SciencesPo (version 1.3.8)

politicalDiversity: Political Diversity Indices

politicalDiversity is used to analyze political diversity in a unity or across them. It provides methods to estimate the Effective Number of Parties as well as other diversity measures.

Description

Political Diversity Indices

politicalDiversity is used to analyze political diversity in a unity or across them. It provides methods to estimate the Effective Number of Parties as well as other diversity measures.

Usage

politicalDiversity(x, index = "herfindahl", margin = 1, base = exp(1))

Arguments

x

A data.frame, a matrix-like, or a vector containing values for the number of votes or seats each party received.

index

The type of index desired, one of "shannon", "simpson", "invsimpson", "golosov".

margin

The margin for which the index is computed.

base

The logarithm base used in the "shanron" method.

identifies the variable containing party labels. It should be used only when response variable is a frequency variable containing number of votes at the aggregate level. district identifies districts. It i

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 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))

# Non-trivial example:
# The 1980 presidential election in the US (vote share):
party_1980 <- c("Democratic", "Republican", "Independent", "Libertarian", "Citizens", "Others")
US1980 <- c(0.410, 0.507, 0.066, 0.011, 0.003, 0.003)

politicalDiversity(US1980, index= "laakso/taagepera")

politicalDiversity(US1980, index= "herfindahl")


party_2004 <- c("Democratic", "Republican", "Independent", "Libertarian",
"Constitution", "Green", "Others")
US2004 <- c(0.481, 0.509, 0.0038, 0.0032, 0.0012, 0.00096, 0.00084)

politicalDiversity(US2004, index= "herfindahl")

# Using Grigorii Golosov approach:
politicalDiversity(US2004, index= "golosov")

# The 1999 Finland election
votes_1999 <- c(612963, 600592, 563835,
291675, 194846, 137330, 111835, 28084, 26440, 28549, 20442, 10378,
10104, 5451, 5194, 4481, 3903, 3455, 21734)

seats_1999 <- c(51, 48, 46, 20, 11, 11, 10, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)

# Helsinki's 1999
votes_1999 <- c(68885,18343, 86448,
21982, 51587, 27227, 8482, 7250, 365,
2734, 1925, 475, 1693, 693, 308, 980,
560, 590, 185)

#Sainte-Lague allocation:
seats_1999sl <- c(5, 1, 6, 1, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
# D'Hondt allocation:
seats_1999dh <- c(5, 1, 7, 1, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)


# 2010 Brazilian legislative election

party_2010 = 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_2010 = 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 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

# 2014 Election outcome 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

politicalDiversity(seats_2014, index= "laakso/taagepera")

# or:

politicalDiversity(seats_2014, index= "invsimpson")

politicalDiversity(seats_2014, index= "golosov")