Outline of The Model
The main observation of CPT (and its predecessor Prospect Theory) is that people tend to think of possible outcomes usually relative to a certain reference point (often the status quo) rather than to the final status, a phenomenon which is called framing effect. Moreover, they have different risk attitudes towards gains (i.e. outcomes above the reference point) and losses (i.e. outcomes below the reference point) and care generally more about potential losses than potential gains (loss aversion). Finally, people tend to overweight extreme, but unlikely events, but underweight "average" events. The last point is in contrast to Prospect Theory which assumes that people overweight unlikely events, independently of their relative outcomes.
CPT incorporates these observations in a modification of Expected Utility Theory by replacing final wealth with payoffs relative to the reference point, replacing the utility function with a value function that depends on relative payoff, and replacing cumulative probabilities with weighted cumulative probabilities. In the general case, this leads to the following formula for subjective utility of a risky outcome described by probability measure p:
where v is the value function (typical form shown in Figure 1), w is the weighting function (as sketched in Figure 2) and, i.e. the integral of the probability measure over all values up to, is the cumulative probability. This generalizes the original formulation by Tversky and Kahneman from finitely many distinct outcomes to infinite (i.e., continuous) outcomes.
Read more about this topic: Cumulative Prospect Theory
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