Coalition formation theories revisited: an empirical investigation of Aumann's hypothesis

Robert J Aumann, the 2005 Nobel laureate in Economics, hypothesized in 1995 that, in forming a majority coalition government in real life, the party charged with forming the coalition will choose to form the coalition that maximizes its Shapley-Shubik index. We subjected this hypothesis to empirical testing in nine countries. It was found that for the data sets investigated, this hypothesis produces the smallest number of correct predictions. Three variations of this hypothesis appear to perform somewhat better: restricting the maximization process to the set of closed majority coalitions, or likewise but with a further requirement that the coalition selected be of minimal size or of minimal range. However, none of these variations achieves a level of predictive performance comparable to the Leiserson-Axelrod closed minimal range theory or to the Gamson-Riker minimum size principle. We therefore conclude that Aumann’s hypothesis should be rejected, and that considerations of maximizing a priori voting power do not seem to account for the actual behavior of political parties in forming governmental coalitions.