This article (sadly, Springer isn't making the full text available to Joe Public, this link is to an abstract only) brings together Arrow's Impossibility Theorem and Turing's notion of computability. In it, H. Reiju Mihara closes off one of the possible escape hatches from Arrow's Theorem on the impossibility of finding a voting system that is both fair and rational. The requirement that the voting system be computable, it turns out, nullifies certain attempts to wiggle out of the rationality requirement.
On the other hand, as cool as it is, this result only applies to societies with an infinite number of people in them, which does tend to limit the practical importance of the work.