Risk aversion (psychology)

Risk aversion is a preference for a sure outcome over a gamble with higher or equal expected value. Conversely, the rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking behavior.Problem 1 (N = 152): Imagine that the U.S. is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows:If Program A is adopted, 200 people will be saved. (72%)If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-thirds probability that no people will be saved. (28%)Which of the two programs would you favor?.Problem 2 (N = 155): If Program C is adopted, 400 people will die. (22%)If Program D is adopted, there is a one-third probability that nobody will die and a two-thirds probability that 600 people will die. (78%) Risk aversion is a preference for a sure outcome over a gamble with higher or equal expected value. Conversely, the rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking behavior. The psychophysics of chance induce overweighting of sure things and of improbable events, relative to events of moderate probability. Underweighting of moderate and high probabilities relative to sure things contributes to risk aversion in the realm of gains by reducing the attractiveness of positive gambles. The same effect also contributes to risk seeking in losses by attenuating the aversiveness of negative gambles. Low probabilities, however, are overweighted, which reverses the pattern described above: low probabilities enhance the value of long-shots and amplify aversion to a small chance of a severe loss. Consequently, people are often risk seeking in dealing with improbable gains and risk averse in dealing with unlikely losses. Most theoretical analyses of risky choices depict each option as a gamble that can yield various outcomes with different probabilities. Widely accepted risk-aversion theories, including Expected Utility Theory (EUT) and Prospect Theory (PT), arrive at risk aversion only indirectly, as a side effect of how outcomes are valued or how probabilities are judged. In these analyses, a value function indexes the attractiveness of varying outcomes, a weighting function quantifies the impact of probabilities, and value and weight are combined to establish a utility for each course of action. This last step, combining the weight and value in a meaningful way to make a decision, remains sub-optimal in EUT and PT, as people’s psychological assessments of risk do not match objective assessments. Expected Utility Theory (EUT) poses a utility calculation linearly combining weights and values of the probabilities associated with various outcomes. By presuming that decision-makers themselves incorporate an accurate weighting of probabilities into calculating expected values for their decision-making, EUT assumes that people’s subjective probability-weighting matches objective probability differences, when they are, in reality, exceedingly disparate. Consider the choice between a prospect that offers an 85% chance to win $1000 (with a 15% chance to win nothing) and the alternative of receiving $800 for sure. A large majority of people prefer the sure thing over the gamble, although the gamble has higher (mathematical) expected value (also known as expectation). The expected value of a monetary gamble is a weighted average, in which each possible outcome is weighted by its probability of occurrence. The expected value of the gamble in this example is .85 X $1000 + .15 X $0 = $850, which exceeds the expected value of $800 associated with the sure thing. Research suggests that people do not evaluate prospects by the expected value of their monetary outcomes, but rather by the expected value of the subjective value of these outcomes (see also Expected utility). In most real-life situations, the probabilities associated with each outcome are not specified by the situation, but have to be subjectively estimated by the decision-maker. The subjective value of a gamble is again a weighted average, but now it is the subjective value of each outcome that is weighted by its probability. To explain risk aversion within this framework, Bernoulli proposed that subjective value, or utility, is a concave function of money. In such a function, the difference between the utilities of $200 and $100, for example, is greater than the utility difference between $1,200 and $1,100. It follows from concavity that the subjective value attached to a gain of $800 is more than 80% of the value of a gain of $1,000. Consequently, the concavity of the utility function entails a risk averse preference for a sure gain of $800 over an 80% chance to win $1,000, although the two prospects have the same monetary expected value. While EUT has dominated the analysis of decision-making under risk and has generally been accepted as a normative model of rational choice (telling us how we should make decisions), descriptive models of how people actually behave deviate significantly from this normative model. Prospect Theory (PT) claims that fair gambles (gambles in which the expected value of the current option and all other alternatives are held equal) are unattractive on the gain side but attractive on the loss side. In contrast to EUT, PT is posited as an alternative theory of choice, in which value is assigned to gains and losses rather than to final assets (total wealth), and in which probabilities are replaced by decision weights. In an effort to capture inconsistencies in our preferences, PT offers a non-linear, S-shaped probability-weighted value function, implying that the decision-maker transforms probabilities along a diminishing sensitivity curve, in which the impact of a given change in probability diminishes with its distance from impossibility and certainty.