An interactive approach for discrete multiple criteria decision making problems is developed. The approach requires the decision maker to compare pairs of presented alternatives. These alternatives may be existing alternatives or dummy alternatives created from existing alternatives. Inferior alternatives are sequentially eliminated by either using the responses of the decision maker directly or by constructing cones of inferior solutions based on these responses. The approach converges to the most preferred solution so long as the decision maker has a nondecreasing quasiconcave value function. The aim is to keep the number of pairwise comparisons required of the decision maker as small as possible. Computational experience on randomly generated problems is reported and the results are compared with the results of similar approaches.