The Proportionality of Electoral Systems: Electoral Welfare and Electoral Inequality

This paper argues that measuring the degree of proportionality in an electoral system is equivalent to measuring the degree of electoral inequality, defined in terms of inter-party differences in the seats-to-votes ratio. It proposes an index of the degree of electoral inequality which is based on Atkinson's (1970) index, applied originally to measuring income inequality. This index satisfies all the criteria proposed in the literature for evaluating measures of electoral proportionality. In addition, such an Atkinson-type index of electoral inequality can also be given a welfarist interpretation by directly relating its value to the level of electoral welfare. Under such an interpretation, the disproportionality in an electoral system may be interpreted as being the result of the system imputing voting shares to the different political parties which are different from their actual voting shares. The larger this difference, the greater the degree of disproportionality in the system. The use of this index is illustrated by an application to the outcomes of Irish General Elections from 1923 till 1997.