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)

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

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

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. 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

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

Hamilton Electoral Method: II Inconsistency 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, 1.30, 3.60 ) 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

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 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 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 to obtain large representativity and governability. 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 Election 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 Greece, 2009: –PASOK43.90% votes53.33% seats Netherlands, 2010 –VVD20.49% votes20.67% seats Fragmentation: 31 – 30 – 24 – 21 – 15 – 10 – 10 – 5 – Designing electoral systems: properties, thresholds, methods. Application to Sweden

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

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

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

Comparison Usual (non-continuous) vs Continuous thresholds 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

Motivation and some undesirable behavior Analysis Examples Alternative Designing electoral systems: properties, thresholds, methods. Application to Sweden 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. Designing electoral systems: properties, thresholds, methods. Application to Sweden 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% Designing electoral systems: properties, thresholds, methods. Application to Sweden The Swedish electoral system

The allocation of 310 seats among 29 constituencies Party Votes Perma.Proport. Current Social Democrats Moderate Green Liberal Centre Sweden Democrats Left Christian Democrats Total Designing electoral systems: properties, thresholds, methods. Application to Sweden Deficiency of proportionality in the current allotment

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 Stockholms kommun Göteborgs kommun Östergötlands län Skåne läns södra Västra Götalands läns västra Jönköpings län Uppsala län Skåne läns norra och östra Hallands län Gävleborgs län Dalarnas län Örebro län

Designing electoral systems: properties, thresholds, methods. Application to Sweden The final size of constituencies is not proportional ConstituencyElectorsPerman. seatsCurrent seatsProport. 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

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

PartyVotes%Seats 1988 Green 296, Christian Democratic158, Left Party 246, Green Party 185, Green Party 291, Sweden Democrats162, Designing electoral systems: properties, thresholds, methods. Application to Sweden Equity and Threshold

Election Winner party%Votes%SeatsDif. 1982Social Democratic Social Democratic Social Democratic Social Democratic Social Democratic Social Democratic Social Democratic Social Democratic Social Democratic Mean 1.48 Designing electoral systems: properties, thresholds, methods. Application to Sweden 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) 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

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

Designing electoral systems: properties, thresholds, methods. Application to Sweden The size of constituencies using Webster ConstituencyElectorsSeatsConstituencyElectors seats Stockholms län Skåne läns västra Stockholms kommun Värmlands län: Göteborgs kommun Västra Gö. läns norra Östergötlands län Södermanlands län Skåne läns södra Västerbottens län Västra G. läns västra Västra Götal. läns östra: Jönköpings län Norrbottens län Uppsala län Västmanlands län Skåne länsöstra Västernorrlands län Hallands län Kalmar län Gävleborgs län Västra Götala. läns södra Dalarnas län Kronobergs län Örebro län Blekinge län Malmö kommun Jämtlands län Gotlands län

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: The political parties obtained the next number of votes: , ,437435,420524, , , ,333696, (several parties) Then, if we use the 0.5% threshold we would be decreasing the votes: 0.005* =29802 votes , ,407633,390722, , ,304251,303894, 0 (all parties) Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 2010

PartyVotes -0.5%Seats Votes -1% Seats Current Social D , Moderate , Green , Liberal , Center , Sweden D , Left , Kristian D , Designing electoral systems: properties, thresholds, methods. Application to Sweden Continuous Threshold for Sweden, 2010

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

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

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

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

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

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

Biproportional Allotment for Sweden, 2010

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

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