Neither the T index nor the D2 score measure “two-partyness”: a comment on Gaines and Taagepera

This comment critiques the paper by Gaines and Taagepera (2013) outlining two new measures that compare how far election outcomes diverge from a particular ideal of “perfect two-partyness” (one in which all votes are divided equally between the top two parties). Their first proposed T index is an unstable amalgam of two different measures, one linear and the other not. Applied to analysing sets of election outcomes, it systematically mis-signals “two-partyness” in its accepted meaning, producing perverse results. Their second index, D2, has a varying minimum size level depending on the size of the largest party (P1) and the number of observable parties competing. In many circumstances D2 scores bifurcate – the same scores are produced by both very low and very high P1 levels. Applied to distributions, the D2 score artefactually homogenizes very dissimilar distributions, again misreads even two-party configurations, and always overstates “two-partyness” in multi-party systems. I conclude that neither the T nor D2 indices are fit for purpose. They should not be further used in electoral analysis.