Electing the Pope

Few elections attract so much attention as the Papal Conclave that elects the religious leader of over a billion Catholics worldwide. The Conclave is an interesting case of qualified majority voting with many participants and no formal voting blocks. Each cardinal is a well-known public gure with publicly available personal data and well-known positions on public matters. This provides excellent grounds for a study of spatial voting: In this brief note we study voting in the Papal Conclave after the resignation of Benedict XVI. We describe the method of the election and based on a simple estimation of certain factors that seem to influence the electors' preferences we calculate the power of each cardinal in the conclave as the Shapley-Shubik index of the corresponding voting game over a convex geometry.