Group Consensus Modeling With Utility Preference And Its Application Study

In complex group decision making (GDM), reaching a consensus needs both the adequate communication and exchange between the individual decision makers (DMs) and the input of a moderator, who may take various effective actions, such as providing financial compensation to convince DMs to gradually modify their opinions and to reach a final consensus. Normally, the moderator always expects to obtain an optimal consensus opinion with minimum resource consumption. But as individuals, they always hope to get enough attention with their interest highly valued, as they have a significant impact on the consensus reached. That is, they expect the consensus opinion to be not only within their own opinion interval, but also the closer to their ideal values the better. In other words, DMs have some utility preference for the consensus opinion. Obviously, such preference becomes an important indicator to measure the effectiveness of a GDM. As a result, if the moderator takes the minimum consumption of resources as the target, then even he/she obtains the optimal consensus in the mathematical sense, he/she cannot meet the requirements of all individual utility. Therefore, the moderator must allocate further resources to meet the majority of the DMs’ utility preference needs.Based on the above analysis, this paper constructs new consensus models that aim to maximize the GDM utility under the premise of limited consensus cost and different utility/preference constraints for both the individual DMs and the moderator. The utility preference discussed in this paper include not only a simple linear form denoted by trapezoidal membership functions, but also some complex nonlinear forms (i.e., the parabolic form and the S-type form fitted by sine function), which can better simulate DMs’ psychology in real-life situations. The objective function derived from the proposed models can also be seen as a measurement of the consensus degree. By numerical analysis, we verfy the rationality and validity of the proposed maximum utility consensus models based on simple linear utility preferences. Combining incentive compatibility principle, this paper uses the pollutant reduction negotiations between the government and manufacturing enterprises as a case background, and builds a group reduction consensus model based on nonlinear preference constraints and limited consensus cost and further economically interprets the model parameters.Results of numerical analysis and application show that, if we maintain the moderator’s preference unchanged, then DM’s different preferences will make the final opinions fall in exact corresponding zones of their original intervals. Additionally, if we only change the preference structure of the moderator while keeping each individual DM’s unchanged, then we will find that, according to the moderator’s preference sequence, i.e. the moderator prefers the smaller, the intermediate and the larger values in turn, then the optimal solutions of both the consensus opinion and all of the individual opinions show an overall increasing trend. This result indicates that the moderator has a dominant role in the development trends throughout the whole decision-making process to some extent. As for the case study, Government has played a macro-control role in the negotiation process of consensus GDM. Moreover, once the difference of utility preferences betweenthe the moderator and all the individuals gets larger, the utility level of the whole group is bound to dramatically decreases, which indicates the facts that it’s necessary for the moderator to fully communicate with all the individual DMs at the beginning of the GDM. The modeling mechanism used in this paper will be reference for solving real-life consensus GDM problems.