UC Irvine

The effective number of parties, N = 1/Σp(i)2 (where p(i) is the fractional share of the ith party), usually suffices to describe adequately a constellation of parties of different strengths. Difficulties arise when disparity in party sizes is such that the largest share (p1) surpasses 0.50 (meaning absolute dominance), while N still indicates a multi-party constellation. In such cases N(∞) = 1/p1 is proposed as a supplementary indicator: a value less than 2 indicates absolute dominance. An 'NP' index proposed earlier is a combination of N and N(∞); its values are close of those of N(∞), but NP sometimes falls below 2 even when many parties are relevant for coalition formation. Appendix A offers an alternative approach based on indices of deviation from a norm, but it proves cumbersome.