Electoral Systems and District Magnitude: beyond the Median

One of the most broadly accepted theories in electoral politics is the relationship between district magnitude and the number of parties: lower magnitude is assumed to reduce the number of parties. Since most countries have many district magnitudes, either the magnitude of the median district or the magnitude of the district electing the median legislator is used as an indicator. The median is chosen because it is not sensitive to the shape of the distribution. I call for an opposite practice. I show the importance of the shape of the distribution of magnitudes in each country and contend that characterizing an electoral system by its median district often leads to misleading conclusions. In some countries the distribution of district magnitudes is so skewed that the largest district is seven times greater than the median district (e.g. Portugal), while in others all district magnitudes are only slightly different from the median (e.g. Ireland). I reflect on different measures of central tendency and the information they each capture and miss and put forth several indicators of the distribution of magnitudes in a country. I illustrate these points using hypothetical and real-world examples of electoral systems.