Finding strategyproof social choice functions via SAT solving

Abstract

A promising direction in computational social choice is to address open research problems using computer-aided proving techniques. In conjunction with SAT solving, this approach has been shown to be viable in the context of classic impossibility theorems such as Arrow's impossibility as well as axiomatizations of preference extensions. In this paper, we demonstrate that it can also be applied to the more complex notion of strategyproofness for irresolute social choice functions. These types of problems, however, require a more evolved encoding as otherwise the search space rapidly becomes much too large. We present an efficient encoding for translating such problems to SAT and leverage this encoding to prove new results about strategyproofness with respect to Kelly's and Fishburn's preference extensions. For example, we show that no Pareto-optimal majoritarian social choice function satisfies Fishburn-strategyproofness.