Comparison of Consensus Methods for Priority Ranking Problems

Various consensus methods proposed for ranking problems yield controversial rankings and/or tied rankings which are vulnerable to considerable dispute. These include Borda‐Kendall (BK) and minimum‐variance (MV) methods. This paper compares three continuous (ratio‐scale) consensus scoring methods with BK and MV ranking methods. One method, termed GM, is an eigenvector scaling of the geometric‐mean consensus matrix. GM allows for (1) paired‐comparison voting inputs (as opposed to all‐at‐once ranking), (2) pick‐the‐winner preference voting, and (3) ratio‐scale preference voting. GM is relatively simple to calculate on small computers or calculators, and merging of “close” candidates into tied rankings can be achieved by using an e‐threshold tie rule discussed in this paper. The GM method thus can be used for paired‐comparison voting to calculate both a ratio‐scaled consensus index (based on a consensus eigenvector) and a ranking of candidates that allows for ties between “close” candidates. Eigenvalue analysis is used as a means of evaluating voter inconsistencies.