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COMPARISON OF CONSENSUS METHODS FOR PRIORITY RANKING PROBLEMS
Author(s) -
Jensen Robert E.
Publication year - 1986
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1986.tb00221.x
Subject(s) - ranking (information retrieval) , voting , preference , computer science , eigenvalues and eigenvectors , majority rule , simple (philosophy) , variance (accounting) , mathematics , scale (ratio) , statistics , data mining , econometrics , information retrieval , artificial intelligence , economics , political science , law , philosophy , physics , accounting , epistemology , quantum mechanics , politics
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.