Polyhedral computations in social choice

Polyhedral methods have been used for many years in social choice where they can be applied to compute the probabilities (and even exact numbers) of election results that yield unexpected phenomena, for example the famous Condorcet paradox. So far such computations have almost exclusively been restricted to elections with three candidates. Now our software Normaliz can compute many such probabilities also for four candidates. We will explain the method, discuss some examples and sketch the algorithmic approach.