# Hagenbach-Bischoff method

The Hagenbach-Bischoff procedure is a method of proportional representation ( seat allocation procedure ), as it is used for B. in elections with the principle of proportional representation (see proportional representation ) is required to convert votes into members of parliament. The Hagenbach-Bischoff method is an algorithm of the D'Hondt method developed by the Swiss physicist Eduard Hagenbach-Bischoff (1833–1910) . This type of description of the D'Hondt process can be found u. a. in the Swiss Federal Law on Political Rights ( SR 161.1, Art. 40 et seq.), which applies to the National Council elections . Due to its calculation steps, according to which, as with the quota procedure, in the first step each party is allocated seats according to their rounded quota and then the remaining seats are allocated, it is also known as the quasi-quota procedure.

1. Step: basic distribution
The number of all valid votes cast in the election is divided by the number of seats to be allocated + 1. The result, increased to the nearest whole number, forms the distribution number (also called the election number ). Each party or list is allocated as many seats as the distribution number is contained in its number of votes as an integer . The following applies to the number of seats for a party:
${\ displaystyle {\ text {number of seats}} = \ left \ lfloor {\ frac {\ text {number of votes}} {\ left \ lfloor {\ frac {\ text {total number of votes}} {{\ text {total number of seats}} + 1 }} + 1 \ right \ rfloor}} \ right \ rfloor}$ 2. Step: If there is still a seat available:
The quotient is calculated for each party and the next seat is assigned to the party with the highest quotient (maximum number).${\ displaystyle \ textstyle {\ frac {\ text {number of votes}} {{\ text {seats already allocated}} + 1}}}$ 3. Step: If there is still a seat available, the 2nd step is repeated.

etc.

## example

Accepted election result:

Zu verteilende Sitze: 10

Partei  Stimmen
A      4160
B      3380
C      2460


Step 1: basic distribution

Distribution number = (4160 + 3380 + 2460) / (10 + 1) = 10000/11 rounded up = 910

(In the case of an integer quotient, this is increased by 1.)

A: 4160/910 nach unten gerundet = 4
B: 3380/910 nach unten gerundet = 3
C: 2460/910 nach unten gerundet = 2


In other words, in the first step 4 + 3 + 2 = 9 mandates are distributed.

Step 2: Calculate the maximum numbers for the next seat

A:  4160/5 = 832
B:  3380/4 = 845 (*)
C:  2460/3 = 820


The next (last) seat is given to party B.

Verteilung: 4 - 4 - 2