Accentuating the rank positions in an agreement index with reference to a consensus order

Abstract

In this paper, we propose an index that measures the agreement level between an individual opinion and a collective opinion when both are expressed by rankings of a set of alternatives. This index constitutes an interesting weighted version of the well-known Kendall's ranks correlation index. The originality of the proposed index arises from the fact that it accounts for the relevance of the specific position of the alternatives in an individual order to quantify the agreement level of the individual order with respect to a collective temporary order. The paper also introduces a new consensus measure model. The core of the consensus model is the proposed agreement index. We present an illustrative example to describe the consensus process. We can obtain a faster convergence to a consensus solution using this new index compared to Kendall's index.

A Multi-objective Genetic Algorithm for Inferring Inter-criteria Parameters for Water Supply Consensus

“…In Table 4 we have a row showing the similarity (proximity) between the individuals' rankings and the collective ranking. This value was calculated by the proximity index proposed by Leyva and Alvarez [11].…”

“…developed by Leyva and Alvarez [11] for expressing the differences in the ranking discrepancies between the group temporary ranking and the individual rankings (see [12] ). The measure considers the rankings of a set of alternatives from the most important to the least important.…”

An ELECTRE III based consensus‐reaching process to improve a collective solution

“…To evaluate the collective result as the similarity between individual preferences and collective preference, we use an individual agreement index and a global agreement measure. The agreement index is the weighted Kendall index (Leyva López and Alvarez Carrillo, 2015) and is based on the well‐known Kendall's rank correlation coefficient (Kendall, 1938). A brief explanation of the is included in Appendix B. Kendall's distance counts the number of pairwise disagreements between two orders.…”

“…It indicates the level of agreement between the rankings. Because the proximity level is calculated with the weighted Kendall index (Leyva López and Alvarez Carrillo, 2015), the value is related to the number of disagreements found between the rankings. Inversions found in the highest level of ranking are penalized more strongly than those found in the lowest level of ranking.…”

Adaptation strategies of dam safety management to new climate change scenarios informed by risk indicators

“…The goal is to define a consensus ranking that presents the maximum degree of consensus within the M rankings. This technique has received growing consideration over the past few years and has been widely used in a variety of domains (Leyva López and Alvarez Carrillo 2015;Luo et al 2018;Meila et al 2012;Plaia et al 2019).…”