A comprehensive loss analysis-based decision support method for e-democratic multi-agent cooperative decision-making

E-democracy provides a virtual online platform characterized by information transparency and equal interaction, which facilitates the participation of multiple agents in government decision making. This paper proposes a comprehensive loss analysis-based decision support method and applies it to a case study of e-democratic multiagent cooperative decision-making. Multiple agents represent different interests and provide opinions with the goal of maximizing their own revenues. Agents' opinions are naturally prone to differences and even conflicts, which may have a negative impact on the harmony of the social system. To this end, this study develops a twostage type-alpha constrained minimum-revenue-loss consensus (TS-alpha-CMRLC) model. In Stage 1, an alpha-CMRLC model is adopted to obtain the optimal solutions of agents' opinions with minimizing the social revenue loss and preventing excessive revenue loss. In Stage 2, the concept of reputation loss is defined and an alpha-CMRLC model considering reputation loss is proposed. In this matter, the agent with high reputation but low consensus can reduce its revenue loss through the cost of reputation loss. The research results show that an increase in some agents' reputation losses leads to a decrease in their revenue losses, but it may cause an increase in the social revenue loss. We perform a comprehensive loss analysis to evaluate the performance of reputation loss. Finally, the case study and comparative analysis reveal the feasibility and advantages of the proposed method.