The Research Of Some Theories And Application In Group Decision Making

Group decision making is an important branch of modern decision-makingresearch, which is also known as collective choice in economic and political fields.Itplays more and more important role in modern society. Group decision-making cannot only reflect the consultation results of the participants, which is more fairness andtrustworthiness than individual decision or dictatorship. Its main problem is to researchhow to turn any a member of collective preference into a collective preference, andthen two best results can be selected by the means.Simultaneously,group decision making is a cross-edge discipline. In the past twodecades, group decision-making became an emerging field of decision sciences. Itsresearch areas related to the operations research,social choice theory, topology,probability theory, welfare economics and many other disciplines. These advantagescaused a wide range of scholars interested.The order of the arrangements are asfollows.The first chapter is devoted to study the current situation and significance of groupdecision making theory in domestic and international.And for the problem, we give abrief introduction about the research background and theories. The following is someproperties of the preference relation. At last, some ranking rules are denoted which areused very usually.In the second chapter, we introduct a new weak transitivity and we give anapplication. That is an important property of Suzumura-consistency. An importantproperty of this weak transitivity is that it is necessary and sufficient for the existence of an ordering extension of a relation.In the third chapter, the problem of suzumura consistency rational choice functionrevealed preference representation is investigated. Based on the revealed preferencedefining, revealed preference axiom of Suzumura-consistency rational choice functionis proposed. It is shown that a choice function is rationalized by a Suzumura-consistency if and only if it satisfies the axiom.The fourth chapter illustrates how an impossibility result in population ethics canbe turned into a possibility by weakening transitivity to Suzumura-consistency.The fifth chapter, as for group decision making issue, the k-Major rule wasproved to satisfy a few rational conditions of ordinal anonymity, neutrality, localnondictatorship, and pareto rule that proposed in some papers. Following, someproperties of the rule were also achieved.The last chapter is conclusion and expectation．...