Decision Analysis with Indeterminate or Incoherent Probabilities
by Robert F. Nau (Annals of Operations Research 19 375-403, 1989)
Abstract: This paper presents a new method of modeling indeterminate and incoherent probability judgments in decision analysis problems. The decision maker's degree of belief in the occurence of an event is represented by a unimodal (in fact, concave) function on the unit interval, whose parameters are elicited in terms of lower and upper probabilities with attached confidence weights. This is shown to provide a unified framework for performing sensitivity analysis, reconciling incoherence, and combining expert judgments.
Comments: This paper is actually the sequel to "Indeterminate Probabilities on Finite Sets." Here, the axiomatic model of confidence-weighted probabilities (second-order indeterminacy) is applied to the solution of decision analysis problems. A decision ranking criterion is developed to choose among decisions in situations where the decision-maker's probabilities are partially indeterminate or incoherent. (See also the description of these papers in my research summary.)