stockholm, may 30-31, 2011 workshop on electoral methods designing electoral systems: properties,...

Stockholm, May 30-31, 2011

Workshop on Electoral Methods

Designing electoral systems: Properties, thresholds, methods.

Application to the Riksdag election in Sweden

Victoriano Ramírez-González

University of Granada (Spain)

[email protected]

http://www.unipi.gr/ems2010

OUTLINE

1. Introduction to electoral systems

2. Properties of an electoral system

3. Continuous thresholds

4. Application to the current electoral system in Sweden

Designing electoral systems: properties, thresholds, methods. Application to Sweden

Properties for a proportional electoral system


• 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.


Introduction to electoral systems

• 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).


Introduction to electoral systems (cont.)

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.


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 A B C D E Votes 433000 340000 240000 142000 45000 Quota 4.33 3.4 2.4 1.42 0.45 Seats 4 3 2 2 1 Hamilton-14 A B C D E Votes 433000 340000 240000 142000 45000 Quota 5.05 3.97 2.8 1.66 0.53 Seats 5 4 3 2 0

Hamilton Electoral Method: II

• Inconsistency


Hamilton-6 A B C Votes 425000 135000 40000 Quota 4.25 1.35 0.40 Seats 4 1 1

Hamilton-2 B C Votes 135000 40000 Quotas 1.54 0.46 Seats 2 0

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, 1.30, 3.60 )

0 1 2 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.


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, …


Jefferson method (also called d’Hondt method)

• Example: To allot 24 seats

• Lower quota.

• It penalizes the fragmentation of the political parties.

• It benefits the large political parties.

990, 430, 400, 270, 180, 80, 50

9.9, 4.3, 4.0, 2.7, 1.8, 0.8, 0.5

*0.0113

11.18, 4.86, 4.52, 3.05, 2.03, 0.90, 0.57 0

11, 4, 4, 3, 2, 0, 0

Votes

Quota

Hondt Votes


Webster method (Sainte-Laguë method)

• Example: To allot 24 seats

• It is impartial.

990, 430, 400, 270, 180, 80, 50

9.9, 4.3, 4.0, 2.7, 1.8, 0.8, 0.5

*0.01

9.9, 4.3, 4.0, 2.7, 1.8, 0.8, 0.5

10, 4, 4, 3, 2, 1, 0

Votes

Quota

Webster Votes


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.


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.


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.


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.


Why Governability?

• Are both representativity and governability mutually self-excluding?

– No, it is possible to obtain large representativity and governability.

• A country must:

– Be well represented.– Enjoy governance.


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).


U.K. 2010-Election

U.K. 2010-Election Political party % votes Seats Conservative 36.1 306 Labour 29.0 258 Liberal Democrat

23.0 57

UKIP 3.1 0 BNP 1.9 0 SNP 1.7 6 Green 1.0 1 Sinn Fein 0.6 5 Democratic Unionist

0.6 8

Plaid Cymru 0.6 3 SDLP 0.4 3 Other parties 2.0 3 100.00 650


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

• Greece, 2009:– PASOK 43.90% votes 53.33% seats

• Netherlands, 2010– VVD 20.49% votes 20.67% seats Fragmentation: 31 – 30 – 24 – 21 – 15 – 10 – 10 – 5 – 2 - 2


Threshold: Proportionality

10 000 20 000 30 000 40 000

10

20

30

40


Usual threshold (non-continuous)

10 000 20 000 30 000 40 000

10

20

30

40

50


Continuous threshold

10 000 20 000 30 000 40 000

10

20

30

40

50


Comparison Usual (non-continuous) vs Continuous thresholds

10 000 20 000 30 000 40 000

10

20

30

40

50


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.


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.


• Motivation and some undesirable behavior

• Analysis

• Examples

• Alternative


Application to the Rikstag election in Sweden

• 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.


Some clarifications

• 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%


The Swedish electoral system

• 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

Total 5 875 385 310 349

349


Deficiency of proportionality in the current allotment


The final size of constituencies is not proportionalConstituency Electors Perman. Seats

310Current 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

264 666 12 13 13

Jönköpings län 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


The final size of constituencies is not proportional

Constituency Electors Perman. seats Current seats Proport. seats

Malmö kommun 214 326 9 10- 11Skåne läns västra 213 580 9 10 10Värmlands län: 213 239 9 12+ 10Västra Götalands läns norra 205 328 9 12+ 10Södermanlands län 204 779 9 11+ 10Västerbottens län 201 902 9 11+ 10Västra Götalands läns östra: 200 322 9 10 10Norrbottens län 194 788 9 9- 10Västmanlands län 192 258 8 11+ 9Västernorrlands län 191 150 8 9 9Kalmar län 184 737 8 9 9Västra Götalands läns södra 144 186 6 6- 7Kronobergs län 138 781 6 6- 7Blekinge län 118 279 5 6 6Jämtlands län 100 144 4 4- 5Gotlands län 46 237 2 2 2

• 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: M.S C FL KD A.S V MP SD

Votes: 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


More votes but fewer seats

Party Votes % Seats

1988 Green 296,935 5.5 20

Christian Democratic 158,182 2.9 0

1991 Left Party 246,905 4.5 16

Green Party 185,051 3.4 0

2006 Green Party 291,121 5.2 19

Sweden Democrats 162,463 2.9 0


Equity and Threshold

Election Winner party %Votes %Seats Dif.

1982 Social Democratic 45.61 47.56 1.95









Mean 1.48


Bonus for the winner party

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)

RepresentativityLocal. YesGlobal. Yes (high)Equity. No (for the threshold)More votes not less seats. Almost Yes

Representativity of the citizens (right size of constituencies) NoSo,

Some undesirable behaviors are possible


• 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)


Alternative


The size of constituencies using WebsterConstituency 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

• 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

votes1797695, 1761964, 407633, 390722, 361002, 309808, 304251, 303894, 0 (all parties)


Continuous Threshold for Sweden, 2010

Party Votes -0.5% Seats Votes -1% Seats CurrentSocial D. 1797695, 112 1767893 115 112Moderate 1761964, 109 1732162 112 107 Green 407633, 25 377831 24 25Liberal 390722, 24 360920 23 24Center 361002, 22 331200 21 23Sweden D. 309808, 19 280006 18 20Left 304251, 19 274449 18 19Kristian D. 303894, 19 274092 18 19 349 349 349





List-2006 Votes Quota % Current -0.5% -1%

Social Democratic Party 1,942,625 122.13 35.0 130 129 133 Moderate Party 1,456,014 91.74 26.2 97 96 98 Center Party 437,389 27.50 7.9 29 28 27 Liberal Party 418,395 26.30 7.5 28 26 25 Christian Democratic Party 365,998 23.01 6.6 24 23 22 Left Party 324,722 20.41 5.8 22 20 19 Green Party 291,121 18.30 5.2 19 18 17 Sweden Democrats 162,463 10.21 2.9 0 9 8




Social Democratic Party 2,062,761 131.59 37.7 138 136 141 Moderate Party 1,199,394 76.51 21.9 80 79 80 Liberal Party 499,356 31.86 9.1 33 32 31 Center Party 465,175 29.67 8.5 31 29 29 Christian Democratic Party 390,351 24.90 7.1 26 24 24 New Democracy 368,281 23.49 6.7 25 23 22 Left Party 246,905 15.75 4.5 16 15 13 Green Party 185,051 11.81 3.4 0 11 9




Social Democratic Party 2,321,826 150.79 43.2 156 156 160 Moderate Party 983,226 63.86 18.3 66 65 66 Liberal Party 655,720 42.59 12.2 44 43 42 Center Party 607,240 39.44 11.3 42 39 39 Left Party Communists 314,031 20.40 5.8 21 19 18 Green Party 296,935 19.28 5.5 20 18 17 Christian Democratic Party 158,182 10.27 2.9 0 9 7




Social Democratic Party 2,533,250 159.17 45.6 166 164 168 Moderate Party 1,313,337 82.52 23.6 86 84 85 Center Party 859,618 54.01 15.5 56 54 55 Liberal Party 327,770 20.59 5.9 21 20 19 Left Party Communists 308,899 19.41 5.6 20 18 17 Christian Democratic Party 103,820 6.52 1.9 0 5 3 Green Party 91,787 5.77 1.7 0 4 2


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

Biproportional Allotment for the 2010 election in Sweden (Threshold: -0.5)


Soc. Mod. Green Lib Cen. SD Left C.D Stockholms l.42 159222 286249 53788 59461 41369 29886 31617 44880 Stock. Ko. 31 111688 183421 65351 45939 33895 16950 39565 28244 Goteborgs 19 80543 96981 34205 26829 12183 15608 27246 19484 Ostergotlands 92164 80141 21225 19017 17561 14862 14242 16357 Skane lans sod 50557 87893 16176 19622 12717 19923 7597 9916 Vastra lans vas 59477 73853 15794 20194 13563 12504 10506 16525 Jonkopings 66316 57901 11438 12134 16859 13888 8775 27822 Uppsala 58862 64750 18993 16878 17838 10003 11845 12265 Skane lans ost. 54529 60930 10195 12677 12871 21312 6113 9420 Hallands 52319 67878 11568 15286 17178 10507 6904 10994 Gavleborgs 67893 41009 10918 9444 12982 12616 12814 7235 Dalamas 67139 44997 10652 8747 14086 12470 10533 7925 Orebro 70818 43791 11846 11415 9807 11136 10311 11235 Malmo 48450 55160 14861 11768 4795 13256 10118 5274 Skane lans vast 49900 58628 9869 13967 8164 17448 5847 6989 Varmlands 68520 45578 9997 10652 13379 8502 10231 8312 Vastra lans norr 56060 46582 12003 13393 11449 10513 9907 11092 Sodermanlands 59463 47889 13065 11299 9850 11370 8637 8095 Vasterbottens 72008 30184 12246 10296 12699 4651 17034 9125 Vastra ostra 57095 47049 9440 10387 13914 9725 8223 11092 Norrbottens 85035 26852 8630 7082 7618 6309 15240 5388 Vastmanlands 58222 43462 9459 12016 8266 9992 9154 7406 Vasternorrlands 70341 34550 8757 8253 11185 7264 9642 6983 Kalmar 55116 41631 8713 7847 13829 8964 7679 9341 Vastra sodra 37817 34334 7315 8883 9273 8350 6136 7745 Kronobergs 35555 34762 7044 6667 11559 7424 5380 7111 Blekinge 6 36520 27387 5289 5431 5771 9830 5075 3973 Jamtlands 5 33013 18193 5339 3155 10487 3122 5340 2340 Gotlands 2 12855 9731 3259 1785 41369 1225 2342 1128 Total seats 112 109 25 24 22 19 19 19


Biproportional Allotment for Sweden, 2010 Soc. Mod. Green Lib Cen. SD Left C.D Total Stockholms lan 10 17 3 3 2 2 2 3 42 Stock. Común 7 11 4 2 2 1 2 2 31 Goteborgs 5 6 2 1 1 1 2 1 19 Ostergotlands 5 5 1 1 1 1 1 1 16 Skane lans sod 3 5 1 1 1 1 0 1 13 Vastra lans vas 3 4 1 1 1 1 1 1 13 Jonkopings 4 3 1 1 1 1 0 2 13 Uppsala 3 4 1 1 1 0 1 1 12 Skane lans ost. 3 3 1 1 1 1 0 1 11 Hallands 3 4 1 1 1 0 0 1 11 Gavleborgs 4 2 1 1 1 1 1 0 11 Dalamas 4 3 1 0 1 1 1 0 11 Orebro 4 2 1 1 0 1 1 1 11 Malmo 3 4 1 1 0 1 1 0 11 Skane lans vast 3 4 1 1 0 1 0 0 10 Varmlands 4 3 0 1 1 0 1 0 10 Vastra lans norr 3 2 1 1 1 0 1 1 10 Sodermanlands 4 3 1 1 0 1 0 0 10 Vasterbottens 4 2 1 1 1 0 1 0 10 Vastra ostra 3 3 0 1 1 1 0 1 10 Norrbottens 6 2 1 0 0 0 1 0 10 Vastmanlands 3 3 0 1 0 1 1 0 9 Vasternorrlands 5 2 0 0 1 0 1 0 9 Kalmar 3 3 0 0 1 1 0 1 9 Vastra sodra 3 2 0 1 0 0 0 1 7 Kronobergs 3 3 0 0 1 0 0 0 7 Blekinge 3 2 0 0 0 1 0 0 6 Jamtlands 3 1 0 0 1 0 0 0 5 Gotlands 1 1 0 0 0 0 0 0 2 Total 112 109 25 24 22 19 19 19 349

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)

RepresentativityLocal. YesGlobal. Yes (high)Equity. YesMore 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)


Conclusions for this alternative

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

[email protected]

stockholm, may 30-31, 2011 workshop on electoral methods designing electoral systems: properties,...

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