inaugurated by Vilfredo Pareto around 1900. The fundamental notion of Pareto’s analysis was that of preference, and he conceived of utility as a numerical index expressing the preference relations between commodities. While Pareto’s ordinal approach was highly innovative, his understanding of measurement remained the unit-based one. The second part of chapter 5 reconstructs an important debate on the measurability of utility that took place in Austria from 1907 to 1912. Franz Čuhel and Ludwig von Mises rejected Eugen von Böhm-Bawerk’s idea that it is possible to identify a unit to measure utility, and, independently of Pareto, they advocated an ordinal approach to utility. Especially through Mises’s influence, the ordinal approach to utility rose to prominence among Austrian economists after World War I. The final part of chapter 5 discusses the differences between the Austrian and Paretian approaches to ordinal utility.