Fear and hope

Whereas prospect theory is firmly grounded in cognitive psychology, Lola Lopes (1987) introduced a competing model in which emotion rather than cognition plays the leading role. It is called SP/A theory. The S, P and A refer to ‘security’, ‘potential’ and ‘aspiration’. Lopes describes a decision-maker who can be either hopeful or cautious. If the decision-maker is hopeful, he starts by evaluating risky prospects from the best outcomes and works ‘down’. If he is cautious, he focuses on security and evaluates risky prospects starting with the worst outcomes and works ‘up’. Whether he is ‘security’ or ‘potential’ minded shapes the way that his attention is drawn to particular outcomes. In addition to this evaluation of security and potential, each risky prospect is also assessed against an aspiration level. It is important to the decision-maker that the outcomes meet or exceed the aspiration level. It is possible for the decision-maker to become confused if the evaluation seems okay but the aspiration level is not met (or vice versa). For applications of decision theory where emotions are seen as an important part of any explanation of the behaviour involved, SP/A may turn out to be the best model to use. In Phillips & Pohl (2018) we use SP/A theory to explain why a terrorist group might delay its actions. This is just one possible application of SP/A theory to the study of terrorism.

Don’t forget the orthodoxy

In 1947, von Neumann and Morgenstern set down expected utility theory as a mathematical, axiom based, prescriptive model of choice. The axioms were interpreted as rules of rational behaviour and the model treated more as a predictive or descriptive model than it was ever designed to be. Studies began to emerge to see whether people really did choose in accordance with ‘rational choice’ or whether the axioms were ‘violated’.This activity helped to reconnect economics and psychology, a relationship that had been on again, off again but mostly off again. The Allais Paradox, along with the Ellsberg Paradox (Ellsberg 1961), gradually began to attract more and more attention. At first, nobody really knew what to make of Allais’ (1953) results. What did they mean? Nothing, really, if you think of expected utility theory as a prescriptive model of choice. But if you want to view expected utility theory as something more than that, something that can describe or even predict human choices, then a violation of one of the axioms has more and more significance.

While Kahneman and Tversky worked on a descriptive model of choice and Loonies, Sugden and Bell worked on their regret theory, other economists attempted to adjust expected utility theory so that it could cope with rogue preferences. Apart from the obvious mission to ‘save’ expected utility theory,3 there were good reasons not to throw the baby out with the bathwater. For one, people do tend to correct their preferences over time. For example, when subjects discussed their choices, they often changed their minds about the options presented in the standard Allais Paradox such that they agreed with the independence axiom (Moskowitz 1974). About one-quarter of people fall into this category, remembering that not everyone’s choices violate the independence axiom in the first place. Even as a predictive model, expected utility does not perform too badly. If it could be adjusted in some way, we might keep everything that makes it a good prescriptive model and expand its applicability as a predictive model.

The generalisations of expected utility theory include (see Machina 1987, p. 132):

  • 1. Karmarkar’s (1978,1979) subjectively weighted utility;
  • 2. Quiggin’s (1982) rank dependent or‘anticipated’ expected utility;
  • 3. Chew’s (1983) weighted utility; and
  • 4. Yaari’s (1987) dual expected utility.


All of these vary the form of the expected utility function from (*, )/>,• to


some other functional form that allows for behaviour that would lead to a violation of the independence axiom. Another approach has been to show that the departures from the independence axiom such as those associated with the Allais Paradox do not seriously impair the operation of expected utility theory.This was the approach taken by Machina (1982).

As this small sample of the literature shows, the task of generalising expected utility theory was a burgeoning research program. In many ways, this has been overshadowed by the mainstream of behavioural economics and because the mainstream draws primarily on prospect theory, the alternatives are not widely explored. This has not been a mistake because we had to proceed where we could and it was impossible to tell at the beginning where the behavioural economics research program would take us. Now we can survey the whole landscape of behavioural economics, orthodox economics and non-mainstream behavioural economics produced since 1979, and it would be a mistake to ignore the types of work that we have been discussing just now. The hidden value could be significant. After all, the way in which humans assess probabilities is central to prospect theory and mainstream behavioural economics. However, it is possible to develop models that abandon probabilities altogether. This is one of the more radical approaches that was identified during the 1980s as a way to avoid the problems associated with the Allais Paradox. Such models, which treat uncertainty without using probabilities, are based on ‘state preference theory’ (e.g. Hirshleifer 1966). But that is a subject for another day.

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