The Studies Of The Logic Of Strategy-Proofness Voting Theory

Strategy-proofness or non-manipulability are often considered to be a very ideal attributes, it requires that the voters could not benefit from lying about their true preferences. And then, it can inhibit the strategy voting in social choice, urge voters to cast their votes for true preferences, and make the election results reflect the true wishes of people.Since the1970s, Gibbard-Satterthwaite strategy-proofness impossibility theorem has been established, people begin to research on how to avoid manipulation voting widely, namely the strategy-proofness voting problem. Mathematicians have begun to use mathematical language to prove impossibility theorem, computer scientists focuse on the algorithmic problems in social choice, and logicians focuse on the logical verification and analysis of social process(social software).So, research on strategy-proofness voting problem, which in itself is to study the logical cognitive mechanism of cross-cultural interaction. The theoretical results of this study will not only enrich contemporary theory of logic, but also are the specific application of logic in economics and politics, etc.This dissertation studies strategy-proofness voting theory from the perspective of logic. In general, this dissertation involves the following five aspects:First, from the perspective of logic, we attempted to give a systematic account of strategy-proof voting theory of four stages:sprout stage, semi-completion stage and completion stage and in-depth development stage, and discussed the methods to avoid strategy voting.Second, based on the set theory as a mathematical tool, we studied the theoretical basis of strategy-proof voting-Gibbard-Satterthwaite strategy-proofness voting impossibility theorem. And then, using Saari method and inductive method, we formally proved the Gibbard-Satterthwaite strategy-proofness impossibility theorem. Finally, we rethought the proof of the Gibbard-Satterthwaite strategy-proofness impossibility theorem. Third, based on voting logic(VL), we characterized Gibbard-Satterthwaite strategy-proofness impossibility theorem, and discussed the undecidability of VL and decidability special case.Fourth, we briefly introduced the concept of social choice function, strategy game,etc. Based on Coalition Logic of Propositional Control (CL-PC), we presented social choice function logic (SCFL) and characterized the related properties of strategy-proof voting. Finally, we solved the problem of determining whether a social choice function is strategy-proof.Fifth, we regarded the voting process as multi-agent strategy game, and put forward the multi-agent strategic logic (MASL). Based on MASL, we discussed the related properties of strategy-proof voting. Then, we extended the language to epistemic multi-agent strategic logic (EMASL), and characterized the knowing dictatorship, the knowing strategy-proof.Study of strategy-proof voting theory started relatively earlier in abroad, involves extensive field and has had fruitful results. At present, logical research on strategy-proof voting is relatively little in China. This paper reviewed contemporary logical studies on strategy-proof voting. And research on these problems was bound to develop and expand the existing logical theory. Therefore, the results will promote the development of logic theory in China, and make related research stand in the forefront of the field from an international perspective.