Editing D'Hondt method (section)

==Example==
In this example, 230,000 voters decide the disposition of 8 seats among 4 parties. Since 8 seats are to be allocated, each party's total votes are divided by 1, then by 2, 3, and 4 (and then, if necessary, by 5, 6, 7, and so on). The 8 highest entries (in bold text) range from '''100,000''' down to '''25,000'''. For each, the corresponding party gets a seat. Note that in Round 1, the quotient shown in the table, as derived from the formula, is precisely the number of votes returned in the ballot.

{| class="wikitable"
! Round <br/>(1 seat per round)
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! Seats won <br />(bold)
|-
|Party A quotient <br/>seats after round
|'''100,000<br/>1'''
|50,000<br/>1
|'''50,000<br/>2'''
|33,333<br/>2
|'''33,333<br/>3'''
|25,000<br/>3
|25,000<br/>3
|'''25,000<br/>4'''
|'''4'''
|-
|Party B quotient <br/>seats after round
|80,000<br/>0
|'''80,000<br/>1'''
|40,000<br/>1
|'''40,000<br/>2'''
|26,667<br/>2
|26,667<br/>2
|'''26,667<br/>3'''
|20,000<br/>3
|'''3'''
|-
|Party C quotient <br/>seats after round
|30,000<br/>0
|30,000<br/>0
|30,000<br/>0
|30,000<br/>0
|30,000<br/>0
|'''30,000<br/>1'''
|15,000<br/>1
|15,000<br/>1
|'''1'''
|-
|Party D quotient <br/>seats after round
|20,000<br/>0
|20,000<br/>0
|20,000<br/>0
|20,000<br/>0
|20,000<br/>0
|20,000<br/>0
|20,000<br/>0
|20,000<br/>0
|'''0'''
|}

While in this example, parties B, C, and D formed a coalition against Party A: Party A received 3 seats instead of 4 due to the coalition having 30,000 more votes than Party A.
{| class="wikitable"
! Round <br/>(1 seat per round)
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! Seats won <br/>(bold)
|-
|Party A quotient <br/>seats after round
|100,000<br/>0
|'''100,000<br/>1'''
|50,000<br/>1
|'''50,000<br/>2'''
|33,333<br/>2
|'''33,333<br/>3'''
|25,000<br/>3
|25,000<br/>3
|'''3'''
|-
|Coalition B-C-D <br/>quotient seats after <br/>round
|'''130,000<br/>1'''
|65,000<br/>1
|'''65,000<br/>2'''
|43,333<br/>2
|'''43,333<br/>3'''
|32,500<br/>3
|'''32,500<br/>4'''
|'''26,000<br/>5'''
|'''5'''
|}
The chart below shows an easy way to perform the calculation. Each party's vote is divided by 1, 2, 3, or 4 in consecutive columns, then the 8 highest values resulting are selected. The quantity of highest values in each row is the number of seats won.

For comparison, the "True proportion" column shows the exact fractional numbers of seats due, calculated in proportion to the number of votes received. (For example, 100,000/230,000&nbsp;&times;&nbsp;8&nbsp;=&nbsp;3.48) The slight favouring of the largest party over the smallest is apparent.

{|class="wikitable"
! Denominator !! /1 !! /2 !! /3 !! /4 !! Seats <br />won (*) !! True <br/>proportion
|-
| Party A || '''100,000*''' || '''50,000*''' || '''33,333*''' || '''25,000*''' || align="center" | '''4'''
| align="center" | 3.5
|-
| Party B || '''80,000*'''  || '''40,000*''' || '''26,667*''' || 20,000  || align="center" | '''3'''
| align="center" | 2.8
|-
| Party C || '''30,000*'''  || 15,000  || 10,000  || 7,500   || align="center" | '''1'''
| align="center" | 1.0
|-
| Party D || 20,000   || 10,000  || 6,667   || 5,000   || align="center" | '''0'''
| align="center" | 0.7
|-
! colspan=5 | Total
! align="center" | 8
! align="center" | 8
|}

=== Further examples ===
A worked-through example for non-experts relating to the 2019 elections in the UK for the European Parliament written by [[Christina Pagel]] for [[UK in a Changing Europe]] is available.<ref>{{Cite web|url=https://ukandeu.ac.uk/eu-elections-voting-system-explained-dhondt-worry/|title=EU elections voting system explained: D'Hondt worry|date=2019-05-20|website=UK in a changing Europe|access-date=2019-10-06}}</ref>

A more mathematically detailed example has been written by British mathematician Professor [[Helen Wilson (mathematician)|Helen Wilson]].<ref>{{cite web|url=https://www.ucl.ac.uk/~ucahhwi/dhondt.pdf|title=The D’Hondt Method Explained|website=ucl.ac.uk|author=Helen J. Wilson|access-date=23 June 2023}}</ref>