Minimum conflict consensus with budget constraint based on social network analysis

Abstract

In the consensus reaching process (CRP), the asymmetric trust relationships among decision-makers (DMs) and discrepancies of DMs’ opinions may exacerbate the intra-group conflicts. In this paper, we investigate a consensus-building approach based on minimum conflicts under budget constraint to alleviate the conflicts. First, a conflict measurement method based on opinion similarity and the degree of asymmetric trust is presented to construct the conflict network among DMs. Then, the weights of DMs are obtained by analyzing the structure of the conflict network. To achieve a consensus, a minimum conflict consensus model with budget constraint (MCCMBC) is built. Considering that the impact of acceptance degree of recommendations on consensus results, we further develop the ε-MCCMBC, the rejection-based (RB)-MCCMBC, and the divergent-based (DB)-MCCMBC to handle compromise limit, rejection, and divergent behaviors, respectively. Furthermore, three kinds of minimum cost budget models are constructed to provide the reference budget of CRP. Finally, the validity of the proposed consensus models is verified by the case of trans-boundary water pollution treatments in China’s Poyang Lake Basin. The results show that: under the optimal budget, the group conflict degree and the collective opinion derived from the MCCMBC lie somewhere between that of the RB-MCCMBC and DB-MCCMBC. In addition, the moderator needs to spend more budget to facilitate the CRP when DMs adopt rejection or compromise limit behaviors.