Opinion-based optimal group formation

Most of classical decision making processes aim at selecting the best alternative or at ranking alternatives based on the opinions of decision makers. Often, such a process occurs among people (experts or decision makers) who are expected to achieve some shared consensus in ranking the alternatives. However, this is not likely to happen (especially for a large and heterogeneous collection of people) and decision makers tend to reveal groups characteristics derived from their different opinions. A major problem is that inconsistency in opinions arises as each expert has a limited knowledge, errors and misinterpretation of data can occur and thus it is not clear how groups can be identified to be internally consistent and non-conflicting. In this paper, we investigate the conditions under which experts can be split into different sub-groups that share coherent and consistent opinions but are mutually in conflict in the ordering of the alternatives. We face this problem by presenting a non-linear integer programming model where each decision maker specifies incomplete preferences on pairs of alternatives and the objective is to obtain groups having the least possible degree of inconsistency. From a theoretical standpoint, we show that the proposed problem is non-convex and NP-Hard. Moreover, we validate the proposed approach with respect to a case study related to the 2018 Italian political elections. Specifically, we analyze the opinions of 33 decision makers and we show that the proposed technique is able to identify subgroups characterized by large internal consistency, i.e., the members of each sub-groups express similar judgements upon the different options, while such options are evaluated very differently by the different sub-groups. Interestingly, while dividing the decision makers in three sub-groups, we obtain group rankings that reflect the structure of the Italian political parties or coalitions at the time, i.e., left-wing, right-wing and populists, even if such kind of information has not been directly provided by the decision makers nor used within the proposed case study. (C) 2018 Elsevier Ltd. All rights reserved.