Seat allocation

library(PRcalc)
library(tidyverse)

Import sample dataset

The first column contains the names of political parties, and the subsequent columns contain the respective number of votes for each party.

# Korean general election in 2016
# See "str(kr_lower_2016_en)", for the full names of parties
# Number of blocks = 1 (national block)
data("kr_lower_2016_en")
kr_lower_2016_en

  Party    Vote
1   LKP 7960272
2   DPK 6069744
3    PP 6355572
4    JP 1719891
5   CLP  626853
6    MP  209872
7   GPK  182301
8   PUP  145624
9   CDP  129978

# Japanese lower house election in 2019 (in English)
# See "str(jp_lower_2021_en)", for the full names of parties
# Number of blocks = 11 (regional blocks)
data("jp_lower_2021_en")
jp_lower_2021_en

    Party Hokkaido  Tohoku Kitakanto Minamikanto   Tokyo Hokuriku   Tokai
1     LDP   863300 1628233   2172065     2590787 2000084  1468380 2515841
2     NKP   294371  456287    823930      850667  715450   322535  784976
3     CDP   682913  991505   1391149     1651562 1293281   773076 1485947
4     JCP   207189  292830    444115      534493  670340   225551  408606
5     JIP   215344  258690    617531      863897  858577   361476  694630
6     DPP    73621  195754    298056      384482  306180   133600  382734
7     SDP    41248  101442     97963      124447   92995    71185   84220
8   Reiwa   102086  143265    239592      302675  360387   111281  273208
9     NHK    42916   52664     87702      111298   92353    43529   98238
10    SSN    46142       0         0           0       0        0       0
11    JFP        0       0         0           0   33661        0       0
12 Yamato        0       0         0           0   16970        0       0
13 Corona        0       0         0           0    6620        0       0
     Kinki Chugoku Shikoku  Kyushu
1  2407699 1352723  664805 2250966
2  1155683  436220  233407 1040756
3  1090666  573324  291871 1266801
4   736156  173117  108021  365658
5  3180219  286302  173826  540338
6   303480  113899  122082  279509
7   100980   52638   30249  221221
8   292483   94446   52941  243284
9   111539   36758   21285   98506
10       0       0       0       0
11       0       0       0       0
12       0       0       0       0
13       0       0       0       0

Calculation

To calculate seat allocation using the prcalc() function, you need to specify the following: data (x), electoral magnitude (m), and allocation method (method). Below is an example of allocating 47 (m = 47) seats using the Hare-Niemeyer method (method = "hn") with the kr_lower_2016 dataset. In this case, the length of m is 1 because number of blocks is 1. Furthermore, by adjusting the threshold argument, it is possible to exclude parties with votes below a certain threshold from seat allocation. The follow is an example of threshold is 3% (0.03). Default is threshold = 0.

# Example of national block (D'Hondt/Jefferson method)
obj1 <- prcalc(kr_lower_2016_en, m = 47, method = "hn", threshold = 0.03)
obj1

Raw:
  Party    Vote
1   LKP 7960272
2   DPK 6069744
3    PP 6355572
4    JP 1719891
5   CLP  626853
6    MP  209872
7   GPK  182301
8   PUP  145624
9   CDP  129978

Result:
  Party Vote
1   LKP   17
2   DPK   13
3    PP   13
4    JP    4
5   CLP    0
6    MP    0
7   GPK    0
8   PUP    0
9   CDP    0

Parameters:
  Allocation method: Hare-Niemeyer quota 
  Extra parameter: 
  Threshold: 0.03 

Magnitude: 47

In a block system, you need to specify m for each block separately. Since jp_lower_2021 has 11 blocks, the length of m also needs to be 11.

# Example of regional block (D'Hondt/Jefferson method; 11 blocks)
obj2 <- prcalc(jp_lower_2021_en, 
               m = c(8, 13, 19, 22, 17, 11, 21, 28, 11, 6, 20), 
               method = "dt")
obj2

Raw:
    Party Hokkaido  Tohoku Kitakanto Minamikanto   Tokyo Hokuriku   Tokai
1     LDP   863300 1628233   2172065     2590787 2000084  1468380 2515841
2     NKP   294371  456287    823930      850667  715450   322535  784976
3     CDP   682913  991505   1391149     1651562 1293281   773076 1485947
4     JCP   207189  292830    444115      534493  670340   225551  408606
5     JIP   215344  258690    617531      863897  858577   361476  694630
6     DPP    73621  195754    298056      384482  306180   133600  382734
7     SDP    41248  101442     97963      124447   92995    71185   84220
8   Reiwa   102086  143265    239592      302675  360387   111281  273208
9     NHK    42916   52664     87702      111298   92353    43529   98238
10    SSN    46142       0         0           0       0        0       0
11    JFP        0       0         0           0   33661        0       0
12 Yamato        0       0         0           0   16970        0       0
13 Corona        0       0         0           0    6620        0       0
     Kinki Chugoku Shikoku  Kyushu    Total
1  2407699 1352723  664805 2250966 19914883
2  1155683  436220  233407 1040756  7114282
3  1090666  573324  291871 1266801 11492095
4   736156  173117  108021  365658  4166076
5  3180219  286302  173826  540338  8050830
6   303480  113899  122082  279509  2593397
7   100980   52638   30249  221221  1018588
8   292483   94446   52941  243284  2215648
9   111539   36758   21285   98506   796788
10       0       0       0       0    46142
11       0       0       0       0    33661
12       0       0       0       0    16970
13       0       0       0       0     6620

Result:
    Party Hokkaido Tohoku Kitakanto Minamikanto Tokyo Hokuriku Tokai Kinki
1     LDP        3      6         7           8     6        5     8     8
2     NKP        1      1         3           3     2        1     3     3
3     CDP        3      4         5           5     4        3     5     3
4     JCP        0      1         1           1     2        1     1     2
5     JIP        1      1         2           3     2        1     2    10
6     DPP        0      0         1           1     0        0     1     1
7     SDP        0      0         0           0     0        0     0     0
8   Reiwa        0      0         0           1     1        0     1     1
9     NHK        0      0         0           0     0        0     0     0
10    SSN        0      0         0           0     0        0     0     0
11    JFP        0      0         0           0     0        0     0     0
12 Yamato        0      0         0           0     0        0     0     0
13 Corona        0      0         0           0     0        0     0     0
   Chugoku Shikoku Kyushu Total
1        5       3      8    67
2        2       1      4    24
3        3       1      4    40
4        0       0      1    10
5        1       1      2    26
6        0       0      1     5
7        0       0      0     0
8        0       0      0     4
9        0       0      0     0
10       0       0      0     0
11       0       0      0     0
12       0       0      0     0
13       0       0      0     0

Parameters:
  Allocation method: D'Hondt (Jefferson) method 
  Extra parameter: 
  Threshold: 0 

Magnitude: 
   Hokkaido      Tohoku   Kitakanto Minamikanto       Tokyo    Hokuriku 
          8          13          19          22          17          11 
      Tokai       Kinki     Chugoku     Shikoku      Kyushu 
         21          28          11           6          20 

{PRcalc} offers various allocation methods. Below is an example similar to the previous one, but with the allocation methods changed to the Hare-Niemeyer ("hn") method and the Sainte-Laguë method ("sl").

# Hare-Niemeyer method
obj3 <- prcalc(jp_lower_2021_en, 
               m = c(8, 13, 19, 22, 17, 11, 21, 28, 11, 6, 20), 
               method = "hn")
obj3

Raw:
    Party Hokkaido  Tohoku Kitakanto Minamikanto   Tokyo Hokuriku   Tokai
1     LDP   863300 1628233   2172065     2590787 2000084  1468380 2515841
2     NKP   294371  456287    823930      850667  715450   322535  784976
3     CDP   682913  991505   1391149     1651562 1293281   773076 1485947
4     JCP   207189  292830    444115      534493  670340   225551  408606
5     JIP   215344  258690    617531      863897  858577   361476  694630
6     DPP    73621  195754    298056      384482  306180   133600  382734
7     SDP    41248  101442     97963      124447   92995    71185   84220
8   Reiwa   102086  143265    239592      302675  360387   111281  273208
9     NHK    42916   52664     87702      111298   92353    43529   98238
10    SSN    46142       0         0           0       0        0       0
11    JFP        0       0         0           0   33661        0       0
12 Yamato        0       0         0           0   16970        0       0
13 Corona        0       0         0           0    6620        0       0
     Kinki Chugoku Shikoku  Kyushu    Total
1  2407699 1352723  664805 2250966 19914883
2  1155683  436220  233407 1040756  7114282
3  1090666  573324  291871 1266801 11492095
4   736156  173117  108021  365658  4166076
5  3180219  286302  173826  540338  8050830
6   303480  113899  122082  279509  2593397
7   100980   52638   30249  221221  1018588
8   292483   94446   52941  243284  2215648
9   111539   36758   21285   98506   796788
10       0       0       0       0    46142
11       0       0       0       0    33661
12       0       0       0       0    16970
13       0       0       0       0     6620

Result:
    Party Hokkaido Tohoku Kitakanto Minamikanto Tokyo Hokuriku Tokai Kinki
1     LDP        3      5         7           8     5        5     8     7
2     NKP        1      1         3           2     2        1     3     4
3     CDP        2      3         4           5     4        3     5     3
4     JCP        1      1         1           2     2        1     1     2
5     JIP        1      1         2           3     2        1     2    10
6     DPP        0      1         1           1     1        0     1     1
7     SDP        0      0         0           0     0        0     0     0
8   Reiwa        0      1         1           1     1        0     1     1
9     NHK        0      0         0           0     0        0     0     0
10    SSN        0      0         0           0     0        0     0     0
11    JFP        0      0         0           0     0        0     0     0
12 Yamato        0      0         0           0     0        0     0     0
13 Corona        0      0         0           0     0        0     0     0
   Chugoku Shikoku Kyushu Total
1        5       2      7    62
2        2       1      3    23
3        2       1      4    36
4        1       0      1    13
5        1       1      2    26
6        0       1      1     8
7        0       0      1     1
8        0       0      1     7
9        0       0      0     0
10       0       0      0     0
11       0       0      0     0
12       0       0      0     0
13       0       0      0     0

Parameters:
  Allocation method: Hare-Niemeyer quota 
  Extra parameter: 
  Threshold: 0 

Magnitude: 
   Hokkaido      Tohoku   Kitakanto Minamikanto       Tokyo    Hokuriku 
          8          13          19          22          17          11 
      Tokai       Kinki     Chugoku     Shikoku      Kyushu 
         21          28          11           6          20 

# Sainte-Laguë/Webster method
obj4 <- prcalc(jp_lower_2021_en, 
               m = c(8, 13, 19, 22, 17, 11, 21, 28, 11, 6, 20), 
               method = "sl")
obj4

Raw:
    Party Hokkaido  Tohoku Kitakanto Minamikanto   Tokyo Hokuriku   Tokai
1     LDP   863300 1628233   2172065     2590787 2000084  1468380 2515841
2     NKP   294371  456287    823930      850667  715450   322535  784976
3     CDP   682913  991505   1391149     1651562 1293281   773076 1485947
4     JCP   207189  292830    444115      534493  670340   225551  408606
5     JIP   215344  258690    617531      863897  858577   361476  694630
6     DPP    73621  195754    298056      384482  306180   133600  382734
7     SDP    41248  101442     97963      124447   92995    71185   84220
8   Reiwa   102086  143265    239592      302675  360387   111281  273208
9     NHK    42916   52664     87702      111298   92353    43529   98238
10    SSN    46142       0         0           0       0        0       0
11    JFP        0       0         0           0   33661        0       0
12 Yamato        0       0         0           0   16970        0       0
13 Corona        0       0         0           0    6620        0       0
     Kinki Chugoku Shikoku  Kyushu    Total
1  2407699 1352723  664805 2250966 19914883
2  1155683  436220  233407 1040756  7114282
3  1090666  573324  291871 1266801 11492095
4   736156  173117  108021  365658  4166076
5  3180219  286302  173826  540338  8050830
6   303480  113899  122082  279509  2593397
7   100980   52638   30249  221221  1018588
8   292483   94446   52941  243284  2215648
9   111539   36758   21285   98506   796788
10       0       0       0       0    46142
11       0       0       0       0    33661
12       0       0       0       0    16970
13       0       0       0       0     6620

Result:
    Party Hokkaido Tohoku Kitakanto Minamikanto Tokyo Hokuriku Tokai Kinki
1     LDP        3      5         7           8     5        5     8     7
2     NKP        1      2         3           2     2        1     3     4
3     CDP        2      3         4           5     4        3     5     3
4     JCP        1      1         1           2     2        1     1     2
5     JIP        1      1         2           3     2        1     2    10
6     DPP        0      1         1           1     1        0     1     1
7     SDP        0      0         0           0     0        0     0     0
8   Reiwa        0      0         1           1     1        0     1     1
9     NHK        0      0         0           0     0        0     0     0
10    SSN        0      0         0           0     0        0     0     0
11    JFP        0      0         0           0     0        0     0     0
12 Yamato        0      0         0           0     0        0     0     0
13 Corona        0      0         0           0     0        0     0     0
   Chugoku Shikoku Kyushu Total
1        5       3      7    63
2        2       1      3    24
3        2       1      4    36
4        1       0      1    13
5        1       1      2    26
6        0       0      1     7
7        0       0      1     1
8        0       0      1     6
9        0       0      0     0
10       0       0      0     0
11       0       0      0     0
12       0       0      0     0
13       0       0      0     0

Parameters:
  Allocation method: Sainte-Laguë (Webster) method 
  Extra parameter: 
  Threshold: 0 

Magnitude: 
   Hokkaido      Tohoku   Kitakanto Minamikanto       Tokyo    Hokuriku 
          8          13          19          22          17          11 
      Tokai       Kinki     Chugoku     Shikoku      Kyushu 
         21          28          11           6          20 

Please click here for the list of various allocation methods provided by {PRcalc} and these abbreviations.

Printing

print() and summary() functions are a method of prcalc object. You can hide a column of “Total” with show_total = FALSE.

print(obj2, show_total = FALSE) # Hide `Total` column

Raw:
    Party Hokkaido  Tohoku Kitakanto Minamikanto   Tokyo Hokuriku   Tokai
1     LDP   863300 1628233   2172065     2590787 2000084  1468380 2515841
2     NKP   294371  456287    823930      850667  715450   322535  784976
3     CDP   682913  991505   1391149     1651562 1293281   773076 1485947
4     JCP   207189  292830    444115      534493  670340   225551  408606
5     JIP   215344  258690    617531      863897  858577   361476  694630
6     DPP    73621  195754    298056      384482  306180   133600  382734
7     SDP    41248  101442     97963      124447   92995    71185   84220
8   Reiwa   102086  143265    239592      302675  360387   111281  273208
9     NHK    42916   52664     87702      111298   92353    43529   98238
10    SSN    46142       0         0           0       0        0       0
11    JFP        0       0         0           0   33661        0       0
12 Yamato        0       0         0           0   16970        0       0
13 Corona        0       0         0           0    6620        0       0
     Kinki Chugoku Shikoku  Kyushu
1  2407699 1352723  664805 2250966
2  1155683  436220  233407 1040756
3  1090666  573324  291871 1266801
4   736156  173117  108021  365658
5  3180219  286302  173826  540338
6   303480  113899  122082  279509
7   100980   52638   30249  221221
8   292483   94446   52941  243284
9   111539   36758   21285   98506
10       0       0       0       0
11       0       0       0       0
12       0       0       0       0
13       0       0       0       0

Result:
    Party Hokkaido Tohoku Kitakanto Minamikanto Tokyo Hokuriku Tokai Kinki
1     LDP        3      6         7           8     6        5     8     8
2     NKP        1      1         3           3     2        1     3     3
3     CDP        3      4         5           5     4        3     5     3
4     JCP        0      1         1           1     2        1     1     2
5     JIP        1      1         2           3     2        1     2    10
6     DPP        0      0         1           1     0        0     1     1
7     SDP        0      0         0           0     0        0     0     0
8   Reiwa        0      0         0           1     1        0     1     1
9     NHK        0      0         0           0     0        0     0     0
10    SSN        0      0         0           0     0        0     0     0
11    JFP        0      0         0           0     0        0     0     0
12 Yamato        0      0         0           0     0        0     0     0
13 Corona        0      0         0           0     0        0     0     0
   Chugoku Shikoku Kyushu
1        5       3      8
2        2       1      4
3        3       1      4
4        0       0      1
5        1       1      2
6        0       0      1
7        0       0      0
8        0       0      0
9        0       0      0
10       0       0      0
11       0       0      0
12       0       0      0
13       0       0      0

Parameters:
  Allocation method: D'Hondt (Jefferson) method 
  Extra parameter: 
  Threshold: 0 

Magnitude: 
   Hokkaido      Tohoku   Kitakanto Minamikanto       Tokyo    Hokuriku 
          8          13          19          22          17          11 
      Tokai       Kinki     Chugoku     Shikoku      Kyushu 
         21          28          11           6          20 

In some cases, result is too long. You can adjust length of result using head argument. If head = 10, only ten rows are displayed. Default is head = Inf. (entire rows)

print(obj2, head = 10) # Show only ten rows.

Raw:
   Party Hokkaido  Tohoku Kitakanto Minamikanto   Tokyo Hokuriku   Tokai
1    LDP   863300 1628233   2172065     2590787 2000084  1468380 2515841
2    NKP   294371  456287    823930      850667  715450   322535  784976
3    CDP   682913  991505   1391149     1651562 1293281   773076 1485947
4    JCP   207189  292830    444115      534493  670340   225551  408606
5    JIP   215344  258690    617531      863897  858577   361476  694630
6    DPP    73621  195754    298056      384482  306180   133600  382734
7    SDP    41248  101442     97963      124447   92995    71185   84220
8  Reiwa   102086  143265    239592      302675  360387   111281  273208
9    NHK    42916   52664     87702      111298   92353    43529   98238
10   SSN    46142       0         0           0       0        0       0
     Kinki Chugoku Shikoku  Kyushu    Total
1  2407699 1352723  664805 2250966 19914883
2  1155683  436220  233407 1040756  7114282
3  1090666  573324  291871 1266801 11492095
4   736156  173117  108021  365658  4166076
5  3180219  286302  173826  540338  8050830
6   303480  113899  122082  279509  2593397
7   100980   52638   30249  221221  1018588
8   292483   94446   52941  243284  2215648
9   111539   36758   21285   98506   796788
10       0       0       0       0    46142

Result:
   Party Hokkaido Tohoku Kitakanto Minamikanto Tokyo Hokuriku Tokai Kinki
1    LDP        3      6         7           8     6        5     8     8
2    NKP        1      1         3           3     2        1     3     3
3    CDP        3      4         5           5     4        3     5     3
4    JCP        0      1         1           1     2        1     1     2
5    JIP        1      1         2           3     2        1     2    10
6    DPP        0      0         1           1     0        0     1     1
7    SDP        0      0         0           0     0        0     0     0
8  Reiwa        0      0         0           1     1        0     1     1
9    NHK        0      0         0           0     0        0     0     0
10   SSN        0      0         0           0     0        0     0     0
   Chugoku Shikoku Kyushu Total
1        5       3      8    67
2        2       1      4    24
3        3       1      4    40
4        0       0      1    10
5        1       1      2    26
6        0       0      1     5
7        0       0      0     0
8        0       0      0     4
9        0       0      0     0
10       0       0      0     0

Parameters:
  Allocation method: D'Hondt (Jefferson) method 
  Extra parameter: 
  Threshold: 0 

Magnitude: 
   Hokkaido      Tohoku   Kitakanto Minamikanto       Tokyo    Hokuriku 
          8          13          19          22          17          11 
      Tokai       Kinki     Chugoku     Shikoku      Kyushu 
         21          28          11           6          20 

In default, numbers of votes and seats are displayed. If you switch to proportion using prop = TRUE.

print(obj2, head = 5, prop = TRUE)

Raw:
  Party   Hokkaido     Tohoku  Kitakanto Minamikanto     Tokyo   Hokuriku
1   LDP 0.33602815 0.39513793 0.35191652   0.3494307 0.3102397 0.41826883
2   NKP 0.11458003 0.11073126 0.13349259   0.1147332 0.1109759 0.09187427
3   CDP 0.26581489 0.24061742 0.22539303   0.2227534 0.2006052 0.22021111
4   JCP 0.08064559 0.07106369 0.07195522   0.0720894 0.1039787 0.06424832
5   JIP 0.08381981 0.06277863 0.10005196   0.1165175 0.1331768 0.10296663
       Tokai      Kinki    Chugoku    Shikoku     Kyushu      Total
1 0.37391371 0.25671430 0.43364470 0.39141012 0.35689743 0.34655083
2 0.11666607 0.12322153 0.13983978 0.13742054 0.16501499 0.12379989
3 0.22084701 0.11628927 0.18379145 0.17184176 0.20085511 0.19998084
4 0.06072855 0.07849061 0.05549641 0.06359837 0.05797618 0.07249639
5 0.10323851 0.33908212 0.09178032 0.10234167 0.08567221 0.14009732

Result:
  Party Hokkaido     Tohoku  Kitakanto Minamikanto     Tokyo   Hokuriku
1   LDP    0.375 0.46153846 0.36842105  0.36363636 0.3529412 0.45454545
2   NKP    0.125 0.07692308 0.15789474  0.13636364 0.1176471 0.09090909
3   CDP    0.375 0.30769231 0.26315789  0.22727273 0.2352941 0.27272727
4   JCP    0.000 0.07692308 0.05263158  0.04545455 0.1176471 0.09090909
5   JIP    0.125 0.07692308 0.10526316  0.13636364 0.1176471 0.09090909
       Tokai      Kinki    Chugoku   Shikoku Kyushu      Total
1 0.38095238 0.28571429 0.45454545 0.5000000   0.40 0.38068182
2 0.14285714 0.10714286 0.18181818 0.1666667   0.20 0.13636364
3 0.23809524 0.10714286 0.27272727 0.1666667   0.20 0.22727273
4 0.04761905 0.07142857 0.00000000 0.0000000   0.05 0.05681818
5 0.09523810 0.35714286 0.09090909 0.1666667   0.10 0.14772727

Parameters:
  Allocation method: D'Hondt (Jefferson) method 
  Extra parameter: 
  Threshold: 0 

Magnitude: 
   Hokkaido      Tohoku   Kitakanto Minamikanto       Tokyo    Hokuriku 
          8          13          19          22          17          11 
      Tokai       Kinki     Chugoku     Shikoku      Kyushu 
         21          28          11           6          20 

If use_gt = TRUE, a result rendered using {gt} package. Furthermore, the digits argument allows specifying the number of decimal places for the output. Default is digits = 3. In {gt} mode, district magnitudes are not displayed.

print(obj2, prop = TRUE, use_gt = TRUE, digits = 3)

Party	Hokkaido	Tohoku	Kitakanto	Minamikanto	Tokyo	Hokuriku	Tokai	Kinki	Chugoku	Shikoku	Kyushu	Total
Raw
LDP	0.336	0.395	0.352	0.349	0.310	0.418	0.374	0.257	0.434	0.391	0.357	0.347
NKP	0.115	0.111	0.133	0.115	0.111	0.092	0.117	0.123	0.140	0.137	0.165	0.124
CDP	0.266	0.241	0.225	0.223	0.201	0.220	0.221	0.116	0.184	0.172	0.201	0.200
JCP	0.081	0.071	0.072	0.072	0.104	0.064	0.061	0.078	0.055	0.064	0.058	0.072
JIP	0.084	0.063	0.100	0.117	0.133	0.103	0.103	0.339	0.092	0.102	0.086	0.140
DPP	0.029	0.048	0.048	0.052	0.047	0.038	0.057	0.032	0.037	0.072	0.044	0.045
SDP	0.016	0.025	0.016	0.017	0.014	0.020	0.013	0.011	0.017	0.018	0.035	0.018
Reiwa	0.040	0.035	0.039	0.041	0.056	0.032	0.041	0.031	0.030	0.031	0.039	0.039
NHK	0.017	0.013	0.014	0.015	0.014	0.012	0.015	0.012	0.012	0.013	0.016	0.014
SSN	0.018	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.001
JFP	0.000	0.000	0.000	0.000	0.005	0.000	0.000	0.000	0.000	0.000	0.000	0.001
Yamato	0.000	0.000	0.000	0.000	0.003	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Corona	0.000	0.000	0.000	0.000	0.001	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Distribution
LDP	0.375	0.462	0.368	0.364	0.353	0.455	0.381	0.286	0.455	0.500	0.400	0.381
NKP	0.125	0.077	0.158	0.136	0.118	0.091	0.143	0.107	0.182	0.167	0.200	0.136
CDP	0.375	0.308	0.263	0.227	0.235	0.273	0.238	0.107	0.273	0.167	0.200	0.227
JCP	0.000	0.077	0.053	0.045	0.118	0.091	0.048	0.071	0.000	0.000	0.050	0.057
JIP	0.125	0.077	0.105	0.136	0.118	0.091	0.095	0.357	0.091	0.167	0.100	0.148
DPP	0.000	0.000	0.053	0.045	0.000	0.000	0.048	0.036	0.000	0.000	0.050	0.028
SDP	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Reiwa	0.000	0.000	0.000	0.045	0.059	0.000	0.048	0.036	0.000	0.000	0.000	0.023
NHK	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
SSN	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
JFP	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Yamato	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Corona	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Allocation method: D'Hondt (Jefferson) method
Extra parameter:
Threshold: 0

summary() function is a useful when number of blocks is large. summary() function displays only the total column.

summary(obj2) # summarize

    Party      Raw Dist
1     LDP 19914883   67
2     NKP  7114282   24
3     CDP 11492095   40
4     JCP  4166076   10
5     JIP  8050830   26
6     DPP  2593397    5
7     SDP  1018588    0
8   Reiwa  2215648    4
9     NHK   796788    0
10    SSN    46142    0
11    JFP    33661    0
12 Yamato    16970    0
13 Corona     6620    0

prop argument is also allowed in summary() function.

summary(obj2, prop = TRUE) # summarize with proportion

    Party      Raw   Dist
1     LDP 0.346551 0.3807
2     NKP 0.123800 0.1364
3     CDP 0.199981 0.2273
4     JCP 0.072496 0.0568
5     JIP 0.140097 0.1477
6     DPP 0.045129 0.0284
7     SDP 0.017725 0.0000
8   Reiwa 0.038556 0.0227
9     NHK 0.013865 0.0000
10    SSN 0.000803 0.0000
11    JFP 0.000586 0.0000
12 Yamato 0.000295 0.0000
13 Corona 0.000115 0.0000

Visualization

{PRcalc} provides plot() method for prcalc object.

plot(obj1)

If the number of blocks is two or more, each block is divided into facets.

plot(obj2)

The angle argument allows rotation of the x-axis scale label; the value of angle must be between 0 and 90.

plot(obj2, angle = 90)

Only some level 2 can be displayed with the subset_l2 argument.

# Output only some parties
plot(obj2, 
     subset_p = c("LDP", "NKP", "CDP", "JIP", "JCP", "DPP"))

It is also possible to display only some level 1 by using the subset_l1 argument.

# Output only some district
plot(obj2, 
     subset_l1 = c("Tokyo", "Kinki"),
     subset_l2 = c("LDP", "NKP", "CDP", "JIP", "JCP", "DPP")) 

If by = "l2", the facet is divided based on level 2 Default is by = "l1" (level 1).

# Divide the facet by parties
plot(obj2, 
     subset_l1 = c("Tokyo", "Kinki"),
     subset_l2 = c("LDP", "NKP", "CDP", "JIP", "JCP", "DPP"),
     by        = "l2")

The number of facet columns can be adjusted with facet_col.

# Three columns
plot(obj2, 
     subset_l1 = c("Tokyo", "Kinki"),
     subset_l2 = c("LDP", "NKP", "CDP", "JIP", "JCP", "DPP"),
     by        = "l2",
     facet_col = 3)

By default, all facets share the same y-axis scale. If you want to use a different scale, set free_y to TRUE.

# Use different y-axis scales for each facet
plot(obj2, 
     subset_l1 = c("Tokyo", "Kinki"),
     subset_l2 = c("LDP", "NKP", "CDP", "JIP", "JCP", "DPP"),
     by        = "l2",
     facet_col = 3,
     free_y    = TRUE)

Comparison

You can compare multiple prcalc ojbects using compare() function. prcalc objects must be grouped in a list structure using list() function.

compare(list(obj2, obj3, obj4))

    Party Model1 Model2 Model3
1     LDP     67     62     63
2     NKP     24     23     24
3     CDP     40     36     36
4     JCP     10     13     13
5     JIP     26     26     26
6     DPP      5      8      7
7     SDP      0      1      1
8   Reiwa      4      7      6
9     NHK      0      0      0
10    SSN      0      0      0
11    JFP      0      0      0
12 Yamato      0      0      0
13 Corona      0      0      0

A named list structure is also available.

list("Jefferson"     = obj2, 
     "Hare-Niemeyer" = obj3, 
     "Webster"       = obj4) |> 
  compare() 

    Party Jefferson Hare-Niemeyer Webster
1     LDP        67            62      63
2     NKP        24            23      24
3     CDP        40            36      36
4     JCP        10            13      13
5     JIP        26            26      26
6     DPP         5             8       7
7     SDP         0             1       1
8   Reiwa         4             7       6
9     NHK         0             0       0
10    SSN         0             0       0
11    JFP         0             0       0
12 Yamato         0             0       0
13 Corona         0             0       0

By using print() function with subset parameter, you can extract subset of the parties.

list("Jefferson"     = obj2, 
     "Hare-Niemeyer" = obj3, 
     "Webster"       = obj4) |> 
  compare() |> 
  print(subset = c("LDP", "NKP", "CDP", "JIP", "JCP", "DPP"))

  Party Jefferson Hare-Niemeyer Webster
1   LDP        67            62      63
2   NKP        24            23      24
3   CDP        40            36      36
4   JCP        10            13      13
5   JIP        26            26      26
6   DPP         5             8       7

If prop = TRUE, the proportion is displayed. It is also available to output tables in HTML format using use_gt = TRUE.

list("Jefferson"     = obj2, 
     "Hare-Niemeyer" = obj3, 
     "Webster"       = obj4) |> 
  compare() |> 
  print(prop = TRUE, use_gt = TRUE)

Party	Jefferson	Hare-Niemeyer	Webster
LDP	0.381	0.352	0.358
NKP	0.136	0.131	0.136
CDP	0.227	0.205	0.205
JCP	0.057	0.074	0.074
JIP	0.148	0.148	0.148
DPP	0.028	0.045	0.040
SDP	0.000	0.006	0.006
Reiwa	0.023	0.040	0.034
NHK	0.000	0.000	0.000
SSN	0.000	0.000	0.000
JFP	0.000	0.000	0.000
Yamato	0.000	0.000	0.000
Corona	0.000	0.000	0.000

Visualization

plot() function is a method of prcalc_compare class. Its return value is ggplot object.

list("Jefferson"     = obj2, 
     "Hare-Niemeyer" = obj3, 
     "Webster"       = obj4) |> 
  compare() |> 
  plot()

If facet = TRUE, the plot is separated by parties.

list("Jefferson"     = obj2, 
     "Hare-Niemeyer" = obj3, 
     "Webster"       = obj4) |> 
  compare() |> 
  plot(facet = TRUE)

If facet = TRUE, you can adjust number of columns and y-axis scale using facet_col and free_y parameters, respectively.

list("Jefferson"     = obj2, 
     "Hare-Niemeyer" = obj3, 
     "Webster"       = obj4) |> 
  compare() |> 
  plot(subset_p = c("LDP", "NKP", "CDP", "JCP", "JIP", 
                    "DPP", "SDP", "Reiwa"),
       facet = TRUE, facet_col = 2, free_y = FALSE)

Customized allocation methods

Although {PRcalc} offers various allocation methods, it may not enough for your needs. In this case you can use fully customizable divisor ("cd"), quota ("cq"), and \(\alpha\)-divergence ("ad").

Custom divisor

For highest averages methods, the number of votes received by each party is divided by the denominator of the determined rule, \(r(k)\). For example, \(k+1\)th divisor of D’Hondt (Jefferson) method is \(r(k) = k + 1\), such as \(1, 2, 3, \dots\). In this case, we can use method = "dt" and we can reproduce this with custom divisors, method = "cd".

The divisor is specified by the extra argument. Since the magnitude is 47 (m = 47), division is performed at most 47 times. Therefore, the length of extra must also be 47 or more. In this case, extra = 1:47.

custom1 <- prcalc(kr_lower_2016_en, m = 47, method = "dt", threshold = 0.03)
custom2 <- prcalc(kr_lower_2016_en, m = 47, method = "cd", threshold = 0.03,
                  extra = 1:47)

list("D'Hondt" = custom1, "Custom divisor" = custom2) |> 
  compare() |> 
  print(use_gt = TRUE)

Party	D'Hondt	Custom divisor
LKP	17	17
DPK	13	13
PP	14	14
JP	3	3
CLP	0	0
MP	0	0
GPK	0	0
PUP	0	0
CDP	0	0

Let’s try a super weird divisor here. It shows the same divisor three times repeatedly before going to the next number. That is, the divisor is c(1, 1, 1, 1, 2, 2, 2, 3, 3, 3, ... , 16, 16, 16), a vector of length 48.

custom3 <- prcalc(kr_lower_2016_en, m = 47, method = "cd", threshold = 0.03,
                  extra = rep(1:16, each = 3))

list("D'Hondt" = custom1, "Weird divisor" = custom3) |> 
  compare() |> 
  print(use_gt = TRUE)

Party	D'Hondt	Weird divisor
LKP	17	18
DPK	13	12
PP	14	14
JP	3	3
CLP	0	0
MP	0	0
GPK	0	0
PUP	0	0
CDP	0	0

If the number of blocks is greater than or equal to 2, the length of extra must be greater than or equal to the maximum value of vector m. For example, if the number of block is 3 and m = c(3, 7, 6), then the length of extra must be greater than or equal to 7.

Custom quota

For largest reminder methods, the first step is to compute quota. For Hare-Niemeyer method, quota is \(\frac{v}{m}\), which \(v\) is total votes and \(m\) is total seats. In 2016 Korean general election (kr_lower_2016_en), the total number of votes cast was 23400107 and the district magnitude was 47. Thus, Hare-Niemeyer quota is \(\frac{23400107}{47} \simeq 497874.6\). This custom quota must be specified with an extra argument.

custom4 <- prcalc(kr_lower_2016_en, m = 47, method = "hn")
custom5 <- prcalc(kr_lower_2016_en, m = 47, method = "cq", extra = 497874.6)

list("Hare" = custom4, "Custom quota" = custom5) |> 
  compare() |> 
  print(use_gt = TRUE)

Party	Hare	Custom quota
LKP	16	16
DPK	12	12
PP	13	13
JP	4	4
CLP	1	1
MP	1	1
GPK	0	0
PUP	0	0
CDP	0	0

The length of extra must be 1 or equal to the number of blocks; if the length of extra is 1, the same quota is applied to all blocks.

custom6 <- prcalc(jp_lower_2021_en, 
                  m      = c(8, 13, 19, 22, 17, 11, 21, 28, 11, 6, 20), 
                  method = "hare")

custom7 <- prcalc(jp_lower_2021_en, 
                  m      = c(8, 13, 19, 22, 17, 11, 21, 28, 11, 6, 20), 
                  method = "cq",
                  extra  = colSums(jp_lower_2021_en[, -1]) / 
                    c(8, 13, 19, 22, 17, 11, 21, 28, 11, 6, 20))

list("Hare" = custom6, "Custom quota" = custom7) |> 
  compare() |> 
  print(use_gt = TRUE)

Party	Hare	Custom quota
LDP	62	62
NKP	23	23
CDP	36	36
JCP	13	13
JIP	26	26
DPP	8	8
SDP	1	1
Reiwa	7	7
NHK	0	0
SSN	0	0
JFP	0	0
Yamato	0	0
Corona	0	0

\(\alpha\)-divergence

\(\alpha\)-divergence (method = "ad") is a highly flexible (not fully customizable) highest averages method. A divisor (\(r(k)\)) is calculated as follow:

\[ r(k) = \begin{cases} \frac{1}{e} \frac{(k + 1)^{k + 1}}{k^k}& \mbox{if}\quad\alpha = 1,\\ \frac{1}{\log{\frac{k + 1}{k}}} & \mbox{if}\quad\alpha = 0,\\ \Bigl(\frac{(k + 1)^\alpha - k^\alpha}{\alpha}\Bigr)^{\frac{1}{\alpha - 1}} & \mbox{otherwise.}\\ \end{cases} \]

For example, if \(\alpha = 2\), the divisor of \(\alpha\)-divergence is known to coincide with that of Sainte-Laguë (Webster). \(\alpha\) must be specified with an extra argument.

# Jefferson vs alpha = 10
list(prcalc(kr_lower_2016_en, m = 47, threshold = 0.03, 
            method = "sl"),
     prcalc(kr_lower_2016_en, m = 47, threshold = 0.03, 
            method = "ad", extra = 2)) |> 
  compare() |> 
  print(use_gt = TRUE)

Party	Model1	Model2
LKP	17	17
DPK	13	13
PP	13	13
JP	4	4
CLP	0	0
MP	0	0
GPK	0	0
PUP	0	0
CDP	0	0