1. 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) vramirez@ugr.es

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

3. 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

4. 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.)

5. Thresholds –Continuous thresholds are not oftenly used. I consider it is better not setting thresholds or change. oClassical 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. oMoreover, 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

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

7. Hamilton Electoral Method: II Inconsistency Designing electoral systems: properties, thresholds, methods. Application to Sweden

8. 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, …. 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

9. 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

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

11. Webster method (Sainte-Laguë method) Example: To allot 24 seats It is impartial. Designing electoral systems: properties, thresholds, methods. Application to Sweden

12. 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

13. 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

14. 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

15. 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

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

17. 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

18. U.K. 2010-Election Designing electoral systems: properties, thresholds, methods. Application to Sweden

19. 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: –PASOK43.90% votes53.33% seats Netherlands, 2010 –VVD20.49% votes20.67% seats Fragmentation: 31 – 30 – 24 – 21 – 15 – 10 – 10 – 5 – 2 - 2 Designing electoral systems: properties, thresholds, methods. Application to Sweden

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

21. Usual threshold (non-continuous) Designing electoral systems: properties, thresholds, methods. Application to Sweden

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

23. Comparison Usual (non-continuous) vs Continuous thresholds Designing electoral systems: properties, thresholds, methods. Application to Sweden

24. 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

25. 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

26. Motivation and some undesirable behavior Analysis Examples Alternative Designing electoral systems: properties, thresholds, methods. Application to Sweden Application to the Rikstag election in Sweden

27. 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 Some clarifications

28. 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 The Swedish electoral system

29. The allocation of 310 seats among 29 constituencies Party Votes Perma.Proport. Current Social Democrats 1 827 497112 109 112 Moderate 1 791 766107 106107 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 Designing electoral systems: properties, thresholds, methods. Application to Sweden Deficiency of proportionality in the current allotment

30. Designing electoral systems: properties, thresholds, methods. Application to Sweden The final size of constituencies is not proportional ConstituencyElectors Perman. Seats 310 Current seats Proport. Seats 349 Stockholms län 850 629 3738-42 Stockholms kommun 634 464 2829-31 Göteborgs kommun 389 821 1718-19 Östergötlands län 330 010 1415-16 Skåne läns södra 267 562 1213 Västra Götalands läns västra 264 666 1213 Jönköpings län 256 538 1113 Uppsala län 253 765 1113+12 Skåne läns norra och östra 232 273 1012+11 Hallands län 229 891 1012+11 Gävleborgs län 217 152 1012+11 Dalarnas län 217 072 1011 Örebro län 215 772 912+11

31. Designing electoral systems: properties, thresholds, methods. Application to Sweden The final size of constituencies is not proportional ConstituencyElectorsPerman. seatsCurrent seatsProport. seats Malmö kommun 214 326 910-11 Skåne läns västra 213 580 910 Värmlands län: 213 239 912+10 Västra Götalands läns norra 205 328 912+10 Södermanlands län 204 779 911+10 Västerbottens län 201 902 911+10 Västra Götalands läns östra: 200 322 910 Norrbottens län 194 788 99-10 Västmanlands län 192 258 811+9 Västernorrlands län 191 150 899 Kalmar län 184 737 899 Västra Götalands läns södra 144 186 66-7 Kronobergs län 138 781 66-7 Blekinge län 118 279 566 Jämtlands län 100 144 44-5 Gotlands län 46 237 222

32. 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 Designing electoral systems: properties, thresholds, methods. Application to Sweden More votes but fewer seats

33. PartyVotes%Seats 1988 Green 296,935 5.5 20 Christian Democratic158,1822.9 0 1991 Left Party 246,9054.5 16 Green Party 185,0513.4 0 2006 Green Party 291,1215.2 19 Sweden Democrats162,4632.9 0 Designing electoral systems: properties, thresholds, methods. Application to Sweden Equity and Threshold

34. Election Winner party%Votes%SeatsDif. 1982Social Democratic 45.6147.561.95 1985Social Democratic 44.6845.560.88 1988Social Democratic 43.2144.701.49 1991Social Democratic 37.7139.541.83 1994Social Democratic 45.2546.130.88 1998Social Democratic 36.3937.541.15 2002Social Democratic 39.8541.261.41 2006 Social Democratic 34.9937.252.26 2010 Social Democratic 30.6632.091.43 Mean 1.48 Designing electoral systems: properties, thresholds, methods. Application to Sweden Bonus for the winner party

35. 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

36. 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 Alternative

37. Designing electoral systems: properties, thresholds, methods. Application to Sweden The size of constituencies using Webster ConstituencyElectorsSeatsConstituencyElectors 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

38. 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

39. PartyVotes -0.5%Seats Votes -1% Seats Current Social D.1797695,1121767893115 112 Moderate1761964,1091732162112 107 Green 407633, 25 377831 24 25 Liberal 390722, 24 360920 23 24 Center 361002, 22 331200 21 23 Sweden D. 309808, 19 280006 18 20 Left 304251, 19 274449 18 19 Kristian D. 303894, 19 274092 18 19 349349 349 Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 2010

40. Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 2006

41. Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 1991

42. Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 1988

43. Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 1982

44. 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

45. Biproportional Allotment for the 2010 election in Sweden (Threshold: -0.5) Designing electoral systems: properties, thresholds, methods. Application to Sweden

46. Biproportional Allotment for Sweden, 2010

47. 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 Conclusions for this alternative

48. 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