Priority Ranking and Consensus Formation: The Case of Ties

This paper investigates the problem of obtaining a compromise/consensus from a set of ordinal rankings of n objects supplied by m committee members. Earlier work by Cook and Seiford (Cook, Wade D., Lawrence M. Seiford. 1978. Priority ranking and consensus formation. Management Sci. 24 (16) 1721--1732.) dealt with the problem of consensus when attention was restricted to complete rankings only. That is, no ties were permitted. This paper examines the general problem which allows for tied preferences. A convex polyhedral representation is given of the feasible solution space, and a branch-and-bound procedure is developed for determining an optimal ranking. Computational results for various problem sizes are presented. Generalizations, and directions for further research are discussed.