The Impact of Violations of Expected Utility Theory on Choices in the Face of Multiple Independent Risks

Use of preference information to infer risk tolerance has increased in recent years as a way to inform benefit-risk evaluations in regulatory and medical decision making. However, a framework for the measurement of tolerance for multiple uncertain outcomes has not been formalized when choices do not comply with expected utility theory (EUT). We developed a formal analytic framework for the measurement of preferences through choices under uncertainty with multiple independent risks. Based on the analytic framework, we find that violations of EUT make preferences for uncertain outcomes conditional on other uncertain outcomes in the elicitation (cross-outcome effects), in addition to being nonlinear in probability. Results from our framework also imply that measures of risk tolerance derived from utility, such as maximum acceptable risk, must consider all relevant risks jointly if their effect on choices is expected to violate EUT. Somewhat reassuringly, however, we find that cross-outcome effects are expected to be negligible when the probabilities of other outcomes approach certainty. Finally, we identify a simple test that can help evaluate whether preferences are affected by other uncertain outcomes