A Study On Social Choice Based On Voting

One of the essential problems of social choice is to find a method to realize collective value. Apparently, the most ordinary social choice method is voting. Whereas, it brings more and more dispute about whether the voting result could according with most individual values.Both voting paradox and Arrow's impossibility theorem, explain that voting can't reflect collective preference. This paper analyzes the reason causing voting paradox, introduces Arrow's impossibility theorem and some methods to overcome this theorem. This paper also explains voting can't realize comparison about interpersonal utilities, and might lead to false social choice at some extremely bad cases.This paper proposes to evaluate voting through average-case analysis in a statistical sense, not worst-case analysis. Concretely, we devise a standard to control the validity of voting, and analyze the correctness of voting result through statistical method and simulation. We illuminate the singularity of Arrow's theorem, i.e. when electorate is a large sample, the incorrect probability turns to be sufficient small. Therefore voting is an advisable method of social choice, considering practicability and convenience.Then this paper investigates how parameters effect on the validity and correctness of voting, there are qualitative and quantitative meanings to realistic voting.