D'Hondt method

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The d'Hondt method is a method for allocating seats in party-list proportional representation. This system favors large parties slightly more than the other popular divisor method, Sainte-Laguë, does.

It is used in: Argentina, Austria, Bulgaria, Chile, Denmark (for local elections), Finland, Israel, the Netherlands, Poland, Portugal and Spain, as well as elections to the European Parliament in some countries. The method is named after Belgian mathematician Victor d'Hondt.

Allocation

After all the votes have been tallied, successive quotients are calculated for each list. The formula for the quotient is V/(s+1), where V is the total number of votes that list received, and s is the number of seats that party has been allocated so far (initially 0 for all parties). Whichever list has the highest quotient gets the next seat allocated, and their quotient is recalculated given their new seat total. The process is repeated until all seats have been allocated.

The order in which seats allocated to a list are then allocated to individuals on the list is irrelevant to the allocation procedure. It may be internal to the party (a closed list system) or the voters may have influence over it through various methods (an open list system).

The rationale behind this procedure (and the Sainte-Laguë procedure) is to allocate seats in proportion to the number of votes a list received, by maintaining the ratio of votes received to seats allocated as close as possible. This makes it possible for parties having relatively few votes to be represented.

Example

Party A
Party B
Party C
Party D
Party E
Votes
340,000
280,000
160,000
60,000
15,000
Seat 1
340,000
280,000
160,000
60,000
15,000
Seat 2
170,000
280,000
160,000
60,000
15,000
Seat 3
170,000
140,000
160,000
60,000
15,000
Seat 4
113,333
140,000
160,000
60,000
15,000
Seat 5
113,333
140,000
80,000
60,000
15,000
Seat 6
113,333
93,333
80,000
60,000
15,000
Seat 7
85,000
93,333
80,000
60,000
15,000
Total Seats
3
3
1
0
0

Variations

In some cases, a threshold or barrage is set, and any list which does not receive that threshold will not have any seats allocated to it, even if it received enough votes to otherwise have been rewarded with a seat. Examples of countries using this threshold are Israel (1.5%) and Belgium (5%, on regional basis).

Some systems allow parties to associate their lists together into a single cartel in order to overcome the threshold, while some systems set a separate threshold for cartels. Smaller parties often form pre-election coalitions to make sure they get past the election threshold.

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