Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities

The relationship between electoral systems can be examined on a number of dimensions. Seat allocation methods are conveniently divided into two groups: those based on largest remainders and those based on highest averages. The single transferable vote has its own distinct characteristics. Focusing on certain elements – the quota, thresholds, paradoxes and the conditions under which a majority of seats can be won – enables comparisons to be drawn between seat allocation methods. Certain seat allocation methods conventionally seen as variants of proportional representation (PR) cannot be regarded as such. PR methods can be rank ordered according to whether, when complete proportionality is not attainable, they display electoral bias towards larger or smaller parties. However, a definitive ordering is elusive, since some methods that are generally more favourable to larger parties can in some circumstances set lower thresholds of representation than methods generally favourable to smaller parties.