A consensus reaching process in the context of non-uniform ordered qualitative scales

Abstract

In this paper, we consider that a group of agents judge a set of alternatives by means of an ordered qualitative scale. The scale is not assumed to be uniform, i.e., the psychological distance between adjacent linguistic terms is not necessarily always the same. In this setting, we propose how to measure the consensus in each subset of at least two agents over each subset of alternatives. We introduce a consensus reaching process where some agents may be invited to change their assessments over some alternatives in order to increase the consensus. All the steps are managed in a purely ordinal way through ordinal proximity measures.

Metrizable ordinal proximity measures and their aggregation

“…Once this problem is solved, the OPM obtained can be used in different decision-making and classification problems in which agents show their opinions about a set of alternatives through an OQS equipped with a metrizable OPM: Measuring consensus in a group of agents on a subset of alternatives, and consensus-based clustering procedures, as in García-Lapresta and Pérez-Román [11]; consensus-reaching processes, as in García-Lapresta and Pérez-Román [13];…”

Measuring Dispersion in the Context of Ordered Qualitative Scales

“…Following García-Lapresta and Pérez-Román [5], we now introduce the median operator in the setting of ordinal degrees of proximity.…”

Clustering U.S. 2016 Presidential Candidates Through Linguistic Appraisals

“…According to García-Lapresta and Pérez-Román [10], for measuring the consensus in a group of agents over a set of alternatives, the first step is to consider the degrees of ordinal proximity between the linguistic appraissals over the alternatives. These degrees are arranged in a vector of ordinal degrees δ ∈ ∆ p , for some p ∈ N, from the highest to the lowest degrees (decreasing fashion).…”

“…In order to avoid loss of information, García-Lapresta and Pérez-Román [10] select the median(s) of the mentioned ordinal degrees in such a way that if the number of ordinal degrees of the vector is odd, the median is unique, δ r ∈ ∆, but if the number of ordinal degrees is even, then δ has two medians, δ s , δ t ∈ ∆ with s ≤ t. In order to unify this assignment of medians, the authors consider the pair of medians (δ r , δ r ) in the odd case and (δ s , δ t ) in the even case.…”