Rev. 13 Dec 25
Still taking shape (and AMS/AMS+ need sorting to match)
Some material copied from Wikidedia and from the senedd.wales website.
The method. [Wiki]“The total votes for each party are counted. Then successive quotients are calculated for each party. The party with the largest quotient wins one seat, and its quotient is recalculated. This is repeated until the required number of seats is filled.”
The quotient for each party thus acts as its current voting weight, which is reduced each time it wins a seat. It is calculated as (Current votes for)[1]÷(1+Number of seats won so far)[2].
History. [Wiki]“The method was first described in 1792 by American Secretary of State (and later President) Thomas Jefferson. It was re-invented independently in 1878 by Belgian mathematician Victor D’Hondt and it is by that name that it is most widely known. In some countries, the system is known by the names of local politicians or experts who introduced them locally. For example, it is known in Israel as the Bader–Ofer system.”
The method, with a range of variations, is used in a large number of countries.[3]
Support. The D’Hondt method has significant support in the UK, for a number of reasons, including that
a) it is so widely used elsewhere[3]
b) it depends on a very simple and very comprehensible calculation
c) it slightly favours the larger parties.
Proportionality and fragmentation. The D’Hondt method approximates proportionality by minimizing the largest seats-to-votes ratio among all parties.
Denmark takes steps to diminish the disproportionality by having a number of separate “leveling seats”.[4]
Other countries go the other way and take steps to limit proportionality so as to decrease fragmentation. In their D’Hondt-based systems they disallow parties with less than a given threshold level of support (typically from 2% to 5%).[5]
Disenfranchisement. In some cases, a party can be excluded from the D’Hondt process, by explicit rule or by mathematical necessity, and thus have its supporters effectively disenfranchised.
a) It can be eliminated from consideration because its support is less than a given threshold, as above.
b) If there are more parties standing than there are seats available, as used to happen in the UK’s elections for the EU Parliament, the smallest parties could not possibly win any seats, and could safely be eliminated from the contest.
c) If at any point there as many remaining parties as remaining seats, and D’Hondt grants a party a second seat, the number of available seats decreases but the number of active parties does not. So at that point we could similarly eliminate the party who could not possibly win a further seat.
Vote transfer. It seems unacceptably undemocratic for voters to be mechanically disenfranchised by the system. Much fairer to transfer the votes that eliminated parties had received to the second choices of those who voted for them.[6] PV is the obvious way of doing that[7].
Note that in the absence of such transfers and because of the consequent fear of disenfranchisement, voters will tend to vote tactically and thus make it even more likely that smaller parties will fail.
[1] Which may progressively increase in a system which includes provision for the tranfer of unsuccessful votes.
[2] In pure D’Hondt this is initially zero for all parties, but in the D’Hondt component of AMS (q.v.) it starts as the number of seats won in the prior local constituency component.
[3] [Wiki]“The D’Hondt method is used to elect the legislatures in Åland, Albania, Angola, Argentina, Armenia, Aruba, Austria, Belgium, Bolivia, Brazil, Burundi, Cambodia, Cape Verde, Chile, Colombia, Croatia, the Dominican Republic, East Timor, Estonia, Fiji, Finland, Greenland, Guatemala, Hungary (in a mixed system), Iceland, Israel, Italy (in a mixed system), Japan, Luxembourg, Moldova, Monaco, Montenegro, Mozambique, Netherlands, Nicaragua, North Macedonia, Paraguay, Peru, Poland, Portugal, Romania, San Marino, Serbia, Slovenia, Spain, Switzerland, Turkey, Uruguay and Venezuela”, and also “in some countries for elections to the European Parliament” (including UK, when a member).
[4] [Wiki]“In Denmark the D’Hondt method is used to elect part of the seats in the Folketing and the disproportionality of the D’Hondt method is corrected with leveling seats with Sainte-Laguë method.” Some reseach needed! Explain just how D’Hondt is disproportional. Explain why the disproportionality is worth being “corrected”. Say what Saint-Laguë is.
[5] [Wiki]“Examples of countries using the D’Hondt method with a threshold are Albania (3% for single parties, 5% for coalitions of two or more parties, 1% for independent individuals); Denmark (2%); East Timor, Spain, Serbia, and Montenegro (3%); Israel (3.25%); Slovenia and Bulgaria (4%); Croatia, Fiji, Romania, Russia and Tanzania (5%); Turkey (7%); Poland (5%, or 8% for coalitions; but does not apply for ethnic-minority parties), Hungary (5% for single party, 10% for two-party coalitions, 15% for coalitions of 3 or more parties) and Belgium (5%, on regional basis).”
But it is not recommended for the UK, even if it has the support of all the larger parties.
[6] Each party eliminated would of course be the one with the lowest quotient (current voting weight). Note that should those votes be transferrable the quotient of other parties will change.
[7] [Wiki]“Modified d’Hondt electoral system. The modified d’Hondt electoral system is a variant of the d’Hondt method with an electoral threshold for parties. Votes for parties below the electoral threshold are transferred to other candidates according to the single transferable voting method. This electoral system was used in 1989 and 1992 Australian Capital Territory elections.”