Addressing the influence of limited tolerance and compromise behaviors on the social trust network consensus-reaching process

In social trust network group decision-making, experts typically show limited tolerance and compromise behaviors when modifying their opinions to reach consensus. The first behavior implies that an expert will change their opinion without cost if the suggested opinion closely aligns with that of trusted experts. The second behavior implies that an expert will accept the suggested opinion only if it falls within a predefined compromise boundary relative to trusted experts’ opinions. However, existing maximum expert consensus models (MECMs) do not adequately consider these behaviors, limiting their practical applicability. To address this gap, this study proposes a social trust MECM with budget constraints. Budget constraints can lead to an insufficient number of experts within the consensus, underscoring the need for higher budget allocation to achieve consensus. To address this issue, a minimum cost consensus model (MCCM) considering network-dependent limited tolerance and compromise behaviors (NDLTCBs) was developed to provide a budget increment reference. Notably, network-dependent limited compromise behavior is crucial in the MCCM, especially when compromise values are small, as it may prevent feasible solutions. In such cases, a minimum compromise increment consensus model is created to determine the necessary increase in compromise values for a feasible MCCM solution. Subsequently, an interactive maximum expert consensus-reaching process is introduced. Simulation experiments demonstrate that consensus efficiency, in terms of the number of experts within the consensus, can be enhanced by considering NDLTCBs.