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This paper presents the preference ratios in multiattribute evaluation (PRIME) method which supports the analysis of incomplete information in multiattribute weighting models. In PRIME, preference elicitation and synthesis is based on 1) the conversion of possibly imprecise ratio judgments into an imprecisely specified preference model, 2) the use of dominance structures and decision rules in deriving decision recommendations, and 3) the sequencing of the elicitation process into a series of elicitation tasks. This process may be continued until the most preferred alternative is identified or, alternatively, stopped with a decision recommendation if the decision maker is prepared to accept the possibility that the value of some other alternative is higher. An extensive simulation study on the computational properties of PRIME is presented. The method is illustrated with a re-analysis of an earlier case study on international oil tanker negotiations