First paragraph:
The 'effective' number of parties is a very simple general
concept that entails a complex methodological problem.
Conceptually, the effective number of parties is simply the
number of 'viable' or 'important' or (to put it most
radically) 'real' political parties in a party system that
includes parties of unequal size. In comparative political
party research, we need to distinguish between a four-party
constellation with party vote-shares (0.52, 0.45, 0.02,
0.01), which is 'effectively' a two-party system, and a
four-party constellation with party vote-shares (0.40, 0.25,
0.20, 0.15), which is 'effectively' a case of multipartism.
There should be a way to discount very small parties. The
methodological problem is that there are none readily
available. Of course, it is possible to set an arbitrary
threshold of exclusion, discounting all parties that fail to
reach 1 or 3 or 5 percent of the vote.1 Yet it is clear that
a 5 percent party might be unimportant if other parties
enjoy massive support, and it might be quite important if
other parties are comparably weak; for instance, if the
largest party's vote-share is 15 percent. Then we need to
quantify the idea of the 'effective' number of parties in a
systematic way that allows for taking into account the
relative sizes of parties, which is impossible without using
a measure expressed as a mathematical formula.

Figures and
Tables:

Table 1. Values of NLT, NB and NP for eight
hypothetical vote or seat constellations

Table 2. Aggregate values of three effective number
of parties indices for 38 seat distributions in
sub-Saharan Africa and 42 vote distributions in East
Central Europe/former Soviet Union

Figure 1. Distribution of 80 party constellations
across the spaces of the Laakso-Taagepera (NLT) and new
(NP) effective number of parties indices

Appendix 1. Cases and the Data for the Empirical
Test

Last Paragraph:
While stating that there was no perfect measure of the
effective number of parties became commonplace in scholarly
papers dealing with the matter, and while the validity of
such claims cannot be denied on philosophical grounds, a
possible extension of this philosophy is that there is
always room for improvement. If the effective number of
parties, as defined by Laakso and Taagepera, tends to
produce unrealistically high scores for very concentrated
party systems, thus failing on intuitive content, why not
develop a measure that is devoid of such a shortcoming? And,
even though a partial solution to this problem is already
available, in the form of the Dunleavy-Boucek index, why not
eliminate the problem completely? This is what I have
attempted to do in this study. The new index, defined as ,
solves several problems faced by those who need to count the
effective number of parties. First, it satisfies all basic
requirements of indices of this kind. Second, it produces
reasonably small scores for party constellations that appear
to have few important parties. Third, it registers many
parties in those constellations where there seems to be many
parties. Fourth, it minimizes undesirable side effects such
as the 'kink' effect. This combination of properties makes
the proposed index superior to the earlier ways of counting
the effective number of parties.