How proportional are electoral systems? A universal measure of electoral rules

Abstract

The proportionality principle of electoral systems plays an important role in multiple literatures, including comparative politics, political economy, and conflict studies. The single most important electoral system feature used to determine whether an electoral system might provide for proportional outcomes is district magnitude, i.e., the number of representatives that are elected from a given district. However, once we move beyond “simple” systems, measuring the institutional side of the equation becomes more complex. The legislative electoral systems of three out of five (61%) contemporary democracies rely on multiple institutional rules that affect the proportionality of their seat allocation, for example by combining different district magnitudes in multiple tiers, or delimiting the number of parties that can win seats through legal thresholds. There is no widely accepted measure of district magnitude for such cases. Relying on four simple axioms, this article extends the concept of district magnitude to all these complex electoral systems. We introduce the effective district magnitude, a new index that measures the proportionality of electoral systems based solely on institutional rules. It is applicable for all rules used in national parliamentary elections in democracies worldwide. This new, theory-based index improves the explanatory power of two crucial variables usually associated with district magnitude: vote-seat disproportionality and party system fragmentation.