Conceptualizing and measuring district magnitude for comparative research: How to do it and why it matters

Abstract District magnitude, the number of seats per district, is a critical component of electoral systems. It affects key outcomes such as accountability, legislative fragmentation, and disproportionality in representation by providing incentives for voters, candidates, and representatives. Some democracies have identical-magnitude districts (whether under majoritarian or districted proportional representation), yet many elect their representatives through districts of varying magnitudes. Thus, in cross-country analyses, researchers first come up with a summary score of district magnitudes per country. This is often considered merely a mechanical, pre-analysis step of preparing the data. We show that the national score of district magnitude is a thorny business, consequential for inference on substantive questions. Specifically, different conceptualizations and measurements of district magnitude lead to different scores, and those, in turn, may both mischaracterize countries and lead to different inferences. Moreover, the status quo in the measurement of district magnitude – equally weighing all districts – is often misleading, and the problem is compounded by within-country variation in magnitude and malapportionment, common in Europe and Latin America, respectively. We propose two alternative measures of district magnitude – weighing districts by the share of representatives or voters in them – and provide guidance on the circumstances under which each measure should be utilized. Our analysis has implications for how this key component of electoral systems should be conceptualized, measured, and employed in cross-country analyses.