Voting Operators in the Space of Choice Functions

Assuming the individual and collective opinions are given as choice functions, a new formalization of the voting problem is considered. The notions of a local functional operator and the closedness of domains in choice-functional space relative to local operators are introduced. The problem of voting is reduced to an analysis of three kinds of operator classes and their mutual relations. The functional analogues well known in the theory of Arrow's paradox results are established.