First-order logic formalisation of Arrow’s Theorem

Arrow’s Theorem is a central result in social choice theory. It states that, under certain natural conditions, it is impossible to aggregate the preferences of a finite set of individuals into a social preference ordering. We formalise this result in the language of first-order logic, thereby reducing Arrow’s Theorem to a statement saying that a given set of first-order formulas does not possess a finite model. In the long run, we hope that this formalisation can serve as the basis for a fully automated proof of Arrow’s Theorem and similar results in social choice theory. We prove that this is possible in principle, at least for a fixed number of individuals, and we report on initial experiments with automated reasoning tools.