A fair consensus adjustment mechanism for large-scale group decision making in term of Gini coefficient

Abstract

With social media and e-democracy development, decision-making environments and problems have become increasingly complex. Traditional group decision-making, including a small number of decision makers, cannot deal with many practical decision-making problems. Large-scale group decision-making has received extensive attention as an efficient measure to address this issue. This paper proposes a two-stage optimization consensus mechanism for large-scale group decision-making by the Gini coefficient, which considers both the consensus among decision makers’ opinions and the fairness of consensus adjustment. First, we introduce an improved density peak clustering method to cluster decision makers into subgroups that can avoid different clustering centers being too close. Then, we define the subgroups' weights by the silhouette coefficient, the subgroup judgment distance, and their sizes. Respecting the importance of minority opinions, we design a new method to identify and adjust the weights of the minority opinions, which considers more aspects than previous ones. Further, we use the Gini coefficient to measure the equity of consensus adjustment of the group and subgroup. Moreover, we present a two-stage Gini coefficient-based consensus mechanism to obtain the adjusted consensus individual decision matrices, which can ensure the minimization and fairness of consensus adjustment and allocation under the set constraints. Based on these results, we give a new large-scale group decision-making method. Notably, it is the first method that fully considers the opinions of minor subgroups and the fairness of allocation results. These characteristics are essential in decision-making problems such as resource allocation and urban public construction. Finally, we show the utility and validity of the new method through a case study and make the comparative analysis from numerical and principle aspects.