Is Duverger's Law based on a mistake?

In the Duverger’s Law (DL) literature, any effects detected in holding down the number of parties in plurality rule or majoritarian systems are conventionally ascribed tout court to the electoral system, and vice versa for proportional systems allegedly encouraging more parties. By contrast, we argue that a DL effect can only be identified when tested against a much more sophisticated null hypothesis that starts by recognizing fundamental variations in the effective competition space, driven by the number of observable parties (or candidates, or coalitions) that enter competition at some low but significant level of support, say, receiving 1 per cent of the vote each. The appropriate null hypothesis has three parts, each of which must be refuted in order for a DL effect to be established: 1. The patterns of election district outcomes observed do not differ from those that would be expected under equiprobability, given the number of observable parties (Nop) competing and the effective competition space (ECS) that this creates. 2. The deviations from equiprobability found do not show two-party drift as DL predicts (but either no pattern, or unipolar drift, or multi-party drift). 3. Measured as deviations from equiprobability, the extent of two-party drift is no greater in plurality/majority systems than in proportional systems, (for example, because two-party drift occurs quite evenly in all systems, or because there are individual electoral system variations in two party drift). We operationalize the first two parts of the test for some recent plurality rule elections in India, Great Britain and the USA, by mapping empirical district outcomes onto the logically feasible competition space for districts with different numbers of observable parties. We develop new criteria for assessing Duvergerian versus equi-probability patterning of district outcomes including: the proportions of all districts in an election spread across different Nop levels; the minimum level of combined support for V3 to VN parties; the degree of patterning of the outcome distribution by a two-party relationship, versus the degree of random scatter of results; the divergence of outcomes in two-party contests from a bi-nomial distribution; the divergence of outcomes in a three-party contest from a multi-nomial distribution; and finally in four or more party contests the clustering of outcomes in relation to the peak densities of ‘non-equivalent distributions’ across the V1V2 ‘floorplate’ plot. Our analysis is necessarily preliminary, because the third part of the null hypothesis above inherently requires a cumulative research effort beyond the bounds of any single paper. But the tools and measures we set out here make this next stage of research one that is eminently feasible to achieve