Workshop on Electoral Methods
Designing electoral systems: Properties,
thresholds, methods.
Application to the Riksdag election in Sweden
Victoriano Ramírez-González
University of Granada (Spain)
vramirez@ugr.es
Stockholm, May 30-31, 2011
OUTLINE
1. Introduction to electoral systems
2. Properties of an electoral system
3. Continuous thresholds
4. Application to the current electoral system in Sweden
Properties for a proportional electoral system
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Introduction to electoral systems
• Size of the Parliament
– No problem in designing an E.S. It can have 300, 500,…seats.
• Constituencies
– Tradition.
– Geographic limitations.
– Gerrymandering is important when there are uninominal districts, but it
is not relevant if the total number of seats of the political parties
depends on their total number of votes.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Introduction to electoral systems (cont.)
• Representation of political parties
– Sometimes it is calculated by applying a proportional method in each
constituency and, when doing so, discordant allotments frequently
emerge.
– In other cases the representation of political parties depends on the total
number of votes of each party. We can cite several examples, such as
Germany, Mexico, Sweden, Greece and Italy (but with different criteria
applied in each country).
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Introduction to electoral systems (cont.)
• Thresholds
– Continuous thresholds are not oftenly used. I consider it is better not setting
thresholds or change.
o Classical thresholds imply obtaining a minimal number of votes or a minimum
percentage of votes. Hence:
• If the minimal is small, then the threshold provide non-practical consequences.
• If the minimal is large, unfair results can be obtained. For example, a change of
one vote can lead to a change in a big number of seats.
– E.g. In Italy, a difference of one vote between two parties leads to a
change of more than 60 seats from one party to another party.
• Therefore, classical thresholds are not logical.
o Moreover, a threshold is continuous if a change of one vote leads to a new
allotment which does not differ more than one seat from the previous allotment, for
any of the political parties.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Hamilton Electoral Method: I
• Alabama paradox
(First, the integer part of their exact proportion (quota) is
assigned to each political party. Then, the distribution is completed by assigning an
additional seat to those political parties with greater remainders)
Hamilton-12
Votes
Quota
Seats
A
433000
4.33
4
B
340000
3.4
3
C
240000
2.4
2
D
142000
1.42
2
E
45000
0.45
1
Hamilton-14
Votes
Quota
Seats
A
433000
5.05
5
B
340000
3.97
4
C
240000
2.8
3
D
142000
1.66
2
E
45000
0.53
0
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Hamilton Electoral Method: II
• Inconsistency
A
425000
4.25
4
B
135000
1.35
1
C
40000
0.40
1
Hamilton-2
Votes
Quotas
Seats
B
135000
1.54
2
C
40000
0.46
0
Hamilton-6
Votes
Quota
Seats
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Divisor Methods
• If we multiply the votes by a factor k, fractions appear. How are
the fractions rounded to integers?
• Example: if V = ( 90, 130, 360 ) and k = 0.01, then we have the
fractions:
k V = ( 0.90,
0
1
1.30,
2
3.60 )
3
4
5
6
Threshold for rounding: 0.8, 1.4, 2.4, 3.1, 4.8, 5.2, ….
0

1

2

3
4

5
6
Rounding: 1, 1, 4. To assign 6 seats this is the solution, but to allocate
only 5 seats then we have to decrease k.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Some Divisor Methods
•
Jefferson (d’Hondt). Rounding down .
The thresholds are: 1, 2, 3, 4, 5, 6, …
•
Webster (Sainte-Laguë). Rounding to the nearest entire number
•
The thresholds are: 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, …
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Jefferson method (also called d’Hondt method)
• Example: To allot 24 seats
Votes   990, 430, 400, 270, 180, 80, 50 
Quota   9.9, 4.3, 4.0, 2.7, 1.8, 0.8, 0.5 
Hondt  Votes *0.0113 
 11.18, 4.86, 4.52, 3.05, 2.03, 0.90, 0.57   0
 11, 4,
4,
3,
2,
0,
0
• Lower quota.
• It penalizes the fragmentation of the political parties.
• It benefits the large political parties.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Webster method (Sainte-Laguë method)
• Example: To allot 24 seats
Votes   990, 430, 400, 270, 180, 80, 50 
Quota   9.9, 4.3, 4.0, 2.7, 1.8, 0.8, 0.5 
Webster  Votes *0.01 
  9.9, 4.3, 4.0, 2.7, 1.8, 0.8, 0.5  
 10, 4,
4,
3,
2,
1, 0 
• It is impartial.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Criteria for choosing an electoral method
•
Desirable properties: Exactness, lower quota, impartial, monotonous, consistency,
punish schisms.
Hamilton
Webster
Hondt
Exacness
yes
yes
yes
Lower Quota
yes
No
yes
Impartial
yes
yes
No
Monotonous
No
yes
yes
Consistency
No
yes
yes
Punish Schisms
No
No
yes
d’Hondt is one of the most recommended methods for allocating seats to
parties. Webster should be used when impartiality is very important.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Properties for an electoral system: I
• Applying acceptable methods of apportionment (consistency, no
paradoxes, exactness, homogeneous, etc.)
– Divisor methods (in general).
– Jefferson for allocating seats to the different political parties.
– Webster when impartiality is required.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Properties for an electoral system: II
Representativity
•
A good representativity involves that an electoral system must meet
the following properties:
– Local representativity (i.e. representation of the most voted parties).
– Global representativity (i.e. high proportionality. For example, more than 95%
with the usual indexes to measure it.).
– Equity. Two political parties with a similar number of votes must be allocated an
equal or almost equal number of seats.
– No discordant allotments.
– Fair representation of voters.
•
Usually several (sometimes even all) of these requirements are not
verified.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Properties for an electoral system: III
• Governability
– Bonus in the representation of the winner party.
• Continuity
– Application of continuous methods to transform votes into seats.
– Application of continuous thresholds.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Why Governability?
• Are both representativity and governability mutually self-excluding?
– No, it is possible
governability.
to
obtain
large
representativity
and
• A country must:
– Be well represented.
– Enjoy governance.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Governance in the current electoral systems
• The vast majority of electoral systems.
• Proportional electoral systems with plenty of small or median
constituencies (many countries).
• Electoral laws (e.g. Italy, Mexico, Greece).
• Large thresholds.
• Exceptions: Israel, Netherlands, Estonia (only one constituency and
small or null threshold).
Designing electoral systems: properties, thresholds, methods. Application to Sweden
U.K. 2010-Election
U.K. 2010-Election
Political party
% votes
Conservative
36.1
Labour
29.0
Liberal
23.0
Democrat
UKIP
3.1
BNP
1.9
SNP
1.7
Green
1.0
Sinn Fein
0.6
Democratic
0.6
Unionist
Plaid Cymru
0.6
SDLP
0.4
Other parties
2.0
100.00
Seats
306
258
57
0
0
6
1
5
8
3
3
3
650
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Some current bonus for the winner
• Italy, 2008:
– Il PDL
37.64% votes
44.08% seats
• Germany, 2005:
– SPD
34.25% votes
40.67% seats
• Spain, 2008:
– PSOE
43.20% votes
48.28% seats
43.90% votes
53.33% seats
• Greece, 2009:
– PASOK
• Netherlands, 2010
– VVD
20.49% votes
20.67% seats
Fragmentation: 31 – 30 – 24 – 21 – 15 – 10 – 10 – 5 – 2 - 2
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Threshold: Proportionality
40
30
20
10
10 000
20 000
30 000
40 000
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Usual threshold (non-continuous)
50
40
30
20
10
10 000
20 000
30 000
40 000
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous threshold
50
40
30
20
10
10 000
20 000
30 000
40 000
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Comparison Usual (non-continuous) vs
Continuous thresholds
50
40
30
20
10
10 000
20 000
30 000
40 000
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Is it possible to meet all the properties
mentioned before?
Yes, it is possible to design electoral systems verifying:
» To apply accpetable methos of apportionment
» High proportionality and representativity (for
parties and voters).
» Bonus for the winner (governability).
» Continuity and equity.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
How?
By using only continuous thresholds.
By allocating the seats to the political parties in several stages and as a
function of its total votes.
By allocation the seats to the constituencies in proportion to the number of
electors
By using a biproportional allotment to determine the number of seats for each
party in each constituency.
In the next section, I apply all this to the Swedish case.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Application to the Rikstag election in Sweden
•
Motivation and some undesirable behavior
• Analysis
• Examples
• Alternative
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Some clarifications
•
First of all, the Swedish electoral system can be
considered as very good.
•
But we are here to try to improve it.
So I am going to show all undesirable behaviors (in my
opinion) that have occurred in the past in the Swedish
electoral system or that may emerge in the future.
•
Finally I will show the results when using the
biproportionality, which I consider to be more
appropriate.
Designing electoral systems: properties, thresholds, methods. Application to Sweden
The Swedish electoral system
• The small alarm as a result of the current allocation
– Deficiency of proportionality in the current distribution.
– The same has happened in several regional parliaments.
• Other undesirable behavior may happen in the future
– The final size of constituencies is not proportional to the citizens called
to vote. A more populous constituency may have fewer representatives
than other less populous one (this occurs in the current distribution).
– A political party with more votes can have fewer representatives.
– The electoral system it is no equitable for two political parties,
both with similar number of votes, one of them having less than
4% of total votes and the other one having more than 4%
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Deficiency of proportionality in the current
allotment
• The allocation of 310 seats among 29 constituencies
Party
Votes
Perma.
Proport.
Current
Social Democrats
1 827 497
112
109
112
Moderate
1 791 766
107
106
107
Green
437 435
19
26
25
Liberal
420 524
17
25
24
Centre
390 804
21
23
23
Sweden Democrats
339 610
14
20
20
Left
334 053
9
20
19
Christian Democrats
333 696
11
20
19
5 875 385
310
349
349
Total
Designing electoral systems: properties, thresholds, methods. Application to Sweden
The final size of constituencies is not proportional
Constituency
Electors
Perman. Seats
310
Current seats
Proport. Seats
349
Stockholms län
850 629
37
38-
42
Stockholms kommun
634 464
28
29-
31
Göteborgs kommun
389 821
17
18-
19
Östergötlands län
330 010
14
15-
16
Skåne läns södra
267 562
12
13
13
Västra Götalands läns
västra
Jönköpings län
264 666
12
13
13
256 538
11
13
13
Uppsala län
253 765
11
13+
12
Skåne läns norra och östra 232 273
10
12+
11
Hallands län
229 891
10
12+
11
Gävleborgs län
217 152
10
12+
11
Dalarnas län
217 072
10
11
11
Örebro län
215 772
9
12+
11
Designing electoral systems: properties, thresholds, methods. Application to Sweden
The final size of constituencies is not proportional
Constituency
Electors
Perman. seats
Current seats
Proport. seats
Malmö kommun
Skåne läns västra
Värmlands län:
Västra Götalands läns norra
Södermanlands län
Västerbottens län
Västra Götalands läns östra:
Norrbottens län
Västmanlands län
Västernorrlands län
Kalmar län
Västra Götalands läns södra
Kronobergs län
Blekinge län
Jämtlands län
Gotlands län
214 326
213 580
213 239
205 328
204 779
201 902
200 322
194 788
192 258
191 150
184 737
144 186
138 781
118 279
100 144
46 237
9
9
9
9
9
9
9
9
8
8
8
6
6
5
4
2
1010
12+
12+
11+
11+
10
911+
9
9
666
42
11
10
10
10
10
10
10
10
9
9
9
7
7
6
5
2
Designing electoral systems: properties, thresholds, methods. Application to Sweden
More votes but fewer seats
•
If in the last elections in Sweden, the Moderate political party would have
obtained some more votes, for example their votes multiplied by the factor
of 1.02 in each of their constituencies, then we would have the following
result:
– The distribution of the 310 seats in 28 constituencies unchanged.
– In Goteborgs Kommun the allot change: Moderate gains a seat and Socialist
loses a seat. We have:
Party:
Votes:
M.S
C
FL
KD
A.S
V
MP
SD
1827601, 390804, 420524, 333696, 1827497, 334053, 437435, 339610
310 seats
108
21
17
11
111
9
19
14
349 seats
108
23
24
19
111
19
25
20
Quota
107.9
23.1
24.8
19.7
107.9
19.7
25.8
20.1
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Equity and Threshold
Party
Votes
%
Seats
Green
296,935
5.5
20
Christian Democratic
158,182
2.9
0
1991
Left Party
Green Party
246,905
185,051
4.5
3.4
16
0
2006
Green Party
Sweden Democrats
291,121
162,463
5.2
2.9
19
0
1988
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Bonus for the winner party
Election Winner party
%Votes
%Seats
Dif.
1982
Social Democratic
45.61
47.56
1.95
1985
Social Democratic
44.68
45.56
0.88
1988
Social Democratic
43.21
44.70
1.49
1991
Social Democratic
37.71
39.54
1.83
1994
Social Democratic
45.25
46.13
0.88
1998
Social Democratic
36.39
37.54
1.15
2002
Social Democratic
39.85
41.26
1.41
2006
Social Democratic
34.99
37.25
2.26
2010
Social Democratic
30.66
32.09
1.43
Mean 1.48
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Conclusions for the current electoral system in
Sweden
Acceptable methods. Hamilton’s method is used in order to allocate
the 310 seats of the Rikstag into the constituencies. Consequently, it is
reasonable to replace this method by Webster’s method.
Governability. Yes (small)
Representativity
Local. Yes
Global. Yes (high)
Equity. No (for the threshold)
More votes not less seats. Almost Yes
Representativity of the citizens (right size of constituencies) No
So,
Some undesirable behaviors are possible
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Alternative
•
To determine the constituencies size using Webster’ method for the
349 seats
• To apply a continuous threshold to determine the representation of
the political parties in proportion to their total votes (Webster’
method is used)
• To apply biproportional method of M. Balinski and G. Demange
(Webster is used)
Designing electoral systems: properties, thresholds, methods. Application to Sweden
The size of constituencies using Webster
Constituency
Electors
Seats
Constituency
Electors
seats
Stockholms län
850 629
42
Skåne läns västra
213 580
10
Stockholms kommun
634 464
31
Värmlands län:
213 239
10
Göteborgs kommun
389 821
19
Västra Gö. läns norra
205 328
10
Östergötlands län
330 010
16
Södermanlands län
204 779
10
Skåne läns södra
267 562
13
Västerbottens län
201 902
10
Västra G. läns västra
264 666
13
Västra Götal. läns östra:
200 322
10
Jönköpings län
256 538
13
Norrbottens län
194 788
10
Uppsala län
253 765
12
Västmanlands län
192 258
9
Skåne länsöstra
232 273
11
Västernorrlands län
191 150
9
Hallands län
229 891
11
Kalmar län
184 737
9
Gävleborgs län
217 152
11
Västra Götala. läns södra
144 186
7
Dalarnas län
217 072
11
Kronobergs län
138 781
7
Örebro län
215 772
11
Blekinge län
118 279
6
Malmö kommun
214 326
11
Jämtlands län
100 144
5
Gotlands län
46 237
2
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous Threshold for Sweden, 2010
• We show two posibilities: 0.5% and 1%
• 0.5% means decreasing the number of votes, for each political
party, in a number equal to 0.5% of the total valid votes obtained by
the parties. So, in the 2010 election the total votes were: 5960408
The political parties obtained the next number of votes:
1827497,
1791766,
437435,
420524,
390804,
339610,
334053,
333696,
85023 (several parties)
Then, if we use the 0.5% threshold we would be decreasing the votes:
0.005*5960408=29802 votes
1797695,
1761964,
407633,
390722,
361002,
309808,
304251,
303894,
0 (all parties)
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous Threshold for Sweden, 2010
Party
Social D.
Moderate
Green
Liberal
Center
Sweden D.
Left
Kristian D.
Votes -0.5%
1797695,
1761964,
407633,
390722,
361002,
309808,
304251,
303894,
Seats Votes -1%
112
1767893
109
1732162
25
377831
24
360920
22
331200
19
280006
19
274449
19
274092
349
Seats
115
112
24
23
21
18
18
18
349
Current
112
107
25
24
23
20
19
19
349
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous Threshold for Sweden, 2006
List-2006
Votes
Quota
Social Democratic Party
1,942,625 122.13
Moderate Party
1,456,014 91.74
Center Party
437,389 27.50
Liberal Party
418,395 26.30
Christian Democratic Party
365,998 23.01
Left Party
324,722 20.41
Green Party
291,121 18.30
Sweden Democrats
162,463 10.21
%
35.0
26.2
7.9
7.5
6.6
5.8
5.2
2.9
Current
-0.5%
-1%
130
97
29
28
24
22
19
0
129
96
28
26
23
20
18
9
133
98
27
25
22
19
17
8
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous Threshold for Sweden, 1991
List-1991
Votes
Quota
%
Social Democratic Party
Moderate Party
Liberal Party
Center Party
Christian Democratic Party
New Democracy
Left Party
Green Party
2,062,761
1,199,394
499,356
465,175
390,351
368,281
246,905
185,051
131.59
76.51
31.86
29.67
24.90
23.49
15.75
11.81
37.7
21.9
9.1
8.5
7.1
6.7
4.5
3.4
Current
-0.5%
-1%
138
80
33
31
26
25
16
0
136
79
32
29
24
23
15
11
141
80
31
29
24
22
13
9
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous Threshold for Sweden, 1988
List-1988
Social Democratic Party
Moderate Party
Liberal Party
Center Party
Left Party Communists
Green Party
Christian Democratic Party
Votes
2,321,826
983,226
655,720
607,240
314,031
296,935
158,182
Quota
150.79
63.86
42.59
39.44
20.40
19.28
10.27
%
43.2
18.3
12.2
11.3
5.8
5.5
2.9
Current
156
66
44
42
21
20
0
-0.5%
-1%
156
65
43
39
19
18
9
160
66
42
39
18
17
7
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Continuous Threshold for Sweden, 1982
List-1982
Votes
Social Democratic Party
2,533,250
Moderate Party
1,313,337
Center Party
859,618
Liberal Party
327,770
Left Party Communists
308,899
Christian Democratic Party
103,820
Green Party
91,787
Quota
%
159.17
82.52
54.01
20.59
19.41
6.52
5.77
45.6
23.6
15.5
5.9
5.6
1.9
1.7
Current
166
86
56
21
20
0
0
-0.5%
-1%
164
84
54
20
18
5
4
168
85
55
19
17
3
2
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Which threshold for Sweden?
• - 0.5% is small
• -1% is more interesting
• -1.5% can be aceptable
• -2% or more can be opposite to the
traditional high representativity in Sweden
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Biproportional Allotment for the 2010 election
in Sweden (Threshold: -0.5)
Stockholms l.42
Stock. Ko. 31
Goteborgs 19
Ostergotlands
Skane lans sod
Vastra lans vas
Jonkopings
Uppsala
Skane lans ost.
Hallands
Gavleborgs
Dalamas
Orebro
Malmo
Skane lans vast
Varmlands
Vastra lans norr
Sodermanlands
Vasterbottens
Vastra ostra
Norrbottens
Vastmanlands
Vasternorrlands
Kalmar
Vastra sodra
Kronobergs
6
Blekinge
5
Jamtlands
2
Gotlands
Total seats
Soc.
Mod.
159222
111688
80543
92164
50557
59477
66316
58862
54529
52319
67893
67139
70818
48450
49900
68520
56060
59463
72008
57095
85035
58222
70341
55116
37817
35555
36520
33013
12855
112
286249
183421
96981
80141
87893
73853
57901
64750
60930
67878
41009
44997
43791
55160
58628
45578
46582
47889
30184
47049
26852
43462
34550
41631
34334
34762
27387
18193
9731
109
Green Lib
53788
65351
34205
21225
16176
15794
11438
18993
10195
11568
10918
10652
11846
14861
9869
9997
12003
13065
12246
9440
8630
9459
8757
8713
7315
7044
5289
5339
3259
25
59461
45939
26829
19017
19622
20194
12134
16878
12677
15286
9444
8747
11415
11768
13967
10652
13393
11299
10296
10387
7082
12016
8253
7847
8883
6667
5431
3155
1785
24
Cen.
SD
Left
C.D
41369
33895
12183
17561
12717
13563
16859
17838
12871
17178
12982
14086
9807
4795
8164
13379
11449
9850
12699
13914
7618
8266
11185
13829
9273
11559
5771
10487
41369
22
29886
16950
15608
14862
19923
12504
13888
10003
21312
10507
12616
12470
11136
13256
17448
8502
10513
11370
4651
9725
6309
9992
7264
8964
8350
7424
9830
3122
1225
19
31617
39565
27246
14242
7597
10506
8775
11845
6113
6904
12814
10533
10311
10118
5847
10231
9907
8637
17034
8223
15240
9154
9642
7679
6136
5380
5075
5340
2342
19
44880
28244
19484
16357
9916
16525
27822
12265
9420
10994
7235
7925
11235
5274
6989
8312
11092
8095
9125
11092
5388
7406
6983
9341
7745
7111
3973
2340
1128
19
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Biproportional Allotment for Sweden, 2010
Soc.
Stockholms lan
Stock. Común
Goteborgs
Ostergotlands
Skane lans sod
Vastra lans vas
Jonkopings
Uppsala
Skane lans ost.
Hallands
Gavleborgs
Dalamas
Orebro
Malmo
Skane lans vast
Varmlands
Vastra lans norr
Sodermanlands
Vasterbottens
Vastra ostra
Norrbottens
Vastmanlands
Vasternorrlands
Kalmar
Vastra sodra
Kronobergs
Blekinge
Jamtlands
Gotlands
Total
10
7
5
5
3
3
4
3
3
3
4
4
4
3
3
4
3
4
4
3
6
3
5
3
3
3
3
3
1
112
Mod.
17
11
6
5
5
4
3
4
3
4
2
3
2
4
4
3
2
3
2
3
2
3
2
3
2
3
2
1
1
109
Green Lib
3
4
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
25
3
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
24
Cen.
2
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
22
SD
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
19
Left
C.D
2
2
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
19
3
2
1
1
1
1
2
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
19
Total
42
31
19
16
13
13
13
12
11
11
11
11
11
11
10
10
10
10
10
10
10
9
9
9
7
7
6
5
2
349
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Conclusions for this alternative
Acceptable methods. Yes
(it uses only Webster method and it is
monotonous, consistent, and homogeneous)
Governability. Yes (lower, similar as the current, i.e. small bonus to the
winner)
Representativity
Local. Yes
Global. Yes (high)
Equity. Yes
More votes not less seats. Yes
Representativity of the citizens. Yes (proport. constituencies size)
The biproportional allotment:
Easily obtained with hand-held calculator. NO
(We always need a computer and a program like BAZI)
Designing electoral systems: properties, thresholds, methods. Application to Sweden
Designing electoral systems: properties, thresholds,…
Application to the Riksdag election in Sweden
Thank you very much for your attention!
Tack så mycket för er uppmärksamhet!
Prof. Dr. Victoriano Ramírez-González
vramirez@ugr.es