# D'Hondt method

The D'Hondt method (equivalent to Jefferson's method) is a highest averages method for allocating seats in party-list proportional representation. Argentina, Austria, Belgium, Bulgaria, Chile, Colombia, Croatia, Czech Republic, Ecuador, Finland, Hungary, Iceland, Israel, Japan, Macedonia, Netherlands, Paraguay, Poland, Portugal, Scotland, Serbia, Slovenia, Spain, Turkey and Wales are among the places that use this allocation system, as do elections to the European Parliament in some countries. This system is less proportional than the other popular divisor method, Sainte-Laguë, because D'Hondt slightly favors large parties and coalitions over scattered small parties, whereas Sainte-Laguë is neutral. The method is named after Belgian mathematician Victor D'Hondt.

The system was also used in Northern Ireland for allocating the ministerial positions in the Northern Ireland Executive. A modified form was used for elections in the Australian Capital Territory Legislative Assembly but abandoned in favour of the Hare-Clarke system. It was used during the 1997 Constitution-era for allocating party-list parliamentary seats in Thailand.<ref>Aurel Croissant and Daniel J. Pojar, Jr., Quo Vadis Thailand? Thai Politics after the 2005 Parliamentary Election, Strategic Insights, Volume IV, Issue 6 (June 2005)</ref>

## Allocation

After all the votes have been tallied, successive quotients or 'averages' are calculated for each list. The formula for the quotient is $\frac{V}{s+1}$, 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

## D'Hondt and Jefferson

The d'Hondt method is equivalent to the Jefferson method (named after the U.S. statesman Thomas Jefferson) in that they always give the same results, but the method of calculating the apportionment is quite different. The latter, invented in 1792 for U.S. congressional apportionment rather than elections, uses a quota as in the Largest remainder method but the quota (called a divisor) is adjusted as necessary so that the resulting quotients, disregarding any fractional remainders, sum to the required total (so the two methods share the additional property of not using all numbers, whether of state populations or of party votes, in the apportioning of seats). One of a range of quotas will accomplish this, and applied to the above example of party lists this extends as integers from 85,001 to 93,333, the highest number always being the same as the last average to which the d'Hondt method awards a seat if it is used rather than the Jefferson method.

## 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 coalitions 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'.