Do parties converge to the electoral mean in all political systems?

Many formal models suggest that parties or candidates should locate at the electoral mean . Yet, there is no consistent evidence of such convergence across political systems. Schofield’s (2007) Valence Theorem proves that when valence differences across parties are large, there is non-convergence to the mean. Convergence to the mean depends on the value of the convergence coefficient, c . When c is high there is significant centrifugal tendency acting on the parties and when c is low there is a significant centripetal tendency acting on the parties. In this paper we apply the stochastic valence model of elections in various countries under different political regimes and use the convergence coefficient of these elections to classify political systems. Our results show that the convergence coefficient varies across elections in a country, across countries using the same political system and across political regimes. For countries using proportional representation, namely Israel, Turkey and Poland, the centrifugal tendency is very high and parties move away from the mean. In the majoritarian polities of the United States and the UK, parties are located at the mean, as the centrifugal tendency is very low. In anocracies, the autocrat imposes limitations on how far from the origin the opposition parties can move but the equilibrium is fragile.