Weak pairwise justifiability as a common root of Arrow’s and the Gibbard–Satterthwaite theorems

Abstract

We introduce a novel principle that we call weak pairwise justifiability, which applies to a large class of collective choice rules, including the social choice functions and the social welfare functions about which the Gibbard–Satterthwaite theorem and Arrow’s impossibility theorem are predicated, respectively. We prove that, under appropriate qualifications, our principle is a common root for these two classical results, when applied to rules defined over the full domain of weak preference orders (also for strict).