Rein Taagepera, "Implications of the Effective Number of Parties for Cabinet Formation," Party Politics, 8 (March, 2002), 227-236.

First Paragraph:
How does the number of parties in a representative assembly affect the type of cabinets formed? The question is important because cabinet durations and working styles tend to differ depending on whether one has, say, a multiparty minority cabinet or a one-party majority cabinet -- and the latter looks more likely when the assembly includes few parties. The issue can be investigated on various levels, depending on the speci-ficity of information taken into account. When the seat shares of all parties are known, a game theoretical analysis for this particular constellation is possible, the more so when the parties' ideological stands are also available. But taking into account only a single major indicator, the effective number of parties,1 can yield important generalizations across many countries. This is the approach taken here, to explain how cabinet level concentration of power is constrained by party level concentration of seats.

Figures and Tables:
Table 1. Average frequencies (%) of five cabinet types at various effective numbers of parties
Figure 1. Cumulative percent frequencies of cabinet types versus effective number of legislative parties.
Figure 2. Minimum number of partners (p) needed to form a minimal-winning coalition, depending on the effective number (N) of legislative parties: theoretical limits and averages of actual elections (from Table 2)
Table 2. Minimum number of partners (p) needed to form a minimal-winning coalition, depending on the effective number (N) of legislative parties in actual elections

Last Paragraph:
Lijphart's (1999: 110) measure of 'MW cabinets and one-party cabinets' (MW/OP) may look confusing and artificial but can be reworded -- and one is hard put to find a more suitable single index to express the distribution of cabinet types. Its strong correlation with the effective number of legislative parties is not an empirical happenstance, but is logically imposed to an appreciable degree. In this sense, the effective number of parties is the independent variable driving MW/OP. In turn, going in the opposite direction, MW/OP supplies a way to visualize the meaning of the effective number for constellations where the image of equivalence to some number of equal-sized parties becomes stretched. This conceptually reinforced logical tie between the two core indices to measure the degree of majoritarianism/ consensualism of a country adds credibility to both of them.