A statistical comparative study of different similarity measures of consensus in group decision making

An essential aim in Group Decision Making (GDM) problems is to achieve a high level of consensus among experts. Consensus is defined as general or widespread agreement, and it is usually modelled mathematically via a similarity function measuring how close experts’ opinions or preferences are. Similarity functions are defined based on the use of a metric describing the distance between experts’ opinions or preferences. In the literature, different metrics or distance functions have been proposed to implement in consensus models, but no study has been carried out to analyse the influence the use of different distance functions can have in the GDM process. This paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in GDM. By using the nonparametric Wilcoxon matched-pairs signed-ranks test, it is concluded that different distance functions can produce significantly different results. Moreover, it is also shown that their application also has a significant effect on the speed of achieving consensus. Finally, these results are analysed and used to derive decision support rules, based on a convergent criterion, that can be used to control the convergence speed of the consensus process using the compared distance functions.