Selecting indexes of electoral proportionality: General properties and relationships

Measuring the proportionality of outcomes in terms of each party's vote and seat shares is an important task in electoral analysis. Various indexes have been designed that provide a summary statistic of electoral proportionality/disproportionality. Claims and counter-claims have been made regarding the strengths and weaknesses of particular indexes. Important consequences follow from this methodological pluralism. First, it is not always clear which index has been employed when particular electoral outcomes are discussed. Second, recent additions to the list of indexes have not been thoroughly scrutinised and appraised. Third, the lack of knowledge about the general relationship between indexes means that observations might be different had a different index been used. This article seeks to identify and clarify the particular properties of different indexes of proportionality. Relatively new, and largely untested, indexes of proportionality are examined and some unusual and potentially damaging properties are identified. We also compare different measures of disproportionality in an effort to specify some general properties of the inter-relationships between them. Understanding the particular patterns of electoral competition and vote distributions that affect the relationship between these measures should enable users to anticipate the consequences of preferring one index over others.