A SURVEY OF BEHAVIORAL FINANCE
Figure 1.2. The two panels show Kahneman and Tversky’s (1979) proposed value function υ and probability weighting function π.
non-EU models are what might be called quasi-normative, in that they try to capture some of the anomalous experimental evidence by slightly weak- ening the VNM axioms. The difficulty with such models is that in trying to achieve two goals—normative and descriptive—they end up doing an un- satisfactory job at both. In contrast, prospect theory has no aspirations as a normative theory: it simply tries to capture people’s attitudes to risky gam- bles as parsimoniously as possible. Indeed, Tversky and Kahneman (1986) argue convincingly that normative approaches are doomed to failure, be- cause people routinely make choices that are simply impossible to justify on normative grounds, in that they violate dominance or invariance.
Kahneman and Tversky (1979), KT henceforth, lay out the original ver- sion of prospect theory, designed for gambles with at most two nonzero outcomes. They propose that when offered a gamble
(x, p; y, q),
to be read as “get outcome x with probability p, outcome y with probabil- ity q,” where x 0 y or y 0 x, people assign it a value of
where υ and π are shown in figure 1.2. When choosing between different gambles, they pick the one with the highest value.
This formulation has a number of important features. First, utility is de- fined over gains and losses rather than over final wealth positions, an idea first proposed by Markowitz (1952). This fits naturally with the way gam- bles are often presented and discussed in everyday life. More generally, it is consistent with the way people perceive attributes such as brightness, loud- ness, or temperature relative to earlier levels, rather than in absolute terms.