Arrow's Impossibility Theorem: Two Simple Single-Profile Versions
Source: Brown University
In this paper the authors provide two simple new versions of Arrow's impossibility theorem, in a model with only one preference profile. Both versions are transparent, requiring minimal mathematical sophistication. The first version assumes there are only two people in society, whose preferences are being aggregated; the second version assumes two or more people. Both theorems rely on assumptions about diversity of preferences, and the authors explore alternative notions of diversity at some length. The first theorem also uses a neutrality assumption, commonly used in the literature; the second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used.