Permissibility of Electoral Systems: A New Look at an Old Question Orit Kedar, The Hebrew University of Jerusalem Liran Harsgor, University of Haifa Or Tuttnauer, Universität Mannheim, MZES 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. G iven the voice of the electorate, the electoral system— the mechanism aggregating votes and converting them into seats in the legislature—determines the lay of the land in parliament. The permissibility of the electoral system, and in particular how voices in the electorate are translated to parliament, is a key aspect of representation and the focus of this study. We analyze this translation in countries that em- ploy districted systems, focusing on districted proportional rep- resentation, the most prevalent electoral system in the demo- cratic world. It is well established that district magnitude—the number of seats per district—is a key factor determining represen- tation in general and the permissibility of electoral systems in particular. Parliaments elected by proportional represen- tation with districts, however, often (indeed almost always) have a varying number of seats across districts. Within the same state, some voters cast their ballots in districts of a few representatives while others in districts of a few dozens. The gap between small and large districts can be zero (e.g., Macedonia), as small as one to three seats (e.g., Iceland), or as large as 30, 40, or 50 seats (e.g., Sweden, Spain, or Brazil). The voluminous literature on electoral systems notwith- standing, the effect of variation in district magnitude on per- missibility—the conversion of votes to seats—has been un- explored, and the variation in itself has been almost entirely ignored. 1 The question motivating this study is: how does within- country variation in district magnitude affect permissibility of electoral systems? We theorize and empirically analyze the effect of variation in magnitude on permissibility and find that in tension with the implicit assumption made by pre- vious studies that it is irrelevant for representation, greater variation in district magnitude does lead to greater permissibil- ity. The mechanism is straightforward. The range of districts in a country with substantial variation is often characterized by a long right tail: many districts have few representatives while few have many representatives. Large districts are, by definition, not only more proportionate but also consist of a Orit Kedar (orit.kedar@mail.huji.ac.il) is an associate professor at the Hebrew University of Jerusalem, Jerusalem 9190501, Israel. Liran Harsgor (lharsgor @poli.haifa.ac.il) is an assistant professor at the University of Haifa, Haifa 3498838, Israel. Or Tuttnauer (or.tuttnauer@mzes.uni-mannheim.de) is an Alexander von Humboldt postdoctoral fellow at the Mannheim Centre for European Social Research (MZES), Mannheim 68131, Germany. Data and supporting materials necessary to reproduce the numerical results in the article are available in the JOP Dataverse (https://dataverse.harvard.edu /dataverse/jop). An online appendix with supplementary material is available at https://doi.org/10.1086/709835. Orit Kedar acknowledges financial support by the European Research Council (Starting grant 263630) and the Israel Science Foundation (grant no. 1766/15). 1. Among cross-national studies, we are aware of two that examine the fact that different districts are of different magnitudes: Monroe and Rose (2002) and Kedar et al (2016). We discuss these studies below. Neither, however, addresses permissibility as a dependent variable, nor do they examine the same aspects of variation on the right-hand side as those at play in the case of permissibility. The Journal of Politics, volume 83, number 2. Published online February 24, 2021. https://doi.org/10.1086/709835 q 2021 by the Southern Political Science Association. All rights reserved. 0022-3816/2021/8302-0002$10.00 439