D'Hondt method: Difference between revisions
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Change D'Hondt to d'Hondt per the Oxford Reference: https://www.oxfordreference.com/view/10.1093/oi/authority.20110803095715357. Do some more cleanup and add Phragmén's method.
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m (Change D'Hondt to d'Hondt per the Oxford Reference: https://www.oxfordreference.com/view/10.1093/oi/authority.20110803095715357. Do some more cleanup and add Phragmén's method.) |
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{{Wikipedia}}
The '''d'Hondt method''' or the Jefferson method (both are equivalent, but described differently) is a highest averages method for allocating seats. This system favors large parties slightly more than the other popular [[divisor method]], [[Sainte-Laguë method|Sainte-Laguë]], does. The method described is named in the United States after Thomas Jefferson, who introduced the method for proportional allocation of seats in the United States House of Representatives in 1792, and in Europe after Belgian mathematician Victor
It is used in
==Allocation==
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As a simple example, if there are 2 seats to be filled, with Party A having 300 votes and Party B having 290 votes, then Party A wins the first seat, with their new vote total becoming 150 votes (calculated as 300/((1)+1) = 300/2). This means Party A now has 150 votes and Party B has 290 votes, so Party B wins the second seat, and the procedure is over.
A larger example (<font color="#FF0000">red</font> indicates that party won a seat in that round because it had the most votes of any party in that round; this table can be thought of as going in "rounds", with the first round showing how many votes each party had, and each successive round showing how many votes each party had after applying the
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==Variations==
The Hagenbach-Bischoff system is equivalent to, and is a faster way of doing
In some cases, a [[election threshold|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
== Jefferson's method ==
Jefferson's method is equivalent to
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!State
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== Computational complexity ==
Let <math>s</math> be the number of seats and <math>r</math> be the number of parties. The standard sequential allocation procedure determines the outcome in <math>O(s \log r)</math> time.
== Extensions of theory ==
One of the only ranked PR methods that reduces to
* [[Phragmen's voting rules|Phragmén's method]]
* [[Reweighted Range Voting|Reweighted Range voting]]▼
* [[Sequential proportional approval voting]]
* [[Single distributed vote]]
▲* [[Reweighted Range Voting]]
== Notes ==
Parties can generally guarantee themselves at least as many seats as they would get in
A 10 B 7 C 4 D 3
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etc.
The reason
The divisor in
One easy way to do
== References ==
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