Fixed agenda social choice theory: Correspondence and impossibility theorems for social choice correspondences and social decision functions (Q2366837)

Let \(X\) be a finite set of alternatives, and \(N\) a finite set of voters, each of whom is represented by a weak ordering of \(X\). The feasible set \(X\) is fixed throughout, but voter profiles are allowed to vary. Once conditions analogous to Arrow's are defined for this setup, a result analogous to Arrow's Impossibility Theorem follows. A theorem like Gibbard's on oligarchy is also proved.