## 6 Summary of the Method  
The models and methods described in Sections 4 and 5 are alternatives. The DMs may select the model of preferences they feel more compatible with. Each DM sets their own model parameters, solves their own Problem 11, identifies their best compromise, and defines their limiting boundary according to Assumption 4 or Assumption 7. Then, it is possible to evaluate the number of satisfied and dissatisfied DMs, exploring the decision variable space to solve Problem 1. Since the preference models and their parameters differ from two disjoint subsets of the whole group, the consensus reaching process should be carried in different subgroups. The proposal maintains its validity even if the DMs face different optimization problems (with different objectives and constraints) but with common decision variables ranging in the intersection of the feasible regions of each DM optimization problem. The main reasons for such a general performance come from Propositions 2.c and 3.c and the independent way in which each DM sets their limiting boundary and defines what a satisfactory (unsatisfactory) solution is. The specific characteristics, preferences, and judgments from each DM influence on determining whether particular solutions are satisfactory or not for the respective group member. The collective final decision comes from optimizing (\(N_{sat}\), \(N_{dis}\)) in Problem 1, but the calculation of these objectives is made by aggregating the independent assignments of all the DMs. It should be underlined that the proposal is, to a great extent, robust with respect to malicious intents of manipulation from some group members. To analyze this issue, suppose that some DMs are interested in manipulating the final solution. To achieve this, they should try (providing insincere information), to increase \(N_{sat}(z^{\star})\) and reduce \(N_{dis}(z^{\star})\) in the points \(z^{\star}\) where they are really satisfied, and to decrease \(N_{sat}(z^{\star\star})\) and increase \(N_{dis}(z^{\star\star})\) in the points \(z^{\star\star}\) where they are really dissatisfied. The information required from them is basically of three kinds: (i) parameters of their preference model; (ii) solutions describing the limiting boundary between classes \"satisfactory\" and \"unsatisfactory\"; (iii) their constraints and objective values. This information determines if the DMs are satisfied or dissatisfied and counted in \(N_{sat}\) or \(N_{dis}\). If they report insincere information on any of the three previous aspects, solutions that are really satisfactory for them could become unsatisfactory according to the model, and vice versa. This does not contribute to reaching a final solution really satisfactory for the DMs that provide insincere information. In addition, each DM should be impeded to know the limiting boundaries elicited by other DMs. Under this restriction, the \(i\)-th DM cannot evaluate solutions from the point of view of other DMs, being thus unable to determine what insincere information should provide for maliciously influencing other opinions. Therefore, during collective discussions, the \(i\)-th DM should defend their real preferences and beliefs and try to convince others. The method for finding the maximum consensus can be summarized as steps:  
1. Helped by a decision analyst/moderator, the DMs select the model of multi-criteria preferences that they consider as more appropriate. The group is separated into two disjoint subgroups in correspondence to the model of preferences that were chosen by each DM. 2. In each subgroup, under the guidance of the moderator, the DMs bring their positions closer. They exchange opinions about the objective functions to consider, the objective values, the related model's parameter values, levels of conservatism, and constraints. Each group member sets their multi-objective optimization problem (Problem 11) and their model's parameter values. Interval numbers can be used according to Assumptions 1, 3, and 6. 4.