A network fairness consensus model considering opinion retention utility

Frequent interactions among decision-makers (DMs) in social network group decision-making (SNGDM) intensified their fairness concerns. In the consensus-reaching process of SNGDM, prior research assumes that DMs hold fairness concern for all others in social networks and only focuses on opinion compensation. However, it ignores that DMs in social networks mainly have fairness concern with those they are connected to in social-comparisons, as well as the impact of opinion reservation on the perceived fairness utility in self-comparisons. To address these two issues, this paper redefines fairness measurement in social networks and incorporates opinion retention into DMs’ fairness utility, aiming to analyze consensus fairness considering DMs’ network fairness concern in SNGDM. First, we propose the network fairness concern coefficient based on trust and opinion relationships to measure the different levels of DMs’ fairness concern for others. Then, taking into account the DM’s dual fairness concerns about opinion compensation and opinion retention, the fairness utility function is constructed based on the network fairness coefficient. Accordingly, a maximum fairness utility network consensus model is proposed. Finally, the validity of the proposed model is confirmed by the application example of enterprises’ initial carbon quota allocation. The results show that: (1) The network fairness concern coefficient enables personalized fairness assessment, and (2) Incorporating opinion retention in the fairness utility function mitigates limitations of compensation-focused fairness measures, offering a more holistic framework.