Non-Expected Utility Theories

Abstract

In Chapter 1, we observed that, in numerous experiments, the expected utility theory failed to explain the choice of individuals involved in decision-making under uncertainty. This led to a search for alternative theories of choice under uncertainty. In this chapter, we shall discuss some alternatives called non-expected utility theories, which have recently attracted the attention of many behavioural scientists. The expected utility functional, EU = ∑p _i · u(w _i ) is linear in probabilities, p _i . In other words, in the expected utility functional, the utilities from various outcomes are weighted simply by the associated probabilities. It was suggested by various authors (Ali, 1977; Handa, 1977) that the weights placed by individuals are usually non-linearly related to the probabilities rather than being the probabilities themselves. In the literature on experimental psychology, this was already recognized (Edwards, 1953, 1954, 1962). The weighted utility functionals may be written as

$$V = \sum\limits_{i = 1}^n {\xi ({p_i})u({w_i})} $$

((5.1))

where ξ(·) continuously maps the unit interval onto itself. Normalized weights ξ*(p _i ) = ξ(p _i )/∑ξ(p _i ) may be used instead of ξ(p _i ). It was shown by Karmakar (1979) that the subjectively weighted utility theory (SWU) can explain the Allais paradox as well as the common-ratio effect as discussed in Chapter 1.