The minimum acceptable violation ranking of alternatives from voters’ ordinal rankings

Abstract

Motived by applications of ordinal ranking and adjustment consensus in group decision making, we study the problem of aggregating all voters’ ordinal ranking on a set of alternatives into an adjusted “consensus” ranking. In this problem, every voter ranks a set of alternatives respectively, and we know the adjustment acceptability. The problem is to find an optimal ordinal ranking which minimizes the sum of voter’s acceptable violation. We analyse this problem by utilizing both pairwise preference and order-based ranking, and develop a branch-and-bound algorithm to solve this problem. The effectiveness and efficiency of this algorithm are verified with a small example and numerical experiments.