The Sainte-Laguë index of disproportionality and Dalton’s principle of transfers

Abstract

The Sainte-Laguë index (SLI) has a strong claim to be the index that should be adopted as the standard measure of disproportionality in electoral studies. Its properties are therefore worthwhile understanding more clearly. This article provides a counterexample (the 2010 UK general election) to previous claims that the SLI satisfies Dalton’s principle of transfers with respect to differences between seat shares and vote shares but not ratios of seat and vote shares. Instead, we prove that the SLI satisfies the ratio but not the difference version of the principle. This strengthens the argument for the SLI since the ratio version is the one that accords with notion of electoral disproportionality as inequality in the representation of voters.