Updating utilities and reconciling expert opinion

Decision makers can express different preferences and may select different alternatives as their optimal choices. This often constitutes a serious roadblock for further decision making. We choose in this paper to develop a framework that allows for the simultaneous action of several decision makers (instead of just one) and allows for the variability of preferences among these decision makers. The information provided by the varying opinions of decision makers can be used to optimize our own decision making. To achieve this, likelihood functions are developed for stated preferences among n discrete alternatives and for a ranking of n alternatives. We focus on the problem of tight decisions or close calls in order to explore the efficiency of a Bayesian approach using stated preferences and stated rankings.