| Abstract: | 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. |
