partynat

partynat is an R package for computing indices used in the context of party nationalization research. It provides more than a dozen different indices of static party nationalization, including standard errors and confidence intervals via nonparametric bootstrap, subsampling and jackknife with optional bias correction.

It's a companion package to Medzihorsky, Juraj. (2022). Unifying the Measurement of Variation in Electoral Support

The manual is here.

Installation

You can install it using devtools

library(devtools)

install_github("jmedzihorsky/partynat")

Usage

The main function is

partynat(mat, statistic, weight_choice, weight_territory, boot, jack, subsample, n_rep, bias, size, confidence_level)

• mat is the matrix with vote counts, its columns correspond to choices (parties, lists, candidates, etc) rows correspond to voter groups (constituencies, territories etc).

• statistic specifies which index should be computed (see table below). Defaults to "PNS".

• weight_choice and weight_territory (logical) indicate whether for indices where this is an option choice and territory weight should be applied. Both default to FALSE.

• boot, jack, and subsample (logical) specify whether nonparametric bootstrap, jackknife, or subsampling (leave-k out jackknife) should be applied. In each call of the function at most one of them can be set to TRUE.
  All default to FALSE.

• n_rep specifies the number of replicates if either boot or subsample are set to TRUE. Defaults to 10.

• bias indicates whether bias corrections for the resampling estimates should be applied. Defaults to TRUE.

• size specifies the size of the sample if subsample = TRUE. Defaults to half the number of the observed votes.

• confidence_level sets the level for the confidence intervals if a resampling procedure is applied. The level must be on [0, 1]. Defaults to 0.95.

The function outputs an object of S3 class "partynat", a list composed of

• call The matched call.
• stat The statistics argument in the call. See Indices below.
• name The name of the index.
• total The value of the index for the whole table. If resampling is applied, includes standard errors and confidence intervals.
• choices The values of the index for each choice. Equals to NA for indices that are not defined on the choice level. If resampling is applied, includes standard errors and confidence intervals.
• confidence_level The requested confidence levels.

The S3 class "partynat" further has a summary() and a plot() method attached.

Indices

Index	Source	partynat call
Index of Party Aggregation	Allik (2006)	"IPA2"
Weighted Party (System) Nationalization Score	Bochsler (2010)	"PNSW"
Standardized Party (System) Nationalization Score	Bochsler (2010)	"PNS10"
Territorial Coverage Index	Caramani (2004)	"TCI"
Index adjusted for Party size and number of Regions	Caramani (2004)	"IPR2"
Indicator of Party Aggregation	Chhibber and Kollman (1998)	"IPA1"
Inflation Score	Cox (1999)	"IS"
Variability Coefficient	Ersson, Janda, and Lane (1985)	"VC"
Standardized and Weighted Variability Coefficient	Ersson, Janda, and Lane (1985)	"SWVC"
Coefficient of Party Regionalization	Golosov (2016)	"CPR"
Index of Party (System) Nationalization	Golosov (2016)	"IPN"
Normalized Party (System) Nationalization Score	Golosov (2016)	"NPNS"
Normalized Coefficient of Variation	Golosov (2016)	"NVC"
Index of Party Regionalization	Golosov and Ponarin (1999)	"IPR1"
Party Nationalization Score	Jones and Mainwaring (2003)	"PNS"
Lee index	Lee (1988)	"Lee"
Inflation Index	Moenius and Kasuya (2004)	"II"
Index of variation/Mean Absolute Deviation	Rose and Urwin (1975)	"MAD"
Cumulative Regional Inequality	Rose and Urwin (1975)	"CRI"
Mean Standard Deviation of row shares		"MSD"
Variance of row shares		"Var"
Mutual Information	Frankel and Volij (2011)	"MI"
Dissimilarity index for choice-group independence	Medzihorsky (2022)	"Delta"

Usage

The required data format is a matrix with a cross-tabulation of the vote counts by territory (rows) and party (columns). The counts can be either the official election results, or estimates from a survey. The partynat() function requires integer counts, and implements resampling procedures for survey data. If for some reason you do not have the counts and have instead the constituency percentages, you can simply multiply those by the constituency sizes and round them. Alternatively, you can apportion the votes with seatdist::giveseats(), to make sure the counts add up to the desired margins.

Background

What political scientists mean under party nationalization is that a political party's presence is the same in all territories (such as constituencies or federal states) that comprise a nation. By presence they usually mean electoral support, and by it being the same everywhere they mean at least three different things (see Caramani (1996)):

1. That the party receives the same vote share everywhere. This is called static nationalization.
2. That the party's electoral support changes the same way everywhere. This known as dynamic nationalization.
3. That the effect of something, say a campaign, on the party's support is the same everywhere.

While party scholars agree on what perfect static nationalization should look like --- within-territory party shares are identical to their national shares --- they don't agree on how to measure deviations from this baseline. This shouldn't come as a surprise if we rethink the problem as one of measuring association. From that perspective, static nationalization is party-territory independence. And there is an infinite number of measures of association for categorical variables.

Party scholars have invested considerable effort in developing indices of static nationalization that have the propeties they desire of such indices. Perhaps the most sophisticated effort to date is an index based on the Gini coefficient of inequality, proposed by Bochsler (2010). This index, called "PNSW" here, has a host of appealing formal properties. However, it's numeric values lack clear substantive interpretation.

As an alternative that has an easy substantive interpretation, my working paper proposes an index that gives the smallest fraction of the votes that would need to change for static nationalization to happen. The cost of this easy substantive interpretation is that unlike the PNSW, this index is only sensitive to transfers under the weak version of Dalton's principle. While this rids it of some formal elegance, the working paper shows that it nevertheless still correlates 0.99 with the PNSW in over a thousand elections from over two centuries. The index, called "Delta" here, is a special cases of Gini's dissimilarity index, just like Pedersen's (1979) electoral volatility index.

The dissimilarity index also has a long track record in the study of segregation (see Duncan and Duncan (1955)). From this perspective, we can look on party de-nationalization as a case of voter segregation that can also happen along gender, ethnic, occupational etc. lines. Another successful index of segregation is mutual information. Frankel and Volij (2011) and Mora and Ruiz-Castillo (2011) show that it has a host of appealing properties, including strong decomposability. However, its substantive interpretation is a bit less direct than that of the dissimilarity index.

The working paper also discusses the measurement of dynamic nationalization, and electoral continuity with the dissimilarity index and log-linear models, but these are not currently implemented in partynat.