Games - D'Hondt method

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	Games - D'Hondt method

The D'Hondt method is a highest averages method for allocating seats in party-list proportional representation. Argentina, Austria, Belgium, Bulgaria, Chile, Colombia, Croatia, Finland, Israel, Japan, the Netherlands, Poland, Portugal, Scotland, 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 favors large parties slightly more than the other popular divisor method, Sainte-Laguë, does. 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.

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 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

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