Calculate the disproportionality indices.

Description

Calculate the disproportionality indices.

Usage

index(x, ...)

## S3 method for class 'prcalc'
index(
  x,
  k = 2,
  eta = 2,
  alpha = 2,
  unit = c("l2", "l1", "joint"),
  omit_zero = TRUE,
  ...
)

Arguments

x a prcalc object.
… ignored
k a parameter for Generalized Gallagher index. Default is 2.
eta a parameter for Atkinson index. Default is 2.
alpha a parameter for alpha-divergence. alpha must be larger than 0. Default is 2.
unit A unit of observation. This argument is valid only when p (e.g., votes or population) and q (e.g., seats or magnitudes) are two-dimensional structures. If “l2” (abbr. of "level 2"), the disproportionality is measured based on marginal distribution of level 2, such as parties or district. If “l1” (abbr. of "level 1"), the disproportionality is measured based on marginal distribution of level 1, such as states or region. If “joint”, the disproportionality is measured based on joint distribution of level 1 and 2. If you want to match the result of decompose(), use “joint”. Default is “l2”.
omit_zero If TRUE, parties with 0 votes and 0 seats are ignored. Default is TRUE.

Value

a prcalc_index object.

References

  • Laakso, Markku and Rein Taagepera. 1979. ""Effective" Number of Parties: A Measure with Application to West Europe". Comparative Political Studies. 12 (1): 3–27.

  • Gallagher, Michael. 1991. "Proportionality, Disproportionality and Electoral Systems". Electoral Studies. 10: 33–51.

Examples

library(PRcalc)

data(jp_upper_2019)

obj <- prcalc(jp_upper_2019, m = 50, method = "dt")

obj_index <- index(obj)
obj_index
            ID                         Index    Value
1       dhondt                       D’Hondt 1.116833
2       monroe                        Monroe 0.018918
3       maxdev    Maximum Absolute Deviation 0.010461
4     mm_ratio                 Max-Min ratio      Inf
5          rae                           Rae 0.004664
6           lh             Loosemore & Hanby 0.030315
7      grofman                       Grofman 0.011677
8     lijphart                      Lijphart 0.004069
9    gallagher                     Gallagher 0.014609
10 g_gallagher         Generalized Gallagher 0.014609
11       gatev                         Gatev 0.032939
12    ryabtsev                      Ryabtsev 0.023298
13      szalai                        Szalai 0.555712
14    w_szalai               Weighted Szalai 0.090661
15          ap          Aleskerov & Platonov 1.042141
16        gini                          Gini 0.036069
17    atkinson                      Atkinson 1.000000
18          sl                  Sainte-Laguë 0.018466
19          cs                 Cox & Shugart 1.033646
20      farina                        Farina 0.046282
21      ortona                        Ortona 0.046909
22          cd          Cosine Dissimilarity 0.000867
23          rr Lebeda’s RR (Mixture D’Hondt) 0.104611
24         arr                  Lebeda’s ARR 0.008047
25         srr                  Lebeda’s SRR 0.041482
26        wdrr                 Lebeda’s WDRR 0.055081
27          kl     Kullback-Leibler Surprise 0.016431
28          lr    Likelihood Ratio Statistic      Inf
29       chisq                   Chi Squared 0.004225
30   hellinger            Hellinger Distance 0.087758
31          ad              alpha-Divergence 0.009233
obj_index["gallagher"] # Extract Gallagher index
 gallagher 
0.01460875