The proportionality principle of electoral systems plays an important role in multiple literatures, including comparative politics, political economy, and conflict studies. It is a key variable characterising the domestic political institutions. The single most important electoral system feature used to measure the proportionality of an electoral system has been district magnitude, i.e., the number of representatives that are elected from the district.
Once we move beyond ‘simple’ systems, the concept of district magnitude becomes problematic. First, a growing number of electoral systems includes legal thresholds, requiring parties to gain some minimum vote share before they will be entitled to win any seats. Second, a few countries have moved to mixed electoral systems, and allocate parliamentary seats according to different rules in different tiers. One or more of such complexities are found in the clear majority (66%) of the world’s democratic electoral systems, and there is no widely accepted measure of district magnitude for such cases. Relying on three simple rules, this article extends the concept of district magnitude to all these ‘complex’ electoral systems. This results in a theoretically based new measure to assess the proportionality principle of the electoral systems, the “effective district magnitude”. We report the values for 417 elections in 69 democracies. We demonstrate that the effective district magnitude allows us to improve predictions of both electoral system proportionality and party system fragmentation.
