Group Decision Making in Ordinal Consensus Ranking Problem

The problem of achieving overall consensus on a set of rankings has been studied for more than two centuries and concerns many disciplines: management science, marketing, social science, politics, psychology, etc. The aim of this article is to demonstrate the following methods of group decision making in ordinal consensus ranking problem: method of Kendall and Borda (BAK), maximize heuristic agreement procedure (MAH) by Beck and Lin, consensus ranking model (CRM) by Cook and Kress, hybrid distance-based model (DCM) by Tavana et al., Kendall's and Spearman's footrule distance, Kemeny-Snell distance and a fuzzy model by Blin and Whinston. Use of these techniques is demonstrated in an example - selection of a football stadium project from four alternatives by eight decision makers. The latter part of the article includes comparison of these methods and some generalizations for problems with different weights of individual rankings or problems with ties, and a discussion of existence and uniqueness of solution with regard to Arrow's impossibility theorem.