enp: Effective Number of Parties

In philswatton/polimetrics: Miscellaneous functions useful for political science

Effective Number of Parties

Description

enp implements several measures assessing the effective number of parties or similar concepts. Defaults to Laakso and Taagepera's (1979) Effective Number of Parties. See details for more information.

Usage

enp(p, type = 3, S = NULL, range = F)

Arguments

p	Numeric vector of party vote or seat shares. If type is 5 or 6, numeric vector of seat counts, see details.
type	Single integer denoting which measure to use. See details.
S	Single integer denoting the size of the legislature. Must be used for type 5 and 6, ignored otherwise. See details.
range	Function returns minimum and maximum values along best estimate for type 5 and 6, ignored otherwise. See details.

Details

Supplying the integer corresponding to a particular measure to the type argument will mean that the function uses that measure. Defaults to Laakso and Taagepera's (1979) Effective Number of Parties (type = 3).

Type 1

Rae's (1968) fractionalization index. Ranges from 0 to 1. See Wildgen (1971) for critique. Calculated as:

1-sum(p^2)

Type 2

Hyperfractionalization index first used in Kesselman (1966), further elucidated in Wildgen (1971). Calculated as:

antilog(-sum(p*log(p)))

Type 3

Laakso and Taagepera's (1979) Effective Number of Parties. Calculated as

1/sum(p^2)

Type 4

Molinar's (1991) NP index. Calculated as:

1 + N*((sum(p^2)-p1^2)/sum(p^2))

Where N is Laakso and Taagepera's (1979) Effective Number of Parties.

Type 5

Taagepera's (1997) Effective Number of Parties for incomplete data. Here, p should be a vector of seat counts instead of a vector of proportions. It should contain only the seat counts for known parties (i.e. not decomposed into other).

S must be specified and is the total number of seats.

This is based on Laakso and Taagepera's (1979) Effective Number of Parties, using counts instead of proportions or percentages. This is given by:

S^2/sum(p^2)

where S is the total number of seats. Taagepera shows that the plausible range of the effective number of parties is:

S^2/sum(R^2 + p^2) < N < S^2/sum(R + p^2)

where R is the number of seats allocated to 'other' parties and N is the effective number of parties. The best estimate is the mean of the two extremes, and this is the estimate returned by 5. If range = T, these are also returned.

Type 6

Extension of type = 5. Calculations assume that no component of R is larger than the smallest element of p, pL. The plausible range used for calculating the best estimate becomes:

S^2/sum(R*pL + p^2) < N < S^2/sum(R + p^2)

As before, if range = T, the minimum and maximum are also returned.

Type 7

Taagepera's (1999) alternative NP index.

1 + N - (N/(1/p1))^2

where N is Laakso and Taagepera's (1979) Effective Number of Parties.

Type 8

Golosov's alternative (2010) measure. Calculated as

sum(p/(p + p1^2 - p^2))

Value

Numeric vector of length 1

References

\insertRef

kesselman1966psmisc

\insertRef

rae1968psmisc

\insertRef

wildgen1971psmisc

\insertRef

laakso1979psmisc

\insertRef

molinar1991psmisc

\insertRef

taagepera1997psmisc

\insertRef

taagepera1999psmisc

\insertRef

golosov2010psmisc

philswatton/polimetrics documentation built on Jan. 30, 2023, 3:21 p.m.