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

Abstract

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. Valence Theorem proves that when valence differences across parties are large, there is nonconvergence 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.

Centripetal and centrifugal incentives in mixed-member proportional systems

“…In fact, except for the CDU and the Greens, all parties maximize both candidate and party-list votes at nearly identical positions. Since PR is the dominant segment of the German electoral system, this finding is consistent with empirical findings on policy dispersion in pure PR systems (Gallego and Schofield, 2016). The party with the largest valence advantage, however, maximizes votes or candidate seats in the plurality tier by locating near the mean voter.…”

“…Using data from the 2009 and 2013 German elections, we find centrifugal incentives for all parties in the PR tier and for all but the highest valence party in the FPTP tier. Considering the dominance of the PR tier of the German electoral system, these findings are consistent with Gallego and Schofield’s (2016) conjecture about the effect of plurality versus PR elections. Except for two parties, all parties face nearly identical incentives in both tiers, and can maximize both district seats and party-list votes with the very same policy offer.…”

“…Schofield and Sened, 2005; Schofield and Zakharov, 2010; Schofield et al, 2011). The prevalence of centrifugal incentives in multiparty competition is also supported by a comprehensive empirical analysis by Gallego and Schofield (2016), which provides evidence for centrifugal tendencies in PR systems, whereas in majoritarian systems centripetal tendencies are reportedly strong and parties locate near the mean.…”

Introduction to the Journal of Theoretical Politics special issue in honor of Norman Schofield

“…They show that rather than being an “impossible game” stemming from the absence of political equilibria, the obstacle for political stability of this era was the plethora of equilibria predicted by Schofield’s framework. The second article in this vein, Gallego and Schofield (2016), is by Schofield himself, along with his longtime collaborator Maria Gallego. They apply Schofield’s stochastic model of politics to a variety of countries and political regimes, calculating a “convergence coefficient” for each regime that characterizes the centripetal or centrifugal tendency acting on parties within the system.…”