A two-stage consensus model incorporating manipulative and manipulated behaviors for large group decision-making under social network environment

In large group decision-making (LGDM), some decision-makers (DMs) may engage in manipulative behaviors driven by personal interests, while others may become susceptible to manipulation due to the complexity and uncertainty of the decision-making process. These manipulative and manipulated behaviors hinder the effective achievement of group consensus and undermine the fairness and acceptability of the decision-making process. To address this, we propose a two-stage consensus model that accounts for both manipulative and manipulated behaviors. First, the trust relationships among DMs are adjusted based on the similarity of their evaluations, and the strength of these relationships is calculated using their adjusted mutual trust degrees. Next, a clustering method based on the fracture of relationship strength is introduced to classify DMs into subgroups. By considering DMs' hesitancy, trust relationships, and preference degrees for various alternatives expressed in their evaluations, manipulators are identified and penalized with a weight penalty. The combination of hesitation degree, trust degree, and similarities in alternative ordinals, before and after subjective adjustment, is used to identify and impose penalties on manipulated DMs. Furthermore, various objective adjustment strategies are proposed to better manage the different behaviors of DMs, thereby improving decision-making efficiency and consensus. Finally, an application example and comparative analyses are presented to validate the feasibility of the proposed method. The proposed method effectively manages manipulative and manipulated behaviors, significantly enhancing consensus efficiency, fairness, and acceptability in the decision-making process.