Resolvability for Imprecise Multiattribute Alternative Selection

We consider an alternative selection process that involves multiple and conflicting objectives. A facilitator asks a decision maker (DM), or a decision-making body, questions and obtains responses to help the DM select a most preferred alternative. The DM responses to these questions do not necessarily result in precisely determined parameter values (e.g., weights and value scores corresponding to a given model of preference). The goal of this research is to guide the facilitator in selecting what question to ask next and determining when to terminate the question-response process. We model the facilitator´s question selection problem as a Markov decision process and present conditions that guarantee the existence of a question-response policy to identify a most preferred alternative in a finite number of questions. We also present conditions that guarantee the existence of a question-response policy that will identify a most preferred alternative as the number of questions asked goes to infinity. Both of these sets of conditions are easily identified a priori and may be used to aid a facilitator in determining which questions to ask and when to terminate the alternative selection process because identification of a most preferred alternative is not possible.