Talk:D'Hondt method

2004 Comments

I don't understand how d'hondt system may be applied in open list system. In fact I believe this is not possible.

May anybody review this? Explaining how is that possible or removing the reference to the use in open lists systems.

I know for a fact that it is possible, because it is used in Finland. Each vote is give to a person who is always on a list. The number of elected candidates in a list is counted as in the closed list system. The people who get elected within a list are the ones who have got the most votes.

Clarification on the issue of ranking candidates on an open-list:

The amounts of "personal" (you only vote for a person, not a list) votes for each candidate are first used to determine each candidates ranking on the individual list. The candidate with the highest amount of pvotes gets first place, the candidate with the second highest second place etc. The votes are then distributed as in a closed-list system, using the order established by the personal votes. This procedure is explained in the linked open-list article, which I think is sufficent for the purposes of this article which mainly describes the method of seat distribution. Rackham 03:16, 19 Nov 2004 (UTC)

d'Hondt method in Estonia

Estonian electoral system is a special case in at least two different ways. Firstly, there is a 5% threshold, but it does not mean that "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". In Estonia, for any candidate, even if appearing on a party list which fails to reach the nationwide threshold, receiving the simple quota in one's electoral district is sufficient for receiving the seat in parliament (in the 1st round of vote counting). It is only in the 2nd (district level) and 3rd round (nationwide, modified d'Hondt method) of vote counting that mandates are awarded only to those candidate lists which have received more than the threshold of 5% of the votes nationally. Secondly, Estonia does not use a "typical d'Hondt system" as the (modified) method is used "only" in the 3rd round of vote counting. However, this does not mean that only very few mandates are allocated according to the d'Hondt system. There are 101 seats in the Estonian parliament and in the past elections the breakdown between the mandates awarded in the 1st, 2nd, and 3rd (" d'Hondt* ") rounds of counting have been the following: in 1992: 17, 24, 60*; in 1995: 15, 34, 52*; in 1999: 11, 44, 46*; and in 2003: 14, 60, 27*.--3 Löwi 16:16, 3 October 2005 (UTC)

Anyone do a fuller explanation?

The example of how the d'Hondt method works isn't really very clear. Perhaps a simpler example could be provided with more step-by-step working? I know this isn't a maths textbook, but I don't see the point of an example at all if it doesn't explain it. El T 08:14, 19 October 2005 (UTC.

EVEN my mother language is not english. I´ll try to explain you which is the approach. The problem related the edited is that the way in that divisors are calculated is wrong. I'll modify the page. But in any case the best external link I have found out is the next one http://www.elecciones.mir.es/web2004mir/menu_izq.htm# the problem is that it is in spanish.

Capitalization?

Is is "D'Hondt" or "d'Hondt" ? 68.39.174.238 20:30, 6 January 2006 (UTC)

Definitely d'Hondt. Wikipedia's design can't handle initial letters being lowercase for some reason. El T 15:17, 7 January 2006 (UTC)

Not so definitely, since he was Belgian and it is a custom there to capitalize the first letter of the first prefix in a surname. Check the text at Victor_D'Hondt. And for all dutch-speaking countries it is true that if the given name is missing, the first letter of the first prefix will be capitalized. Therefore the phrase "the D'Hondt method" should contain a capitalized D also if the name was from the Netherlands. See Dutch_name#Surnames. -- Mipmip 15:47, 10 December 2006 (UTC)

Actually there is some inconsistency here! According to Dutch name#Surnames it should not be capitalized:

"In Flanders tussenvoegsels of personal names always keep their original orthography: mevrouw van der Velde, mevrouw J. van der Velde and Jan Vanden Broucke."

whereas the Victor D'Hondt article states the complete opposite:

"Confusion may arrive when reading Dutch articles on D'Hondt, since in Dutch, when using the full name one should write: Victor d'Hondt (with a small d), while the surname all by itself would be D'Hondt (with a capital D). However, in Flemish it is always capitalized, hence: Victor D'Hondt."

I'm not Flemish, so someone who is should check this and correct one of the two articles :) -- Mipmip 15:55, 10 December 2006 (UTC)

I've changed it to d'Hondt, based on how it's spelled in official Northern Ireland legislation: [1]. That could be wrong, of course, so it can be reversed in that case. William Quill (talk) 12:48, 22 March 2008 (UTC)

Why I've removed the image

I've removed the image because it was not representative. They didn't use proper d'Hont, but a modified version. At Finnish parliamentary election, 2003 you can see a party with more votes has less seats, so it can not be pure d'Hont. --83.36.162.72 00:28, 14 April 2006 (UTC)

The parties are: Swedish People's Party 8 seats, 128,824 votes and Christian Democrats 7 seats 148,987 votes --83.36.162.72 00:32, 14 April 2006 (UTC)

It surely can be a natural consequence of applying D'Hondt in many constituencies; in one constituency such 'reverse' outcome cannot be, but when you add up votes and seats in many constituencies, it can happen.--Bancki 12:49, 16 April 2006 (UTC)

Then, it was not an example of applying d'Hondt, but of adding the resolts of havinf applyed d'Hondt several times... ---81.38.174.231 14:40, 16 April 2006 (UTC)

Just add one more seat to the example in the article, and you'll see party B getting 4 seats, against the 3 seats that party A has.201.29.225.26 (talk) 15:12, 7 February 2009 (UTC)

Proportionality

We have to be careful sayin D'Hondt is less proportional than the Sainte-Laguë method, as there is no standard measure of "disproportionality". This is important to remember when discussing all electoral formulas. D'Hondt is a proportional method, in contrast with say Imperiali methods. - Matthew238 07:40, 6 November 2006 (UTC)

Proportionality

There is a common standard method in Maths to evaluate the deviation of a serial of values against a reference. See the standard deviation function (stdev) in the Excel worksheet. So, instead of using the average value as the reference, one may use the values comming from a proportional division and compare these "good" values againts the "bad" values of method results. So it is possible to measure a quality of a proportional method, in a form accepted anywhere. BUT, in politics, a electoral method is good if it fits the politics agenda. So, the discussion of a good method only using math is too much "theorical" and may be away from the reality.

The Webster method and its equivalent Saint-Lague method are considered the best ones for the proportionality. I have check it for some 50 values using the modified "standard" deviation (square of differences between a proportional representation (integer numbers) and the exact proportional division (real numbers). That sentence seems pretty right. AlvaroAnjo 11:46, 22 December 2006 (UTC)

Indeed, Webster / Sainte-Lague is the most proportionate - that's why it's usually chosen to apportion seats over territorial constituencies. Balynski & Young have written a book about that. However, it has other flaws: a party with >50% of the votes can get <50% of the seats and a party can win a seat by splitting in two (or two parties may loose one by merging) - that's why D'Hondt is usually chosen between parties.--Bancki 13:03, 22 December 2006 (UTC)

An applet

Hello,

it would be really neat to have an external link to an applet demonstrating the d'Hondt method. I myself haven't found one yet.Evilbu 18:58, 30 November 2006 (UTC)

I see there is one behind this Prince Edward Island page, but one would have to rework the java somewhat. Maybe write to them for permission? -- Seejyb 21:54, 30 November 2006 (UTC)

d'Hondt method in Bulgaria

Starting with 2007 european parliament elections in Bulgaria, the d'Hondt method was changed in favor of Largest Reminder Method AlexStanev 12:11, 2 December 2007 (UTC)

Removed text from article

An important result of the method is that a single popular candidate can "draw with him" a lot of lesser-known party colleagues with few personal votes. Also, if the party colleagues with less support fail to pass the threshold, then the elected candidate also represents the failed candidates. For example, candidate B promises to eliminate the dog tax, but is not elected. Then, the votes gained by B benefit party colleague A, who proposes the elimination of dog tax (although not compelled to do so), which was originally B's promise.

I removed the above text from the article as it was uncited, and without some form of citation to explain it seemed to make no sense whatsover. Where do dog taxes come into this? And d'hondt is used in party list systems which, as far as I know, don't ever use individual candidate thresholds. If someone thinks it actually makes sense and can tidy it up, by all means reinsert it, but right now I have no earthly idea what it is the article was actually trying to say. - Chrism would like to hear from you 02:13, 31 March 2009 (UTC)

It seems to refer to single transferable vote. ?Tamfang (talk) 03:43, 31 March 2009 (UTC)

It's not true for single transferable vote -- the other candidates have to get their own votes (even if they're lower down on the ballots of the popular candidate's voters). It seems instead to be referring to the open-ballot scheme discussed above as used in Finland. 150.108.157.180 (talk) 17:41, 4 May 2010 (UTC)

An alternative interpretation of the D'Hont system

The D'Hont system is equivalent to the following statistical criterion. If each party is a bin, and the (normalized to sum=1) number of votes is the probability of a stone to fall in that bin, then the distribution given by the D'Hont system gives the most probable distribution of a given number of stones among the bins. For instance, if there are 2 parties A and B, with 100, and 160 votes respectively, and 4 seats. The D'Hont system predicts A=1 and B=3 seats. In the bin/stones analogy the probability of falling in bin A is p(A)=0.38462 and p(B)=0.61538. Then the probability of falling 1 stone in A, and 3 in B is p(1,3)=pA*pB^3*4!/(1!*3!)=0.35853, whereas for instance the probability of falling 2 in A and 2 in B is p(2,2)=pA^2*pB^2*4!/(2!*2!)=0.33612. So that it is more likely to fall 3 stones in B an 1 in A, than falling 2 in A and 2 in B. In the same way the other possibilities can be computed (A=0 B=4, A=3 B=1,...) and the more likely is A=1, B=3. I can't give a mathematical demonstration for this, but I wrote some Octave programs and tested on a huge number of cases and in it was verified in all cases. I wonder if it is a known fact. I know original research material is not suitable to Wikipedia, but perhaps it is a well known property and someone can point to a reference. Mariostorti (talk) 15:46, 27 September 2009 (UTC)

Pronunciation

Presumably - given the apostrophe - the correct pronunciation of d'Hondt is "Dont" and not "de Hont", although annoyingly the latter pronunciation is consistently used in Northern Ireland. Any sources on how it should be pronounced? Mooretwin (talk) 10:55, 26 January 2010 (UTC)

Government Formation

I'm going to wait a few days for objections first, but I'm liable to remove the paragraph on "government formation", seeing as how the process of government formation in parliamentary systems is entirely independent of the voting system. (If you wanted an relevant "government formation" aspect of d'Hondt, you could describe the assignement of ministry positions in the Northern Ireland agreement. That's not at all what the paragraph in the article refers to, though.) —Preceding unsigned comment added by 150.108.157.180 (talk) 17:44, 4 May 2010 (UTC)

I was going to raise the same issue. I quite agree, and personally (as a Finn) I find it vexing how the media in this country are trying to tell us this is how it works. Government formation is done through negotiations among the parties.--Rallette (talk) 12:46, 7 May 2010 (UTC)

D'Hondt and Jefferson

Applied to the above example of party lists, this extends as integers from 85,001 to 93,333

The example has been changed. 85,001 and 93,333 refer to an older version of this page

Current example

	/1	/2	/3	/4	/5	/6	/7	/8	Seats won (*)
Party A	100,000*	50,000*	33,333*	25,000*	20,000	16,666	14,286	12,500	4
Party B	80,000*	40,000*	26,666*	20,000	16,000	13,333	11,428	10,000	3
Party C	30,000*	15,000	10,000	7,500	6,000	5,000	4,286	3,750	1
Party D	20,000	10,000	6,666	5,000	4,000	3,333	2,857	2,500	0

See http://en.wikipedia.org/w/index.php?title=D%27Hondt_method&oldid=326714515

	Party A	Party B	Party C	Party D	Party E
Votes	340,000	280,000	160,000	60,000	40,000
Percentage of votes	38.6%	31.8%	18.2%	6.8%	4.5%
Seat 1	340,000	280,000	160,000	60,000	40,000
Seat 2	170,000	280,000	160,000	60,000	40,000
Seat 3	170,000	140,000	160,000	60,000	40,000
Seat 4	113,333	140,000	160,000	60,000	40,000
Seat 5	113,333	140,000	80,000	60,000	40,000
Seat 6	113,333	93,333	80,000	60,000	40,000
Seat 7	85,000	93,333	80,000	60,000	40,000
Seat 8	85,000	70,000	80,000	60,000	40,000
Seat 9	68,000	70,000	80,000	60,000	40,000
Total Seats	4	3	2	0	0
Votes per Seat	85,000	93,333	80,000	N/A	N/A
Percentage of seats	44.4%	33.3%	22.2%	0.0%	0.0%

85,001 and 93,333 result from Votes per Seat 85,000 93,333 — Preceding unsigned comment added by 194.79.57.4 (talk) 05:56, 15 October 2013 (UTC)

Denmark, D'Hondt and Sainte-Laguë

I'm wondering whether Denmark should figure on both the list of countries using the D'Hondt method and the Sainte-Laguë method. Denmark uses both D'Hondt (135 seats) and Sainte-Laguë (40 seats) to (s)elect the 175 Danish members of the Folketing as documented by the link to the of the description of the Danish electoral system by the Danish Ministry of Economic Affairs and the Interior (note: As portfolios are often divided and combined, the relevant bit is the Interior, whose civil servants are responsible the organisation of all elections in Denmark, though of course aided by municipal civil servants "on the ground"). I've posted this issue on the talkpage of the Sainte-Laguë method as well (section: "Denmark, D'Hondt and Sainte-Laguë - see the article on D'Hondt"), but prefer any comments/discussions/pro et contra to be posted here so as to keep it simple.

Mojowiha (talk) 09:56, 21 July 2014 (UTC)

Example with 9 seats

I´d like to know what would happen if there are 9 seats instead of 8 in the example, because there´s a tie with 20000 — Preceding unsigned comment added by 80.25.238.87 (talk) 12:06, 30 March 2015 (UTC)

I wondered that, too, so I came over to Talk. I don't see anything in a quick Google search to suggest whether the 9th or 10th seats would go to Parties A, B, or D. I guess that an extension would have to be written in to the law, stating what would happen in the event of a tie. For example, perhaps the Largest Remainder Method takes over. In that case, Party A would have -0.09 remainder, Party B would have 0.13, and Party D would have 0.78. This is based on the new "true proportion" column values (9 seats instead of 8) and the number of seats already awarded to each party at this point. So if that rule was used, Party D would be awarded the seat, which seems fair to me.

Here's the table at the point of deciding who to award to next:

denominator	/1	/2	/3	/4	/5	/6	/7	/8	Seats won (*)	True proportion	Remainder
Party A	100,000*	50,000*	33,333*	25,000*	20,000	16,666	14,286	12,500	4	3.91	-0.09
Party B	80,000*	40,000*	26,666*	20,000	16,000	13,333	11,428	10,000	3	3.13	0.13
Party C	30,000*	15,000	10,000	7,500	6,000	5,000	4,286	3,750	1	1.17	0.17
Party D	20,000	10,000	6,666	5,000	4,000	3,333	2,857	2,500	0	0.78	0.78*

Myrkron (talk) 18:57, 12 July 2016 (UTC)

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Allocation Example is NOT using d'Hondt

The initial description of the d'Hondt calculation is correct, stating, "s is the number of seats that party has been allocated so far, initially 0 for all parties."

But then continues, "The total votes cast for each party in the electoral district is divided, first by 1, then by 2, then 3." The Example grid that follows then uses this method, where ALL parties' vote totals are divided by the same divisor each round.

In d'Hondt, the divisor is only incremented for the winner of each round.

Ref: http://www.europarl.europa.eu/thinktank/en/document.html?reference=EPRS_BRI(2016)580901

The older example on this talk page, with 9 seats and 5 parties, is a correct example.

When the correct d'Hondt method is applied to the current example, the same results are achieved, so this could be an alternate way of making the same calculation, but it's not d'Hondt and definitely does not agree with the equation at the top of the section.

Nlaslett (talk) 02:19, 12 September 2018 (UTC)

I have updated it with a correct example. It was my first edit to Wikipedia so I apologise if there are any mistakes in formatting or anything.

--Taxi For Maicon (talk) 14:21, 18 May 2019 (UTC)

As already stated, not only is the Allocation section not using d'Hondt method (divisors), it is using the formula for a completely different Droop/Hagenbach-Bischoff method (quotas). This is unacceptable and needs to get fixed ASAP. Sources: Taagepera, R., & Shugart, M. S. (1989). Seats and votes: The effects and determinants of electoral systems. New Haven: Yale University Press. (p. 31); Nohlen, D. (1990). Wahlrecht und Parteiensystem. Opladen: Leske Verlag + Budrich GmbH. (p. 81); Lijphart, A. (1994) Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945-1990. New York: Oxford University Press. (p. 155-157, 192); Farrell, D. M. (1997) Comparing Electoral Systems. London: Prentice Hall/Harvester Wheatsheaf. (p. 62-64) — Preceding unsigned comment added by 89.102.172.8 (talk) 23:04, 11 February 2020 (UTC)

Contradiction

This passage would seem to contradict itself:

The D'Hondt method minimizes the number of votes that need to be left aside so that the remaining votes are represented exactly proportionally. Only the D'Hondt method (and methods equivalent to it) minimizes this disproportionality. Empirical studies based on other, more popular concepts of disproportionality show that the D'Hondt method is one of the least proportional among the proportional representation methods.

Does D'Hondt minimize disproportionality—or not?  -- Calion | Talk 14:07, 6 July 2022 (UTC)

s and s

In the Procedure section, the algebraic symbol s is used first for the number of seats won so far by a party and then for the total number of seats to be assigned. Change one or the other, but to what? —Tamfang (talk) 05:17, 17 April 2023 (UTC)