Party size baselines imposed by institutional constraints: Theory for simple electoral systems

This theory specifies the party sizes expected on the basis of constraints imposed by simple electoral rules. Duverger's law and hypothesis states that under the single-member plurality rule third parties tend to be eliminated, while proportional representation in multi-seat districts enables more than two parties to thrive. Expanding on Duverger' statements, the seat and vote shares of parties at all size ranks are calculated here, using nothing but two institutional inputs (district magnitude and assembly size) plus the number of voters. These are the baseline values expected if (and only if) institutional constraints were the only factor, with other factors balancing themselves out. The theory is complete in the sense of leading to complete party size structure. Among the relatively simple electoral systems the institutional baselines do reflect the long-term averages in New Zealand, while the residuals indicate the imbalance of inputs by other factors in the case of The Netherlands and Finland, and especially in the case of the UK