Distribution of Federal Council Seats in Switzerland

There will be federal election in Switzerland in 2015 and one of the hot topics is already how the seven seats of the federal council will be distributed. According to Wikipedia

The Federal Council is the seven-member executive council which constitutes the federal government of Switzerland and serves as the Swiss collective head of state. While the entire council is responsible for leading the federal administration of Switzerland, each Councillor heads one of the seven federal executive departments.

By informal agreement, the so called magic formula, the seats of the of the federal council are distributed between the four largest party as follows:

In Swiss politics, the magic formula is an arithmetic formula for dividing the seven executive seats of the Swiss Federal Council between the four ruling parties. The formula was first applied in 1959. It gave the Free Democratic Party (now FDP.The Liberals), the Christian Democratic People's Party and the Social Democratic Party each two seats, while the Party of Farmers, Traders and Independents (now the Swiss People's Party) received one seat.The formula is not an official law, but rather an agreement amongst the rather large coalition of four parties. 

It has been suggested to modify the magic formula as follows:

• Allocation of two seats each to the largest three parties and one seat to the fourth largest party
• Allocation of the seats according to proportional allocation rules to all parties

In a previous post we discussed the different forms of proportional allocation rules and will no apply these to the Swiss federal council allocation. For this calculation we use the data from October 3, 2014 as published here:

The parties have been allocated to left (L), center (C) and right (R) and grossed-up to 100% (the difference to 100% is made up by a dozen of small and very small party votes):

Note than in Swiss politics the term "liberal" has the classical liberal (say Hayekian) connotation and not the US usage for left parties.

For the quota methods all four (actually three because Droop and Hagenbach-Bischoff quota are identical because of the large number of votes) yield the same allocation of seats, 2 to the left, 2 to the center and 3 to the right, details below:

For H-B and Imperiali the seats are fully allocated without the need to use the largest remainder (actually the Imperiali quota almost results on a overallocation of seats, a well known potential problem). The the Hare quota the one unallocated seat goes to the centter where the largest remainder is highest (0.79 versus 0.11 and 0.10).

For the divisor methods the calculation results as follows, also in all cases resulting in the same allocation, 3 to the right, 2 to the center and 2 to the left.

We will repeat the calculation for the individual parties in a future post, in which case there will be differences between the different methods.

It should also be noted that the magic formula is a broad agreement of the large parties for proportional representation in the federal council, but specifics have never been agreed, including

• voting threshold (four largest parties, 4% of votes, 5% of votes, none)
• apparentment to three blocks (apparentment is typical is Swiss voting systems, but generally only for the legislative)