A linear assignment formulation of the multiattribute decision problem

— Af ter proposing a gênerai framework of analysis for multiattributed décision problems, this paper develops a linear assignaient model to aggregate a set of individual ordinal évaluations of alternatives into a global ranking. A "best" aggregation scheme is defined as one which maximizes a linear function of individual agreement over alternative ranking s. Due to the special features of this linear assignment problem, geometrie formulation solutions are found. Both formulations are shown to be equivalent. Implications for aggregation theory and extensions of the model are briefly discussed. SECTION 1: STATEMENT OF THE PROBLEM 1.1. A large number of real-world décision problems cannot be properly assessed from a single viewpoint : a firm attempting to compare a set of alternative investment projects might want to rate them on the basis of (1) the net discounted profit expected from each investment (2) the payoff period and (3) the market share. An economist trying to assign a précise quantitative content to such expressions as the "rate of growth of the gênerai price level" would want to compare priées of a set of commodities over several periods of time; similarly, in system analysis the question of how to take into account multiple criteria often arises; in the field of social choice theory the same problem is encountered and voting mechanisms are but one possible way of resolving it. To set the stage for our analysis it is convenient to adopt a few définitions to capture the sesential similarity between the various problems we have just mentioned (). (*) Reçu décembre 1973, version révisée reçue octobre 1975. (*) The author would like to thank an anonymous référée for his judicious comments and constructive criticisms on an earlier version of this paper. () See B. ROY, [16], for a gênerai extensive discussion of the problem. Revue Française d'Automatique^ Informatique et Recherche Opérationnelle, juin 1976.