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Duverger's law postulates that single-member plurality electoral systems lead to two-party systems. Existing scholarship regards India as an exception to this law at national level, but not at district level. This study tests the latter hypothesis through analysis of a comprehensive dataset covering Indian parliamentary elections in the period 1952—2004. The results show that a large number of Indian districts do not conform to the Duvergerian norm of two-party competition, and that there is no consistent movement towards the Duvergerian equilibrium. Furthermore, inter-region and inter-state variations in the size of district-level party systems make it difficult to generalize about the application of Duverger's law to the Indian case. The study concludes that a narrow focus on electoral rules is inadequate, and that a more comprehensive set of explanatory variables is needed to explain the size of the Indian party system even at the district level.

The study of general election outcomes can be helped by finding better approaches for visualizing large quantities of information and asking questions about its patterning. We review the Nagayama or 'all possibilities' triangle display, and show that it can only legitimately be used to show an overall 'field' of results that is logically feasible, called the effective space of competition, which varies with the number of observable parties. We apply this reductionist view to analysing outcomes in three leading plurality rule systems (the USA, India and Great Britain), focusing on evidence of the Duvergerian psychological effect acting on voters during campaign periods. The Effective Competition Space view illuminates some key differences across countries, and variations with rising numbers of parties competing. We next consider a more holistic approach, the 'crown' diagram, which links electoral district outcomes more closely to the most important politico-ideological dimension in each country. Both views suggest some tentative evolutionary hypotheses for the variegated development of plurality rule systems over time. Britain is a highly nationalized party system, but one that has moved substantially away from Duvergerian predictions of two-party focusing, and towards multiParty Politics. The USA seems to be a case of 'stunted development'. India shows a partial Duvergerian conformity, yet combined with a substantial vertical scatter of non-Duvergerian results. Applications to over-time and regional analysis within countries are also sketched. [Reprinted by permission of Sage Publications Ltd., copyright holder.]

The study of general election outcomes can be helped by finding better approaches for visualizing large quantities of information and asking questions about its patterning. We review the Nagayama or 'all possibilities' triangle display, and show that it can only legitimately be used to show an overall 'field' of results that is logically feasible, called the effective space of competition, which varies with the number of observable parties. We apply this reductionist view to analysing outcomes in three leading plurality rule systems (the USA, India and Great Britain), focusing on evidence of the Duvergerian psychological effect acting on voters during campaign periods. The Effective Competition Space view illuminates some key differences across countries, and variations with rising numbers of parties competing. We next consider a more holistic approach, the 'crown' diagram, which links electoral district outcomes more closely to the most important politico-ideological dimension in each country. Both views suggest some tentative evolutionary hypotheses for the variegated development of plurality rule systems over time. Britain is a highly nationalized party system, but one that has moved substantially away from Duvergerian predictions of two-party focusing, and towards multiparty politics. The USA seems to be a case of 'stunted development'. India shows a partial Duvergerian conformity, yet combined with a substantial vertical scatter of non-Duvergerian results. Applications to over-time and regional analysis within countries are also sketched.

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.