Sa., Okt. 21st 2023
Behind the scenes of the elections, mathematics plays an important role. Once all votes have been cast, a mathematical formula decides who gets a seat in the National Council.
In the election to the National Council, it is not just the number of votes that is relevant, but also the exact distribution of seats among the parties.
How exactly the calculation is made is defined in the Federal Law on Political Rights. “The number of valid party votes of all lists is divided by the number of mandates to be allocated increased by one. The next higher whole number is called the distribution number. Each list is allocated as many mandates as the distribution number is contained in its number of votes,” is explained in paragraph 40.
This procedure is called the Hagenbach-Bischoff procedure, named after the Basel physicist Eduard Hagenbach-Bischoff (1833 -1910), who developed it.
The first and most complicated step in the process is the calculation of the so-called distribution number. For this, all votes cast in the election for all candidates are added together. This number is divided by the number of seats to be allocated plus one. For the canton of Zurich, for example, with its 36 National Council seats, this would mean that the total number of votes would be divided by 37. The whole is then rounded up to the next highest whole number.
If you add percentages to this formula, you can also use it to calculate what percentage of the votes a party must receive to win a seat in the National Council. In the canton of Zurich, this is around three percent; in the canton of Basel-Stadt, with its four seats, 20 percent of the vote is needed for a National Council seat.
The distribution figure then acts as a key for the allocation of seats. For each party, it is determined how often the distribution number fits into the number of votes received. The number of votes received by a party is therefore divided by the distribution number. If parties are connected by list connections, the votes of the parties are added together for this calculation. Excess votes are forfeited.
As a rule, not all seats are allocated in this procedure, so further calculation steps are required until all mandates have been allocated. To do this, the parties’ vote totals are divided by the number of seats already allocated to them plus one. The party with the highest result wins the next seat. This procedure is repeated until all seats have been allocated.
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