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D'hondt Method
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The system was also used in Northern Ireland for allocating the ministerial positions in the Northern Ireland Executive .


ALLOCATION


After all the votes have been tallied, successive quotients or 'averages' are calculated for each list. The formula for the quotient is rac{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 in a list only ballot, but includes the number of seats already won where combined with a separate ballot, as happens in Wales and Scotland).


Whichever list has the highest quotient or average 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 (2%), Turkey (10%), and Belgium (5%, on regional basis). In The Netherlands , a party must win enough votes for one full seat (note that this is not necessary in plain D'Hondt), which with 150 seats in the lower chamber gives an effective threshold of 0.67%. In Estonia , candidates receiving the simple quota in their electoral districts are considered elected, but in the second (district level) and third round of counting (nationwide, modified d'Hondt method) mandates are awarded only to candidate lists receiving more than the threshold of 5% of the votes nationally.

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 Coalition s to make sure they get past the election threshold. In the Netherlands, cartels ''(lijstverbindingen)'' cannot be used to overcome the threshold, but they do influence the distribution of remainder seats; thus, smaller parties can use them to get a chance which is more like that of the big parties.

The d'Hondt method can also be used in conjunction with a quota formula to allocate most seats, applying the d'Hondt method to allocate any remaining seats to get a result identical to that achieved by the standard d'Hondt formula. This variation is known as the Hagenbach-Bischoff System, and is the formula frequently used when a country's electoral system is referred to simply as 'd'Hondt'.