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The interpretation bias of cracking Arrow's impossible theorem

May 20, 2020 03:18 Source: "China Social Sciences", May 20, 2020, 1929th author: Zuo Yonghua Dujiang

　　For the past ten years，Random phenomenon in the international public domain frequent，reveals the diversity and management complexity of the content of public affairs。Actually，As early as the 1950s，American economist、The Nobel Prize winner Kenneth J. Arrow is in its economic book "Society Choice and Personal Value"，Strictly proves that there is no preference assembly method that meets the basic specifications，It is a foreee based on individual preferences、It is difficult to succeed and efficient for individual interests to form public decisions。Election as a typical group、Public behavior，Arrow impossibility theorem with election -oriented Arrow can be widely interpreted in the field of public affairs。It can be said，Arrow's impossible may be related to the logical basis characterized by the entire Western world with formal rationality。

　　Generally speaking，Part of the interpretation of the impossibility theorem of Arrow's impossible.。Actually，ARROW When the theorem was initially constructed，Name it as general possibility theorem，Explain that Arrow himself does not give up society choice function，Even if its conclusion is the social selection function Bet365 app download under its axiom system or impact，or dictatorship。ARROW's proof of the impossible theorem，and the follow -up of many related certificates，All strive to improve the ARROW axiom system，Find the root cause of the impossible through technical analysis，So as to get out of the impossible theorem。These work itself explains that Arrow's impossibility is impossible.，and the impossible possibility of getting out of Arrow is a huge challenge。At the 2002 International Public Options Conference，American scholar Roger Congleton pointed out，The theoretical foundation of the public selection is not reliable，is "floating swamp land"。But，Consolidate the theoretical foundation of public selection.，Breaking the logical chain in the proof of the impossible possibility、The possibility theorem of building a completeness is equally difficult。

　　Public selection theoretical basic issues, that is, social selection function axiom，Specifically includes self -consistent system、Compatibility and completeness，and the existence of the choice function based on the axiom。visible，The theoretical basis of the public choice is the nature and characteristics of the selection function，The typical "Yuan Theory" problem。This is necessary to keep a vigilance of the "technical treatment" of the axiom system。Actually，In basic political theory、Economic Theory and even bet365 live casino games decision theory，Interpretation of the impossible theorem of Arrow is generally biased。Many studies believe，Anonymous of the ARROW axiom system、Neutral、Positive response and transmission lead to strict and absolute dictatorship。This view has certain limitations。Both ARROW's original axiom system or the refined system is contrary to the "non -independent axiom" in it，But the axiom system is not spontaneous leading to dictatorship (that is, strict dictatorship)，Instead, in the process of adjusting the order of individual preferences to adjust the order of individual preferences by relying on "technical processing power"，Therefore, it is unexpected result。"The Power of Technical Treatment" also realizes the preparation of "individual order"，Individuals with self -dedication are dependent on this "individual order"。This obviously violates the theoretical specifications of the public selection，That is, the social selection function must be constructed based on individual real preferences。If individuals choose to hide their own preferences when entering the election game field，So the new preference combination formed after the individual preferences are adjusted，I deviate from the orbit of the theoretical foundation of the public。

　　Of course，Maintaining the vigilance of "technical treatment" can make up for this problem。Current，Equipment theory、Research bet365 best casino games Progress of the Turns for the Modeling and related topology methods，help to make up for these theoretical deficiency，Construct a clearer theoretical basis at the same time，Accurately portray ARROW axiom，Therefore, to a certain extent eliminates the external distortion of the theoretical conclusion caused by "technical processing power"。For example，Set value mapping portrait preference is the independence of mapping the collection value model, especially the preference projection portrait。Another example，The collection of all members can effectively eliminate the "individual order" preparation of "technical treatment forces"，to reduce the substantial impact of "individual order"。At the same time，Use the collection value mapping，Obstacles encountered in the process of gathered by individual preferences、Formation of the collection of key voters，and the hierarchy of the dictatorship of social preference，Can get clearer portrayal。Another，ARROW's preferred domain in the original righteous system，Represents individual freedom and broad nature，But it also completely denies the consistency and consensus of the social level。Some new methods can load the topological structure for non -binding preference domains，The scope limit of not being subject to the preferred domain，So as to portray consistency under formal freedom。That Bet365 lotto review is to say，As long as a certain topology structure is embedded in the preference domain，Consistent portrayal。For example，Political tendency given by Single Peak preferences on preferences，Requires at least one consensus standard at the social level，The specific political tendency reflected in the measurement and judgment preference order。

　　The theoretical basis of the public selection，Arrow's impossible Theorem Study is mainly concentrated in two aspects: first，Standardization and precise portrayal of the ARROW axiom system; second，Limited logic analysis limitations of the impossible theorem，Going out of impossible。The Nobel Prize winner Amartya Sen and Eric Maskin provided direction for the latter。Where，Sen expanded the significance of the ARROW axiom system，Valid conditions of the selection function by expanding the selection function、Limit the compatibility of entering the axiom system to solve the impossible paradox; Maskin starts with the stability of the specific operation method，Most voting system is the most stable，and promote the natural harmony of the axiom system from a practical perspective。

　　In short，As a public choice theoretical basis，Standardized axiom system must be able to withstand interpretation and induction reasoning，Especially interpretation push -up，so as to clearly and accurate portrayal。This can be done through Bet365 app download mathematical technology，But also requires in -depth development of mathematical technology，Especially the development of the value of the value topology。The limitations of existing documents，Revealing the existence of the selection function is different from the proof of the general mathematical axiom system。These literatures are expanded based on preference conversion，It is a proof that reflects specific operations; but only the presence of the selection function at the "Yuan theory" level analysis，is the most rational proof。After all，Social selection function is not a general choice，but the choice and structure of the "selection method"。other，Simple pursuit of logic and rigorous formalization proof can easily lose the essence of technical analysis，That is to say，A complete argument in form is difficult to reveal the practical significance of mathematical technology technology，This is also a problem that should be avoided when analyzing the theoretical foundation of the public。

　　(this article is the general project of the National Social Science Fund "based on the ARROW righteous system and the impossibility of public choice" (17bjl025) phased achievement)

　　(Author: Jiangxi Normal University Jiangxi Institute of Economic Development Research Institute; Institute of Economics of the Chinese Academy of Social Sciences)

Editor in charge: Changchang