A two-stage distributionally robust maximum expert consensus model with asymmetric costs and risk aversion

The maximum expert consensus model (MECM) emerges as a widely used consensus optimization model in group decision making (GDM). However, contemporary complexities in decision-making environment lead to the asymmetry and uncertainty of adjustment costs of decision-makers (DMs), which are critical during the consensus reaching process (CRP). Additionally, the risks emerging with the uncertainty during CRP should also be analyzed. Therefore, this paper focuses on developing the two-stage distributionally robust MECM (DRO-MECM) with asymmetric adjustment costs under an uncertain environment to improve the CRP. Specifically, we propose a MECM with asymmetric costs. Moreover, we build the two-stage DRO-MECM based on the mean-CVaR under two uncertain scenarios, allowing it to manage uncertain costs effectively while considering the risk preferences of DMs. The first stage aims to maximize the number of DM within consensus and the second stage seeks to minimize the consensus cost. Finally, the applicability of the proposed models is demonstrated by applying them to the allocation of healthcare and security capacity enhancement subsidy funds in China. The efficiency of the models is further corroborated by sensitivity analysis and comparison analysis.