SciencesPo (version 1.4.0)

Proportionality: Indexes of (Disproportionality) Proportionality

Description

Calculates several indexes of (dis)-proportionality, which are for the most part used to show the relationship of votes to seats.

Usage

Proportionality(v, s, index = "Gallagher", ...)
"Proportionality"(v, s, index = "Gallagher", margin = 1, ...)

Arguments

v

a numeric vector with the percentage share of votes obtained by each party.

s

a numeric vector with the percentage share of seats obtained by each party.

index

the desired method or type of index, see details below for the correct name.

margin

The margin for which the index is computed.

...

additional arguments (currently ignored)

Value

Each iteration returns a single score.

Details

The following measures are available:

• Loosemore-Hanby (Percent) Loosemore-Hanby Index of disproportionality
• Rae (Percent) Rae Index of disproportionality
• Cox-Shugart Cox-Shugart Index of proportionality
• Inv.Cox-Shugart The inverted Cox-Shugart index
• Farina Farina index of proportionality, aka cosine proportionality score
• "Gallagher" (Percent) Gallagher index of disproportionality
• "Inv.Gallagher" The inverse of Gallagher index
• "Grofman" Grofman index of proportionality
• "Inv.Grofman" Grofman index of proportionality
• "Lijphart" Lijphart index of proportionality
• "Inv.Rae" The inverse of Rae index
• "Rose" Rose index of disproportionality
• "Inv.Rose" The inverse of Rose index
• "Sainte-Lague" Sainte-Lague index of disproportionality
• "DHondt" D'Hondt index of proportionality
• "Gini" Gini index of disproportionality
• "Monroe" Monroe index of inequity

References

Duncan, O. and Duncan, B. (1955) A methodological analysis of segregation indexes. American Sociological Review 20:210-7.

Gallagher, M. (1991) Proportionality, disproportionality and electoral systems. Electoral Studies 10(1):33-51.

Loosemore, J. and Hanby, V. (1971) The theoretical limits of maximum distortion: Som analytical expressions for electoral systems. British Journal of Political Science 1:467-77.

Koppel, M., and A. Diskin. (2009) Measuring disproportionality, volatility and malapportionment: axiomatization and solutions. Social Choice and Welfare 33, no. 2: 281-286.

Rae, D. (1967) The Political Consequences of Electoral Laws. London: Yale University Press.

Rose, Richard, Neil Munro and Tom Mackie (1998) Elections in Central and Eastern Europe Since 1990. Glasgow: Centre for the Study of Public Policy, University of Strathclyde.

Taagepera, R., and B. Grofman. Mapping the indices of seats-votes disproportionality and inter-election volatility. Party Politics 9, no. 6 (2003): 659-77.

See Also

PoliticalDiversity, LargestRemainders, HighestAverages. For more details, see the Indices vignette: vignette("Indices", package = "SciencesPo").

Examples

#' # 2012 Queensland state elecion
pvotes= c(49.65, 26.66, 11.5, 7.53, 3.16, 1.47)
pseats = c(87.64, 7.87, 2.25, 0.00, 2.25, 0.00)

Proportionality(pvotes, pseats) # default is Gallagher

Proportionality(pvotes, pseats, index="Rae")

# Proportionality(pvotes, pseats, index="Cox-Shugart")

# 2012 Quebec provincial election:
pvotes = c(PQ=31.95, Lib=31.20, CAQ=27.05, QS=6.03, Option=1.89, Other=1.88)
pseats = c(PQ=54, Lib=50, CAQ=19, QS=2, Option=0, Other=0)

Proportionality(pvotes, pseats, index="Rae")