How Do We Make ‘Decisions’?

Decisions are often ‘risky’ in the sense that their outcomes are not known with certainty. Presented with a choice between a risky prospect that offers a 50 percent chance to win $200 (otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighed by their probability of occurrence). Preference for a sure outcome over a risky prospect of equal expected value is called risk averse; when choosing between prospects with possible outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, first formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room that is well lit so, suggested Bernoulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one’s possession. It has since been assumed that people have a subjective utility function and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is [0.50*u($200)], where u is the person’s concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curve, respectively). It follows from a concave function that the subjective value attached to a gain of $100 is more than 50 percent of the value attached to a gain of $200, which entails preference for the sure $100 gain and hence, risk aversion.

Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to win $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance of losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This results in a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.