Study Of Collective Rationality Conditions Based On The Judgment Aggregation Logic

How to aggregate individual rationality into collective rationality is the main problem faced by the cognitive study of social rationality, it is also one of the hot interdisciplinary questions among economics, philosophy, politics, law and computer science etc. The famous American economist Professor Kenneth Arrow ([6]) used the axiomatic method depicting individual rationality and collective rationality, and proved the impossibility of aggregating the rational individual preference into the rational collective preference. It becomes an important problem in many studying areas that how to understand the impossibility and to dissolve it for finding reasonable collective rationality aggregating methods,judgment aggregation provided a-new idea for the breakthrough of the problem. Preference aggregation and judgment aggregation are the two basic models for studying collective rationality aggregation.Preference aggregation has been deeply studied in the social choice theory. In social choice theory, it is the main question how to make a collective decision based on the preference of individuals in the group.Judgment aggregation which emerge recently has many theoretical advantages compared with preference aggregation. Judgment aggregation becomes the center of studying collective rationality aggregation gradually. From the perspective of logic, judgment aggregation consider how to aggregate many logical consistent formula into one logical consistent formulue.Now the existing research results([21,72]etc.) show that:there has been close connection between judgment aggregation and preference aggregation, the similar impossibility conclusions like Arrow Therem in the area of preference aggregation existed also in the area of judgment aggregation.The impossibility conclusions in the areas of preference aggregation and judgment aggregation revealed the imsossibility to aggregate individual rationality into collective rationality under some reasonable conditions. Recently modern logic has been used widely and developed rapidly in the areas of studying knowledge update,belief revision and preference upgrade etc., then the modern logic becomes the efficient theoretic tool to resolve the problem of aggregating collective rationality. Using the modern logic tools,we analyzed the close connection between judgment aggregation and preference aggregation,then proved the generality of judgement aggregation model compared with preference aggregation.Based on the judgment aggregation model,we study the collective rationality aggregation problem deeply,so as to explore feasible escape routes for it.This research would lay solid theoretical foundation for making collective decision schemes,thus further promote the formal study of social collective cognition.Firstly, this paper combed carefully the preference aggregation model and the judgment aggregation model which are the two basic models for studying collective rationality aggregation and drawed forth the difficult problems of collective rationality aggregation. Then,we used the modern logic tools to analyze and depict the problems of the collective rationality aggregation,discussed the close connection between judgment aggregation and preference aggregation from the logic prespective and illustrated that preference aggregation is a special case of judgment aggregation. Of which we analyzed mainly a judgment aggregation modal logic JAL.The syntax of JAL language is very simple,and so is its semantics.Having very powerful expression, the languag of JAL can be interpreted directly by the judgment aggregation rules.Based on JAL,we constructed a preference aggregation logic system JAL(hK) using the language of the first-order logic.Thus the preference aggregation questions could be converted into the judgment aggregation questions to be handled,so that the generality of the judgment aggregation model is highlighted and the theoretical advantages of the judgment aggregation model in analyzing the collective rationality aggregation is illustrated.And then, on the basis of a stict proof for a judgment aggregation impossibility conclusion,we put forward many ways for resolving the problems of the collective rationality aggregation,such as limitting the input of the judgment aggregation rules,loosening the output conditions of the judgment aggregation rules,abandoning the independence etc..Putting forward feasible schemes for every resolving way, we highlight the important theoretical significance and extensive practical application value of our research.Finally,we summarized and discussed the results of this paper and ascertain our future research.