SciencesPo (version 1.02.12)

ENPs: Computes the Effective Number of Parties

Description

The Effective Number of Parties ENP is a measure of fragmentation. The intutiton is to count parties while weighting them by their relative strength in the legislature.

Usage

ENPs(seats = NULL, total = NULL, method = c("Laakso/Taagepera", "LSq",
  "Golosov"))

Arguments

seats

a numeric value or a vector (may be proportion).

total

a numeric value for the total either of seats or votes

method

the method using for computing the ENP, the default is Laakso/Taagepera, see details below.

Value

• The Effective Number of Parties

encoding

UTF-8

Details

Very often, political analysts say things like two-party system and multi-party system to refer to a particular kind of political party systems. However, these terms alone does not tell exactly how fragmented--or concentrated a party system actually is. For instance, after the 2010 general election in Brazil, 22 parties obtained representation in the country's Lower Chamber. Nonetheless, nine parties returned only 28 MPs together. Thus, an algorithm to (weigh) or to calculate the Effective Number of Parties in such circumstances helps to go beyond the simple number of parties in a legislative branch.

A widely accepted algorithm was proposed by M. Laakso and R. Taagepera: $$N = \frac{1}{\sum p_i^2}$$, where N denotes the effective number of parties and p_i denotes the $it^h$ party's fraction of the seats.

The same process can be used to compute the vote share for each party. This formula is the reciprocal of a well-known concentration index (the Herfindahl-Hirschman index) used in economics to study the degree to which ownership of firms in an industry is concentrated. Laakso and Taagepera correctly saw that the effective number of parties is simply an instance of the inverse measurement problem to that one. This index makes rough but fairly reliable international comparisons of party systems possible.

Another measure is the Least squares index (LSq), which typically measures the disproportionality produced by the election. Specifically, by the disparity between the distribution of votes and seats allocation.

Recently, Grigorii Golosov proposed a new method for computing the effective number of parties in which both larger and smaller parties are not attributed unrealistic scores as those resulted by using the Laakso/Taagepera index.I will call this as (Golosov) and is given by the following formula: $$N = \sum_{i=1}^{n}\frac{p_{i}}{p_{i}+p_{i}^{2}-p_{i}^{2}}$$

References

Gallagher, Michael and Paul Mitchell (2005) The Politics of Electoral Systems. Oxford University Press.

Golosov, Grigorii (2010) The Effective Number of Parties: A New Approach, Party Politics, 16: 171-192.

Laakso, Markku and Rein Taagepera (1979) Effective Number of Parties: A Measure with Application to West Europe, Comparative Political Studies, 12: 3-27.

Nicolau, Jairo (2008) Sistemas Eleitorais. Rio de Janeiro, FGV.

Taagepera, Rein and Matthew S. Shugart (1989) Seats and Votes: The Effects and Determinants of Electoral Systems. New Haven: Yale University Press.

Examples

# Here are some examples help yourself:
A <- c(.75,.25)
B <- c(.35,.35,.30)
C <- c(.75,.10,rep(0.01,15))

ENPs(seats=A, total=1)
ENPs(seats=B, total=1, method="Golosov")

# Non-trivial example:
# 2010 Election outcome
party = c("PT","PMDB","PSDB", "DEM","PR","PP","PSB","PDT","PTB", "PSC","PV",
"PC do B","PPS","PRB", "PMN", "PT do B", "PSOL","PHS","PRTB","PRP","PSL","PTC")
votes = c(13813587, 11692384, 9421347, 6932420, 7050274, 5987670, 6553345,
4478736, 3808646, 2981714,2886633, 2545279, 2376475, 1659973, 1026220,
605768, 968475, 719611, 283047, 232530, 457490, 563145)

# 2010 Election outcome passed as proportion of seats
seats_2010 = c(88, 79, 53, 43, 41, 41, 34, 28, 21,
17, 15, 15, 12, 8, 4, 3, 3, 2, 2, 2, 1, 1)/513

ENPs(seats=seats_2010, total=NULL, method="Golosov")

# 2014 Election outcome passed as proportion of seats
seats_2014 = c(70, 66, 55, 37, 38, 34, 34, 26, 22, 20, 19, 15, 12,
11, 10, 9, 8, 5, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1)/513

ENPs(seats_2014, method="Golosov")