Comment on Gallagher's ‘proportionality, disproportionality and electoral systems’

Abstract

Michael Gallagher, in a recent article published in this journal, argues against the notion that there is some single, obviously best standard of proportionality against which real-world PR methods can be judged. As he notes in his conclusion, all PR methods ‘set out to minimize disproportionality. They ditTer from each other not because some try harder than others, or because some are ‘fairer’ than others, but because they embody different ideas as to how disproportionality should be measured’ (p. 49). We certainly agree with this point; indeed, we have found it useful in structuring our own research agenda. But the conclusions we have drawn from it are somewhat different from those that Gallagher draws. Hence this note. Let us first recap the argument showing that there is no single notion of disproportionality against which real-world methods of PR can fairly be judged. The argument consists simply of pointing out two indisputable facts: first, that every method of PR currently in use minimizes some particular notion of disproportionality; second, that the notions of disproportionality inherent in the various PR methods differ. To illustrate the first point, one can do no better than recall the origin of the wellknown Sainte-Lagui? method of PR. Sainte-Laguti introduced his method in a French mathematical journal in 1910. If one reads his article (see Lijphart and Gibberd, 1977 for an English translation), one finds that Sainte-Lague proposes a mathematical index of disproportionality and that his method of PR is defined as the one that allocates seats in such a fashion as to minimize this index. In this regard, SainteLag& was not unusual. As he notes in his article, d’Hondt also had in mind a specific notion of disproportionality-which his method minimized. Even those PR methods whose inventors do not seem to have had the minimization of a measure of disproportionality explicitly in mind (for example, the largest remainders method invented by Alexander Hamilton) none the less all do minimize some such measure.