Permissibility of electoral systems: A new look at an old question

Permissibility of electoral systems, and in particular the conversion of voices in the electorate to the legislature, is broadly considered to depend on the number of seats per district (district magnitude) in a country. Yet the most prevalent electoral system in the democratic world, proportional representation with districts, is often characterized by an almost entirely overlooked variation: Within the same country districts vary in their magnitude, sometimes by a factor of 20. How does such variation affect permissibility of electoral systems? Drawing on a broad cross-section of democracies, we demonstrate that contrary to what the literature implicitly assumes, other things equal, a combination of large and small districts results in greater permissibility than a set of districts of similar magnitude. We find that where districts are of similar (different) magnitude the degree of permissibility is lower (higher) than that found by current literature.