An analysis of consensus approaches based on different concepts of coincidence

Abstract

Soft consensus is a relevant topic in group decision making problems. Soft consensus measures are utilized to reflect the different agreement degrees between the experts leading the consensus reaching process. This may determine the final decision and the time needed to reach it. The concept of coincidence has led to two main approaches to calculating the soft consensus measures, namely, concordance among expert preferences and concordance among individual solutions. In the first approach the coincidence is obtained by evaluating the similarity among the expert preferences, while in the second one the concordance is derived from the measurement of the similarity among the solutions proposed by these experts. This paper performs a comparative study of consensus approaches based on both coincidence approaches. We obtain significant differences between both approaches by comparing several distance functions for measuring expert preferences and a consensus measure over the set of alternatives for measuring the solutions provided by experts. To do so, we use the nonparametric Wilcoxon signed-ranks test. Finally, these outcomes are analyzed using Friedman mean ranks in order to obtain a quantitative classification of the considered measurements according to the convergence criterion considered in the consensus reaching process.

A Variance-Based Consensus Degree in Group Decision Making Problems

“…In this paper, we develop a strategy already used in previous documents [15][16][17] consisting in contrasting a statistical hypothesis through a non-parametric hypothesis test. The hypothesis to be tested is stated as follows:…”

“…The measurement of the distance between the experts' preference values facilitates the computation of the consensus level among them [26]. Some of the following distance functions are the most commonly used in its calculation [15][16][17]26]:…”

“…where A = {a 1 ,...,a n } and B = {b 1 ,...,b n } are two sets of real numbers. In order to find the similarity between preference values through the similarity function, any of these distance functions could be used by setting similarity as s = 1-d [15][16][17].…”

“…We compare this proposed consensus measure with a more frequently used approach based on an aggregator and different distance functions [15][16][17] and acceptable results are obtained in comparison with the usual approach mentioned above. Finally, we present a ranking of these measures.…”

“…Generally, for the computation of consensus levels it is necessary to calculate and aggregate the distance measures employed to represent the proximity of the preferences of each pair of experts on each pair of alternatives [4,[9][10][11][12][13][14]. We have shown [15][16][17] that consensus level values are affected by the distance function and the aggregation operator used in the calculation.…”