Question selection for multi-attribute decision-aiding

A decision-maker (DM), or a group of DMs, must select a most preferred alternative from a finite set of alternatives. Each alternative has a single consequence. There are multiple and conflicting attributes. All value scores are known precisely. However, all that is known about the vector of trade-off weights is that it is a member of a given set, the trade-off weight set. A facilitator can ask questions and use the responses to update the trade-off weight set and hence the set of non-dominated alternatives, i.e., those alternatives that are candidates for being a most preferred alternative. The DM can terminate this process at any point. Termination typically occurs when the non-dominated set contains a sufficiently small number of alternatives. The facilitator's role is to ask questions that efficiently lead the DM to a most preferred alternative. The objective of this research is to aid the facilitator in selecting the best question to ask next. We model the question–response process as a sequential decision-making problem under uncertainty and develop a dynamic programming-based approach that guarantees a finite, and hence potentially computable, representation of the expected optimal cost-to-go function. An example serves to illustrate the approach.