Elicitation methods in decision making under risk allow a researcher to infer thensubjective utilities of outcomes as well as the subjective weights of probabilities from observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes into account the inevitable distortion of preferences by random errors and minimizesnthe effect of such errors on the inferred utility and probability weighting functions. Under mildnassumptions, the optimally efficient method for eliciting utilities (weights) of many outcomes (probabilities) is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, an individual's utility function is elicited through the midpoint chaining certainty equivalent method employing the probability elicited at the first stagenas an input. Finally, an individual's probability weighting function is elicited through the probability equivalent method.