The impact of violations of expected utility theory on choices in the face of multiple 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 risks. Based on the analytic framework, we find that violations of EUT can lead to interaction effects between uncertain outcomes, not just nonlinearities in the disutility of risks. Our framework also implies 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 for one uncertain outcome are affected by other uncertain outcomes.