Patrick Dunleavy and Françoise Boucek, "Constructing the Number of Parties," Party Politics, 9 (May 2003), 291-315.

First Paragraph:
'Normal science' processes work by the accretion of knowledge in cumulative, coral-reef fashion, allowing a scientific consensus to emerge which can sustain further work at the frontiers of knowledge, without constant foundational critiques disturbing the core concepts and theories of the discipline. In the study of political parties, the effective number of parties index has gradually reached a high level of acceptance since its first exposition by Laakso and Taagepera (1979). The index is a measure of the level of concentration in political life which assigns more influence to large parties and screens out very small parties in its computation: 'The assumption in the comparative politics literature has long been that some kind of weighting is necessary' (Lijphart, 1994: 67). Influential authors such as Lijphart (1984) advocated the general adoption of the measure, and 10 years later he described it as 'the purest measure of the number of parties' (Lijphart, 1994:70). He also claimed (p. 68) that: 'In modern comparative politics a high degree of consensus has been reached on how exactly the number of parties should be measured.' Lijphart's confidence in the measure has continued to grow: 'The problem of how to count parties of different sizes is solved by using the effective number measure (Lijphart, 1999: 69).

However, we show here that the effective number of parties is a somewhat flawed index, whose use in quantitative analysis can create problems. [first sentence of 2nd paragraph]

Figures and Tables:
Figure 1: The minimum and maximum limits of the space for the 'effective number of parties' families of indices
Figure 2: How the shape of the space for the effective number of parties varies with the number of relevant parties
Figure 3: How the post-war election results for seven liberal democracies are distributed across the space of the effective number of parties index
Figure 4: The behaviour of effective number of parties indices around the 50 percent anchor point, under minimum fragmentation conditions
Figure 5: How the shape of the modified effective number of parties index (Nb) varies with the number of relevant parties
Figure A1: How the shape of the space for the Molinar index varies with the number of relevant parties
Figure A2: Comparing areas for the effective number of parties index (N2) and the Molinar index with seven relevant parties

Last Paragraph:
As the movement continues away from older typologies of party systems and towards a more empirically sensitive description of party systems, correctly constructing the number of parties remains a very important issue (Ware, 1995). Dimensionalizing party systems with multiple indicators remains a promising agenda for research, but we should proceed more sceptically than in the past. There is no perfect number of parties index, but we have set out reasons why Nb scores are preferable to raw N2 numbers in our view, and why spatialized Nb or N2 scores are better still. Finally, we have used a basic method here of looking at the spaces within which index scores are feasible, defined by minimum and maximum party fragmentation conditions at varying levels of V1 and under different numbers of relevant parties. We believe that this approach offers a valuable way of comprehensively evaluating the properties of any new party concentration measures (and indeed other indices) which may be proposed in future. It is vital that the behaviour of indices under the full range of possible conditions is systematically mapped from the outset, instead of years after they were first proposed.