Editing Party-list proportional representation (section)

== Apportionment of party seats ==
Many variations on seat allocation within party-list proportional representation exist. Different [[Apportionment (politics)|apportionment methods]] may favor smaller or larger parties:<ref>{{cite web |last=Benoit |first=Kenneth |title=Which Electoral Formula Is the Most Proportional? A New Look with New Evidence |url=http://polmeth.wustl.edu/analysis/vol/8/PA84-381-388.pdf |url-status=dead |archive-url=https://web.archive.org/web/20100624102008/http://polmeth.wustl.edu/analysis/vol/8/PA84-381-388.pdf |archive-date=2010-06-24}}</ref>

* [[D'Hondt method]] (biased towards large parties)<ref>{{cite web |last=Wilson |first=Helen J. |title=The D'Hondt Method Explained |url=http://www.ucl.ac.uk/~ucahhwi/dhondt.pdf}}</ref>
* [[Sainte-Laguë method]] (roughly unbiased)
* [[Huntington–Hill method]] (roughly unbiased)
* [[Method of smallest divisors|Adams method]] (biased towards small parties)
* [[Hare quota|LR-Hare]] (roughly unbiased)
* [[Droop quota|LR-Droop]] (biased towards large parties)

The apportionment methods can be classified into two categories:

* The [[highest averages method]] (or divisor method), including the [[D'Hondt method]] (Jefferson method) is used in [[Armenia]], [[Austria]], [[Brazil]], [[Bulgaria]], [[Cambodia]], [[Croatia]], [[Estonia]], [[Finland]], [[Poland]], and [[Spain]]; and the [[Webster/Sainte-Laguë method|Sainte-Laguë method]] (Webster method) is used in [[Indonesia]], [[New Zealand]], [[Norway]], and [[Sweden]].
* The [[Largest remainder method|largest remainder (LR) methods]], including the Hamilton (Hare) method and Droop method.

While the allocation formula is important, equally important is the district magnitude (number of seats in a constituency). The higher the district magnitude, the more proportional an electoral system becomes, with the most proportional results being when there is no division into constituencies at all and the entire country is treated as a single constituency.{{Citation needed|date=August 2021}} In some countries the electoral system works on two levels: [[at-large]] for parties, and in constituencies for candidates, with local party-lists seen as fractions of general, national lists. In this case, magnitude of local constituencies is irrelevant, seat apportionment being calculated at national level.

List proportional representation may also be combined with other apportionment methods in various mixed systems, using either [[Additional member system|additional member systems]] or [[parallel voting]].

=== Example ===
Below it can be seen how different apportionment methods yield different results when apportioning 100 seats.

Webster's method yields the same result (though this is not always the case). Otherwise, all other methods give a different number of seats to the parties.

Notice how the D'Hondt method breaks the [[quota rule]] (shown in red text) and favors the largest party by "rounding" an ideal apportionment of 35.91 up to 37.

Adams' method greatly favors smaller parties, giving 2 seats to the smallest party, and would give at least 1 seat to every party receiving at least one vote.
{| class="wikitable"
|+
! rowspan="3" |Party
! rowspan="3" |Votes
! rowspan="3" |[[Entitlement (fair division)|Entitlement]]
! colspan="2" |Largest remainders
! colspan="4" |Highest averages
|-
!Hare
!Droop quota
!D'Hondt (Jefferson)
!Sainte-Laguë (Webster)
!Huntington-Hill
!Adams
|-
!<math>\frac{\text{votes}}{\text{seats}}</math>
!<math>\frac{\text{votes}}{\text{seats}+1}</math>
!<math>\frac{\text{votes}}{\text{seats}+1}</math>
!<math>\frac{\text{votes}}{\text{seats}+0.5}</math>
!<math>\frac{\text{votes}}{\sqrt{\text{seats}(\text{seats}+1)}}</math>
!<math>\frac{\text{votes}}{\text{seats}}</math>
|-
!A
|1017
|'''35'''.91
| style="background:#dfd" |36
| style="background:#dfd" |36
| style="color:red; background:#dfd" | '''37'''
| style="background:#dfd" |36
| style="background:#dfd" |36
|35
|-
!B
|1000
|'''35'''.31
|35
| style="background:#dfd" |36
| style="background:#dfd" |36
|35
|35
| style="background:#fdd; color:red" |'''34'''
|-
!C
|383
|'''13'''.52
| style="background:#dfd" |14
|13
|13
| style="background:#dfd" |14
|13
| style="background:#dfd" |14
|-
!D
|327
|'''11'''.55
| style="background:#dfd" |12
| style="background:#dfd" |12
|11
| style="background:#dfd" |12
| style="background:#dfd" |12
| style="background:#dfd" |12
|-
!E
|63
|'''2'''.22
|2
|2
|2
|2
|2
| style="background:#dfd" |3
|-
!F
|42
|'''1'''.48
|1
|1
|1
|1
| style="background:#dfd" | 2
| style="background:#dfd" | 2
|-
!'''''Total'''''
!'''''2832'''''
!'''''100 seats'''''
!'''''100'''''
!'''''100'''''
!'''''100'''''
!'''''100'''''
!'''''100'''''
!'''''100'''''
|}

=== Electoral threshold ===
{{Main|Electoral threshold}}