Expected utility theory (EUT) is the dominant theory of decision making under uncertainty in economics, despite decades of research that fails to confirm its predictions. In their fascinating new book, Risky Curves: On the empirical failure of expected utility, Daniel Friedman, R. Mark Isaac, Duncan James and Shyam Sunder compile and examine systematically the research on EUT, and outline the failure of the theory with respect to both individual decision making and aggregate behaviour. Importantly, they also dig deeper into the evidence to draw conclusions about why the theory fails, and to suggest fruitful directions for future research.

Chapter 1 provides a brief introduction. Here the authors contrast the layman's definition of risk with economists’ version. The dictionary definition focuses on the possibility and magnitude of harm, injury or loss, while economists think of risk as the variability of payoffs associated with a particular decision. If you ask someone what risk means to them, the dictionary version is a good approximation of what they are likely to tell you; variability, especially at the high end of the distribution of payoffs, does not immediately come to mind as ‘risky’. The distance between the intuitive, vernacular definition of risk and economists' measure is a theme that recurs throughout the book.

This chapter also introduces the EUT model, which is the source of the risk-as-variance definition, and notes its pervasiveness in the economics of decision making under uncertainty. Scientists judge a model by its predictive ability, and the authors promise to lay out the evidence that EUT has not been a big success empirically. The belief in EUT is very strong among economists, and the authors contend that this belief can act as a kind of brainwashing, blinding researchers to its flaws and to the possibility of developing better alternatives. The authors note three main worries about the consequences of maintaining an incorrect model of decision making: It can mislead a young researcher into asking the wrong questions, and therefore can lead to a failed initial research programme and damaged career; it misleads applied researchers into attributing deviations from the predictions of their models to risk aversion, when other explanations may be more valid, slowing scientific progress; and it impedes the search for better models of decision making.

Chapter 2 traces the history of research on decision making under uncertainty. The essence of the EUT model was developed in Bernoulli's 1738 treatise, which was motivated by the well-known St. Petersburg Paradox.Footnote ¹ This work introduced the idea that the marginal utility of an additional increment of income diminishes as income increases (diminishing marginal utility), and approximated the phenomenon with a mathematical function mapping income into subjective value. The idea that people have a well-behaved function that maps possible outcomes into a one-dimensional measure is pervasive in economics; the function is often referred to as a Bernoulli function. Diminishing marginal utility implies that an individual will always prefer the expected value of a gamble to the gamble itself – that is the average of the utilities of the payoffs will be below the utility of the expected value (the average of the payoffs). For a gamble with a given expected value, greater variance decreases expected utility. Therefore most individuals, having diminishing marginal utility, will exhibit risk (as variance) aversion, preferring a less-risky gamble. Risk aversion can of course differ across individuals, and some individuals may be risk-neutral or even risk-seeking, though this is thought to be relatively rare.

From the beginning, there was evidence that failed to support the EUT model, and the evidence continued to accumulate over time. Subsequent theorists laboured to expand the model to incorporate observed behaviour, for example by introducing additional inflection points to accommodate simultaneous purchase of insurance and lottery tickets. This second chapter also includes a discussion of a fascinating early study attempting to elicit utility functions using decisions over lotteries. In particular, Grayson (Reference Grayson1960) found considerable heterogeneity in the elicited utility functions of his eleven participants, only some of which were consistent with EUT. The authors return to a detailed discussion of this study in Chapter 6.

In Chapter 3 the authors turn to the elicitation of individual risk preferences, a topic that is close to my own interests. Because risk tolerance is an important parameter in many policy-relevant applied models, measuring risk preferences is critical for calibrating policy. Economists’ approach to measuring preferences is embedded in EUT, and essentially amounts to measuring the curvature (concavity) of the utility function. Typically, economists use incentivized tasks – choices between and among lotteries, or valuations of lotteries – to gauge this curvature. Each task invented for this purpose can be thought of as a yardstick, and any yardstick one might use should give the same answer, more or less.

In this chapter the authors review several prominent methods for eliciting risk aversion, and point out the ways in which the results fail to confirm EUT. These include choosing among different gambles or valuing gambles (willingness to pay or accept) in simple or more complex settings. Several disappointing regularities emerge from these studies. First, different measures of risk aversion yield different patterns of risk aversion, with some generally showing that most subjects are risk averse, but others showing a preponderance of risk-seeking behaviour; a related point is that elicited risk aversion parameters show little consistency across measures or over time. Second, there is very little evidence that estimates of risk aversion from any of the measures correlates strongly with behaviour in other lab decisions such as bidding in an auction, or in the major risky decisions that people make in their lives. Third, risk aversion measures are sensitive to aspects of context that, from a theoretical perspective, shouldn't matter; stakes levels, payment procedures, and the composition of sets of decisions all affect elicited risk aversion.

My interest in the measurement of risk aversion dates from a failed experiment from 2004 (unpublished), in which my co-author and I attempted to elicit risk preferences using four different measures, including two incentivized tasks and two survey measures. We had a group of 115 subjects complete all the measures, and then six weeks later they returned to the lab for a retest. Each of the four measures exhibited strong test-retest reliability. But the yardsticks gave different measures. Furthermore, the correlation between the two tasks, and between the tasks and the survey measures, was very low and not always positive (−0.11 to 0.24). That is, if we lined up the 115 subjects according to their measured risk aversion (most risk averse to least risk averse) for one task, and then lined them up again according to another of the tasks, nearly everyone would have to move to a different place in line. Were the yardsticks at fault, or was something else wrong with the study? I discussed these results with a well-known experimental methodologist in another field, and asked him what he made of it. He replied, “I'd say your underlying construct needs a little work.” We subsequently searched the literature for similar findings and located quite a few studies showing inconsistency across measures of risk aversion, including an early paper by Paul Slovic (Reference Slovic1962) where he noted insignificant levels of correlation among a number of risk-aversion measures, incentivized and non-incentivized. The papers we found are published in economics, psychology, and in specialized decision-making journals, and all note low levels of correlations across measures of risk aversion. Yet despite this repeated finding, the result is generally not known by economists, even among those who study decision making under uncertainty. Our underlying construct still is widely used, despite these failures to find empirical support, as academic publications continue with the pervasive assumption of curved Bernoulli utility functions. Perhaps there is a ‘best’ way to measure risk preferences, and this magic measure will usefully predict behaviour outside the lab, but if so we have not found it yet.

Chapter 4 tackles the question of whether EUT performs well in empirical studies focusing on aggregate behaviour. The authors report that studies using hypothetical or incentivized measures of risk aversion rarely correlate well with self-reported health behaviour or health outcomes; indeed health-related decision making seems to focus more on the probability of a bad outcome, the lay definition of risk, rather than variability of outcomes.Footnote ² Gambling behaviour fails to conform to EUT predictions, and it is clear that something other than the maximization of a standard utility function is going on when gamblers make decisions. When engineers do risk analysis on their projects, they focus on the probability of something going badly wrong, and do not consider risk as variance when making design decisions. Consumers’ preferences over insurance contracts seem to defy the assumptions of EUT. Similarly weak or negative findings occur in studies of real estate and financial investments, as well as the aggregate behaviour of financial markets. The equity premium puzzle implies ridiculously high levels of risk aversion.Footnote ³ The authors conclude that ‘curved Bernoulli functions do not help us gain a better understanding of these diverse and important aspects of the world we live in’ (73). Indeed they recommend stepping back from the standard approach and thinking more carefully about risk as the likelihood of harm, injury or loss.

In Chapter 5, the authors ask, ‘What are risk preferences?’ Might the idea of risk preferences as the curvature of a Bernoulli function be ‘a figment of the theorists’ imagination’, the economists’ version of phlogiston? In discussing proposed alternatives to EUT, the authors are critical of most such models for two reasons. First, these models (such as prospect theory, among many others) are seemingly able to provide a better fit to existing data mostly by adding more parameters and therefore more flexibility to the estimation; and second, the outputs of these models are no more able to predict the risky behaviour of individuals than the simpler EUT approach. And while, as Neilson (Reference Neilson2011: 976), writes, ‘For every theory, there exists an experimentalist clever enough to generate evidence violating it’ (p. 976), as studies accumulate it should be possible to distinguish a model that is essentially (though perhaps not in every clever instance) correct from others that are less correct.Footnote ⁴ EUT has not fared well in this respect.

Arguing that preferences may not be ‘intrinsic’, the authors then consider new measures of risk, and therefore of risk aversion, based on the ways in which people perceive risk in practice. These measures revert to the dictionary definition of risk and focus on the likelihood and magnitude of potential losses instead of variance. Their favourite is ‘expected loss’, which they show to be distinct from variance, and they present some suggestive evidence that this measure of risk may have empirical value. However, it does not give us a measure of riskiness for uncertain prospects that are entirely in the gain domain.

Chapter 6 takes up the topic of context, and how specific aspects of context alter an individual's elicited risk preference. These include aspects of the elicitation procedures themselves, as well as elements of a person's current situation. This is analogous to a shift in focus from ‘preferences’ to ‘constraints’ in the standard approach to consumer choice. For example, when eliciting the risk preferences of low-income individuals, whether in developing countries or within the USA, many researchers (myself included) find that these individuals are extremely risk averse and become more so with higher stakes. This could be due to the fact that these folks may face urgent constraints – that is, they may badly need a threshold amount of money to cover a pressingly urgent expenditure – and the fixed payoff option in the choice tasks is enough to cover that expenditure. This chapter includes a careful discussion of a point that should receive more attention than it does. Although there are a number of studies showing that preferences change when situations change, as in the wake of a disaster for example (Imas Reference Imas2016), there is much work left to systematically explore the effects of specific elements of context.

The properties of the elicitation procedures themselves also may be important. For example, simple elicitation procedures, using only 50/50 gambles and round numbers, might be easier for subjects to understand and respond to accurately as compared with procedures with more complex alternatives. We see some evidence of this in our own experimental research (Dave et al. Reference Dave, Eckel, Johnson and Rojas2010). Indeed, there is growing evidence that intelligence is related to measured risk preferences, and lower math ability affects complex measures more than simple ones. This hints at the possibility that the validity of EUT may be masked by the properties of the tasks used to test it, and that carefully designed tasks taking cognition into account will lead to more consistent results. Simplifying elicitations won't help, of course, if the underlying model on which all of the measures are based is incorrect.

In the final chapter, the authors map out their ideas for moving forward. As they note, researchers have spent a great deal of time and attention coming up with increasingly elaborate ways of eliciting preferences and measuring various possible aspects of utility functions for decisions under uncertainty, with little ultimate success. Perhaps they are carefully measuring things that just aren't there. Instead researchers who really want to understand human decision making should pay close attention to humans as social, psychological and biological creatures. Individuals operate within a broad social and economic context, and context probably plays an important role in risk perceptions and risky behaviour. That context also has shaped evolved human responses to risk over the longer term. The large literature on decision-making heuristics and learning also provides important input, especially considering that heuristics are the result of an evolutionary environment. In addition, the extensive body of research by psychologists on risk perceptions and decision making is worth further evaluation by economists, as it has much in common with the approach the authors recommend.

As economists, we probably should try to remember that the utility function is a theoretical construct, invented not so much as an accurate representation of a human being's valuation process, but rather for convenience in thinking systematically about decisions that people make. Perhaps economists have got into trouble because we are under the sway of the seductive logical beauty of our theories. Economists come under fire all the time for their tendency to give priority to formal models over empirical evidence. Milgrom and Roberts observed that, ‘no mere fact ever was a match in economics for a consistent theory’ (Reference Milgrom and Roberts1978: 185), and that may still be true. Recent critiques by Thomas Piketty (Reference Piketty2014) or Paul Romer (Reference Romer2015) echo this sentiment. Perhaps the Bernoulli function is a case in point. In any case EUT is peculiarly resistant to countervailing data.

In the end, this book constitutes a fairly scathing indictment of the standard model of decision making under uncertainty, and by extension the standard model of consumer choice. Perhaps it is not a very strong defence to note that a prominent reason for the model's persistence is the absence of a strong alternative model (a fact noted by the authors). As the authors argue, other models have not proved to be much of an improvement over EUT in terms of their predictive ability. Economists outside the field of decision-making research are probably the most complacent about the validity of the EUT model. One reason for this might be that, twenty years ago, two prominently published papers attempted a kind of horse race between EUT and a subset of the other models available at the time. Harless and Camerer (Reference Harless and Camerer1994) work with 23 different lab-generated data sets to compare the fit of alternative models and note a trade-off between parsimony (number of parameters) and accuracy, with EUT coming out in the top set of models. And Hey and Orme (Reference Hey and Orme1994) conclude that EUT does at least as well as any of the other models they test using lab experiments, if one allows for a bit of decision error. (Neither of these papers attempts to assess predictive accuracy outside the lab.) From these studies it is easy to draw the conclusion that EUT is pretty good after all, and certainly the best we have. As Roth (Reference Roth, Arrow, Colombatto, Perlman and Schmidt1996) argued, in the absence of a compelling alternative, EUT is a ‘useful approximation’ of behaviour. Although there continues to be a great deal of theoretical work on decision making under uncertainty, as far as I know no other similar attempts have been made more recently, and there are no convincing studies showing that other theoretical constructs are better.

The authors are rather quick to suggest that prospect theory is not the path forward, but perhaps it should receive a little more consideration. Prospect theory is motivated by patterns seen in empirical data on decision making, and it encompasses several elements, two of which are loss aversion and probability weighting. I would be quick to agree with the authors that probability weighting is not an appealing theory. One suspects that the pattern it is designed to approximate has some underlying cause that will be discovered and this will provide a better theory. But loss aversion is another story. The data presented in Chapter 6 (from the 1960 experiment by Grayson) show a pervasive ‘kink’ at a payoff of zero, consistent with loss aversion. Furthermore, the risk measure that the authors propose, expected loss, also seems to indicate that losses loom larger than gains in the mind of the decision maker. Aversion to losses seems to be a real component of human decision making and an unavoidable element of the path forward.Footnote ⁵

In sum, the book provides a fascinating argument against EUT, and marshals a wide variety of evidence both from individual decision-making experiments and from aggregate data. If our purpose is to develop a theory that is consistent with empirical evidence, and that can be used to model and predict individual decisions under uncertainty, then we have some work ahead of us. The authors make a strong and quite convincing case for reopening the search for a model of decision making under uncertainty that takes into account the world in which human decision makers live, and the perceptions that individuals have about risks and risky decisions. It is recommended reading for anyone interested in decision making under uncertainty.