What is Prospect Theory?

Prospect theory is an economic theory of behavior that attempts to explain people’s decisions when they are faced with situations that involve risk. According to the theory, people evaluate potential gains and losses as changes from their current state rather than as independent situations in the future, and they try to avoid losses more than they try to seek winnings. People perceive the likelihood of an event inaccurately, especially when the probability is close to zero or one. Prospect theory explains seemingly irrational decisions in situations like gambling and insurance purchases.

In a 1979 paper titled “Prospect Theory,” published in Econometrica, Daniel Kahneman and Amos Tversky outlined the theory. The proposal of prospect theory was instrumental in the foundation of a new field: behavioral economics. This field of study blends principles of economics and psychology. In 2002, Kahneman shared the Nobel Prize in Economics with Vernon L. Smith for their work in establishing the field.

Most economic theory is descriptive; that is, it seeks to explain human behavior through the use of simplifying models. If the real world does not exhibit the behavior that a model predicts, then it is the model that needs to be revised. This was the case with expected utility theory, which predicted that people would accurately assess probabilities and payoffs to make a rational choice in the face of risk. This means that a person should be indifferent between a 50 percent chance of winning 1,000 and a guaranteed payment of 500. An experiment run by Maurice Allais, a French economist, in 1953 cast doubt on expected utility theory.

The experiment posed a series of choices between lotteries, and respondents chose which set of payoffs and probabilities they preferred. Allais found that respondents did not always choose the lotteries that expected utility theory predicted, and his findings became known as the Allais Paradox. Kahneman and Tversky ran a variation of the Allais experiment and obtained similar results. For example, the majority of respondents preferred a guaranteed payoff of 3,000 to an 80 percent chance of receiving 4,000, even though the second option has an expected value that is 200 higher than the expected value of the first.

Kahneman and Tversky attempted to explain the Allais Paradox by examining human decision-making processes. They proposed that each economic agent, or person making an economic decision, has two functions relevant to decisions in the face of risk: the value function and the decision weight function. When calculating his expected utility, the agent uses the payoffs and probabilities from these functions rather than the stated numbers when deciding between lotteries.

The value function assigns a value to a payoff. Unlike the predictions of expected utility theory, the magnitude of negative and positive payoffs is not the same — the negative portion of the value function is steeper than the positive portion, so the absolute value of a loss is greater than the absolute value of an equivalent win. This is where prospect theory gets its name: the agent views each lottery as a prospect for change from his current position. In the case of a guaranteed 300 versus a 50 percent chance of winning 1,000 and a 50 percent chance of losing 400, expected utility theory would say that the lotteries are equivalent because they both have an expected value of 300. Under prospect theory, the potential loss of 400 might outweigh the potential gain of 1,000, so the agent could strongly prefer the guaranteed 300.

The weighting function describes how agents treat probabilities. Under expected utility theory, agents multiply the payoff by the exact probability of its occurrence. Prospect theory recognizes that agents have an imperfect grasp of the meaning of probabilities. The weighting function describes the probability that agents use in their calculations, or the decision weight, for each level of stated probability. The decision weight tends to be lower than the stated probability except at the ends of the function: agents treat probabilities that are close to zero as zero, treat small probabilities as larger than they really are and treat probabilities close to 100 percent as certainties.

Prospect theory applies to any situation in which agents must make a decision based on the evaluation of payoffs and probabilities. Agents might buy insurance when the premium is higher than the expected value of their potential losses since they tend to overestimate small probabilities. Similarly, they might overestimate the chance of winning the lottery and buy tickets that, on average, do not pay off. This theory allows economists to evaluate the reasoning behind these decisions rather than writing them off as irrational.