Smoothed Analysis of Social Choice Revisited

Bailey Flanigan, Daniel Halpern, Alexandros Psomas

Abstract: A canonical problem in social choice is how to aggregate ranked votes: that is, given n voters’ rankings over m candidates, what voting rule f should we use to aggregate these votes and select a single winner? One standard method for comparing voting rules is by their satisfaction of axioms — properties that we want a “reasonable” rule to satisfy. Unfortunately, this approach leads to several impossibilities: no voting rule can simultaneously satisfy all the properties we would want, at least in the worst case over all possible inputs.