The standard-gamble (SG) method has been accepted as the "gold standard" for the elicitation of utility when risk or uncertainty is involved in decisions, and thus for the measurement of utility in medical decisions. It is based on the assumptions of expected-utility theory. Unfortunately, there is now abundant evidence that expected utility is not empirically valid, and that the SG method overestimates risk aversion and the utilities of impaired health states. This paper shows how rank-dependent utility theory, a newly developed theory in decision science, can explain the main violations of expected utility. Thus it provides a means for correcting the SG method and for improving the assessments of quality-adjusted life years for medical decisions in which there is uncertainty about outcomes.