Balancing disproportionality and parliament fragmentation: A simulation study of the mechanical effects of district magnitude on electoral outcomes

I employ computer-aided simulations to reexamine the effect of district magnitude on disproportionality and parliament fragmentation, in proportional representation (PR) elections. In the simulations, I attempt to isolate the purely 'mechanical' effects of electoral rules. The 'psychological' effects are represented by the theoretical probability distribution used to simulate PR election results, and also by the assumption as to the number of competing parties in constituencies. In particular, investigating the effect of DM on the disproportionality versus the parliament fragmentation trade-off, I critically reexamine the study of Carey and Hix (2011), who argue that the low-magnitude constituencies (four to eight seats) achieve a 'good' balance between representativeness (favored by low disproportionality) and government accountability (favored by the low-level of fragmentation in parliament). Even if we accept Carey and Hix's disputable operationalization of the representativeness-accountability trade-off, this study provides evidence that the claim that the low-magnitude electoral districts are optimal is contestable. Also, the simulation results suggest that Carey and Hix's analysis is confounded by the psychological effects; due to strategic voting, low-magnitude districts appear to promote greater proportionality than they actually do.