pol_measure: Polarization measure

In ysohn/polarization: Measurement Methods for Party Polarization

Description

Polarization measure calculation from an N\times 1 vector of voter ideology and an N\times 1 vector of voter party affiliation.

Usage

pol_measure(ideology, party, method, exclude = NULL)

Arguments

ideology	N\times 1 vector of voter ideology.
party	N\times 1 vector of voter party affiliation.
method	Polarization measure. μ_s is the mean ideology of party s, P is the number of parties, ρ_s is the discrepancy between the maximum value and the minimum value of party s members' ideology, \barμ is the mean ideology of the entire set of individuals, and N_s is the number of members of party s. dist Distance measure (McCarty et al., 2016) Distance = \frac{∑_{s\neq p}≤ft|{μ_s-μ_p}\right|}{P(P-1)} range Range measure (Rehm and Reilly, 2010) Range = \frac{∑_{s\neq p}\max≤ft(≤ft|μ_s-μ_p\right|-\frac{ρ_s+ρ_p}{4},0\right)}{P(P-1)} deviation Deviation measure (Rehm and Reilly, 2010) Deviation = √{\frac{∑_s≤ft\{\max≤ft(≤ft|μ_s-\barμ\right|-\frac{ρ_s}{4},0\right)\right\}^2}{P}} ER Esteban and Ray measure (Esteban and Ray, 1994; Rehm and Reilly, 2010) ER = ∑_{p=1}^{P}∑_{s=1}^{P}N_s^2N_p\max≤ft(≤ft|μ_s-μ_p\right|-\frac{ρ_s+ρ_p}{4},0\right)
exclude	A vector of party labels to be excluded (e.g. party label for an independent member).

Value

Polarization measure.

References

Esteban, Joan-Maria, and Debraj Ray. "On the measurement of polarization." Econometrica: Journal of the Econometric Society (1994): 819-851.

Rehm, Philipp, and Timothy Reilly. "United we stand: Constituency homogeneity and comparative party polarization." Electoral Studies 29.1 (2010): 40-53.

McCarty, Nolan, Keith T. Poole, and Howard Rosenthal. Polarized America: The dance of ideology and unequal riches. MIT Press, 2016.

Poole, Keith T., et al. "Scaling roll call votes with wnominate in R." Journal of Statistical Software 42.14 (2011): 1-21.

Zeileis, Achim, Christian Kleiber, and Simon Jackman. "Regression models for count data in R." Journal of statistical software 27.8 (2008): 1-25.

Examples

## Calculate the four versions of party polarization measures after generating
## a vote matrix with 1000 votes in a two party legislature consisting of 100 legislators.
party <- rbind(matrix(1,50,1),matrix(2,50,1))
vote_data <- pol_simul(party = party, M = 1000, partyMean = c(-1,1), partySD = c(.5,.5))
V <- vote_data$votes
rc <- pscl::rollcall(V)
wn_result <- wnominate::wnominate(rc,polarity=c(1),dims=1)
ideology <- wn_result$legislators$coord1D
pol_value <- matrix(0,4,1)
for (i in 1:4){
  pol_value[i,1] <- pol_measure(ideology, party, i)
}


## Measure the party polarization level of the 110th U.S. Senate
## using the range measure after excluding independent members with party label 328.
res <- Rvoteview::voteview_search(chamber = "Senate", congress = c(110))
rc <- Rvoteview::voteview_download(res$id)
pol_value <- pol_measure(as.numeric(rc$legis.data$dim1), rc$legis.data$party_code, 'range', 328)

ysohn/polarization documentation built on Jan. 1, 2021, 1:46 p.m.