Enhanced Minimum-Cost Consensus: Focusing on Overadjustment and Flexible Consensus Cost

Minimum-cost consensus (MCC) using the optimization-based consensus rule (OR) has been developed and widely applied to various group decision-making (GDM) contexts because resources for the consensus-reaching process are generally limited. In view of the shortcomings of traditional MCC, including the overadjustment of individual opinions and reliance on single type of consensus constraints, this study proposes several enhanced MCC (EMCC) models. First, we provide a visual analytical solution for opinion adjustment in MCC using explicit adjustment paths, through which the adjustment direction and feedback coefficient of each individual opinion are embodied and quantified. According to the obtained feedback coefficients, the criterion for determining overadjustment is defined. By incorporating explicit adjustment paths into traditional MCC, several EMCC models with different types of consensus constraints are developed, all of which can effectively avoid overadjustment. Then, the connection between the identification-direction consensus rule and OR is established based on EMCC. We propose the concept of coordination elasticity and discuss the performance of EMCC from the perspective of consensus cost and overadjustment in order to analyze the using conditions of EMCC. Flexible EMCC provides a negotiated solution for dealing with overadjustment by following the principle of individual consensus cost priority. Finally, the characteristics and advantages of the proposed EMCC models are revealed through a case study and comparison with traditional MCC.