Are Voters Equal under Proportional Representation?

The forthcoming article “Are Voters Equal under Proportional Representation?” by Orit Kedar, Liran Harsgor, and Raz A. Sheinerman is summarized by the authors here:

Are voters equally represented under proportional representation? We focus on countries employing proportional representation with districts – the most prevalent electoral system in the democratic world – and draw on an often overlooked fact: in most such countries some voters cast their ballots in districts of few representatives (usually in agricultural areas and small towns) and others (residing in cities) in large districts of many representatives. While in some countries the latter is larger than the former by up to twenty-fold in others the variation is quite small. This implies that in countries with substantial variation in district magnitude some votes are counted by quasi-majoritarian rules and others by proportional ones.

Given that in Western democracies cities tend to be liberal in comparison to rural areas and small towns that are often conservative, we show that the majoritarian boost in small districts is granted to conservative votes while large and proportional districts do not offer a comparable boost to liberal votes. This leads to a systematic ideological inequality in parliamentary representation within countries: the parliamentary pie is often biased in favor of conservative voters compared to their share the electorate.

In our journey to analyze inequality in parliamentary representation we borrow and adapt tools of analysis from the study of income inequality — Gini index and Lorenz curve. Our index of representational inequality (RI) allows us to compare the level of representational inequality across countries. We find that countries with districted PR tend to resemble majoritarian ones in their level of representational inequality more than commonly assumed. We also find that irrespective of the magnitude of the average (or median district) the greater the share of parliament elected via small districts, the larger the level of representational inequality in that country.

Our study challenges the ‘on average’ approach to the study of representation and puts forth new considerations at the doorstep of institutional designers.