Sahotra Sarkar
University of Texas at Austin

``Multiple Criteria, Multiple Agents: Exploiting the Formal Isomorphism"

Abstract:

This paper explores the implications of results from multiagent decision theory to problems of (single agent) multicriteria decision analysis. It begins by estabilishing a formal isomorphism between the decision problems in the two areas. Consequently, each theorem in one area has a formal analog in the other. The existence of these theorems have implications for multicriteria analysis that have not previously been recognized. A standard method in that area, the Analytic Hierarchy Process, is typically criticized because it allows rank reversal: a change in relative ranks of current alternatives when a new alternative is considered. Disquiet about this phenomenon stems from an assumption of independence from irrelevant alternatives. However, that assumption, along with others that are usually regarded as less controversial, gives rise to Arrow-type impossibility theorems in multiagent decision-making which have their analogs in multicriteria theory. If the independence of irrelevant alternatives assumption is abandoned, a reassessment of the status of many multicriteria methods, including the Analytic Hierarchy Process, becomes necessary.

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