Study On Goup Decising Making Theory Conditions' Relationship And Application

This dissertation study on the relationship and applications of conditions in group decision making theory, and substitution of these conditions in different impossibility theorem.The nature of decision making in a process of value discovering and judging, and behavioral choosing object can be assessed by its value. Individual decisions are unstable and have risk to make mistakes. But by aggregating the individual preferences, the varying information can been collected, and the risks that come from the individual decisions will be reduced. Moreover, facing the complicated problems, individual can't give a satisfied answer due to his limitations of ability and knowledge. For this reasons the group decision making has more advantages in the decision making. But in real life, people always face the various choice. As people having different social experience, culture and social status, they may be have different opinions on same issue, and these opinions even are completely opposite. So their choice may be different or even be opposite. How to coordinate individual's different opinions to be a group opinion is the issue that always be faced in real life, and mian issue that the group decision making theory study on. In the process of salving issue of group decision making, the early method is the majority rule. When there are only two alternatives, the majority rule is easy been comprehended. The alternative that the more individuals vote on is been choiced. But when there are more then two alternative, the majority rule can lead to conflicting result, so calling as "Condorcet paradox". This paradox makes people to pursue the rational group decision rule. But in the 50', in the set of seemingly rational conditions, Arrow proposed an impossibility theorem which imply that there are not rational group decision rule exist. The conditions the proposed by Arrow and other reseachers when they reseach rational group decision are to impose some restrictions on the individual and group preference. These conditions reflect the individual and group rational requirement in the process of decision, and become an impotant implements in researching group decision making. In these conditions some of which are related with each other. In this dissertation, the relationship of the conditions that were proposed by the group decision making reseacher and it's applications are been studied on.Firstly, the relation between neutrality and independent decisiveness has been analyzed. By the analysis it has been showed that under the conditions of individual and group preference being connected and transitive and strict a social welfare function which satisfies independent decisiveness and Pareto is neutrality. And then analyzed properties of determine set for the non-binary social choice function which satisfies some restrictive conditions. And then use these properties to establish an Arrow impossibility theorem with non-binary social choice function. And analyzed conditions of the non-binary social choice function and some conditions which were put forward by Quesada. And then use the conditions which were put forward by Quesada to replace the independence of irrelevant alternatives in Arrow's theorem under non-binary social choice function. It is shown that the independence of irrelevant alternatives and the condition of social preference order being complete in Arrow's theorem can be weakened at the same time.Secondly, study on the majority rule, and extent Maskin's theorem to all n, whether odd or even, to to provide a new characterization of majority rule. And then establish a new social choice function with subordinate relations, which only satisfy the condition of unrestricted domain and don't satisfy the conditionsof existence of a dictator and independence of influence of irrelevant individual.Make the social choice functions with subordinate relations become more complete.Finally, basing on the satisfy function which was proposed by Martel, a group programming method , which measuring deviation for deriving group priorities from crisp pairwise comparison judgments provided by multiple decision makers was proposed. This method can deal with missing DMs' judgments problems in deriving group priorities, and can consider DMs' importance in the decisions. And then an analysis example is given.