Editing Additional-member system (section)

== How AMS works ==
[[File:Two vote seat linkage.png|thumb|The AMS uses two votes and compensation is done by taking into account seats won in FPTP districts. This makes the AMS a seat linkage based mixed electoral system.|left]]In an election using the additional member system, each voter casts two votes:<ref>{{Cite web|url=https://commonslibrary.parliament.uk/research-briefings/sn04458/|title=Voting systems in the UK - House of Commons Library}}</ref> a vote for a candidate standing in their local constituency (with or [[independent candidate|without]] an affiliated party), and a vote for a [[party list]] standing in a wider region made up of multiple constituencies (or a single nationwide constituency). In Scotland [[List MP|list members]] ("top-up" seats) are elected by region; in London there is a single London-wide pooling of list votes.

Voters are not required to vote for the same party in the constituency and regional votes. If a voter votes for different parties at the constituency and regional levels this is referred to as [[split-ticket voting]]. In the regional vote, the voter votes for a specific party, but has no control over which candidates from the party are elected. On the other hand, in the constituency vote, the voter votes for a specific candidate rather than a party.{{Cn|date=August 2024}}

=== Counting votes and allocating seats ===
The first vote is used to elect a member from their constituency under the [[First-past-the-post voting|"first-past-the-post"]] first-preference plurality (FPP) system (i.e. in the constituency, the candidate with the most votes takes the seat).

The second vote is used to determine how many additional seats a party may get, which is based on how many seats a party should get in total. Parties receive additional seats to match the vote shares they received as close as possible, making the legislature more representative of voters' preferences.

In the model of the AMS as used in the United Kingdom, the regional seats are divided using a [[D'Hondt method]]. However, the number of seats already won in the local constituencies is taken into account in the calculations for the list seats,<ref>{{Cite web|url=https://www.parliament.uk/about/how/elections-and-voting/voting-systems/|title=Voting systems in the UK - UK Parliament}}</ref> and the first average taken in account for each party follows the number of FPTP seats won. For example, if a party won 5 constituency seats, then the first D'Hondt divisor taken for that party would be 6 (5 seats + 1), not 1. In [[South Korea]], which uses the [[largest remainder method]], constituency seats are taken into account by subtracting the number of constituency seats that the party won from the number of seats initially won by the party proportionally (over all seats).<ref>{{Cite web|date=2020-04-15|title=How Does South Korea's New Election System Work?|url=https://keia.org/the-peninsula/how-does-south-koreas-new-election-system-work/|access-date=2021-11-20|website=Korea Economic Institute of America|language=en}}</ref>

==== Example ====
In a 100 seat assembly 70 members are elected in single-member constituencies. Because the system generally favours the largest party and those parties/candidate that are strong in a particular region, the total result of the constituency (FPP) elections can be very disproportional. In this example, the party with a [[Plurality (voting)|plurality]] in the popular vote (party A) won a majority of all seats (54), while the second largest party (B) only won 11 districts. One of the two smaller parties (party C) won no districts, despite having 13% support nationwide, but a smaller (regional) party with only 3% nationally did get 5 of their candidates elected, as their voters were concentrated in those constituencies.
{| class="wikitable"
! colspan="2" |Party
!Popular vote (%)
!Constituency seats
!Additional seats
!Total seats
!Constituency seats
|-
| style="background:#D10000" |
|Party A
|'''43%'''
|'''54'''
| ?
| ?
| rowspan="5" |[[File:AMS fptp seats.svg|frameless]]
|-
| style="background:#0008A5" |
|Party B
|'''41%'''
|'''11'''
| ?
| ?
|-
| style="background:#03AA00" |
|Party C
|'''13%'''
|'''0'''
| ?
| ?
|-
| style="background:#820084" |
|Party D
|'''3%'''
|'''5'''
| ?
| ?
|-
|
|TOTAL
|100%
|70
|30
|100
|}
In the example, additional seats are assigned on a nationwide level. Parties A and D are already overrepresented, so they are not entitled to additional seats. Parties B and C receive top-up seats, as there are only 30, this is not enough to make the results proportional. 
{| class="wikitable"
! colspan="2" |Party
!Popular vote (%)
!Constituency seats
!Additional seats
!Total seats
!Overhang seats
!Seats deficit
!Additional seats
!Total seats
|-
| style="background:#D10000" |
|Party A
|43%
|54
|'''0'''
|'''54'''
| +11
|
| rowspan="5" |[[File:AMS additional seats.svg|frameless]]
| rowspan="5" |[[File:AMS total seats.svg|frameless]]
|-
| style="background:#0008A5" |
|Party B
|41%
|11
|'''23'''
|'''34'''
|
|7
|-
| style="background:#03AA00" |
|Party C
|13%
|0
|'''7'''
|'''7'''
|
|6
|-
| style="background:#820084" |
|Party D
|3%
|5
|'''0'''
|'''5'''
| +2
|
|-
|
|TOTAL
|100%
|70
|30
|100
|13
|
|}

==== Compared to similar systems ====
If the 30 additional seats in the example were allocated independently by list-PR the system would be called [[parallel voting]] or a ''supplementary member'' system. This would be a [[Mixed-member majoritarian representation|mixed-member majoritarian]] system (MMM), under which even party A received additional seats, even though it is overrepresented even without getting any.

Some systems called [[Mixed-member proportional representation|mixed-member proportional systems]] (MMP), like the ones used for electing the national parliament [[New Zealand]], at least partially compensate for [[overhang seats]] as well, by adding back that many seats to the assembly if needed, but this is not a perfect correction for the disproportionality. In [[Germany]] formerly even [[Leveling seat|more seats]] were adding to the Bundestag, to get fully proportional results, but as per the latest reform, parties simply may not keep overhang seats, meaning they might not be able to keep all constituency seats they "won" in.

In this example, the assembly size would be increased by 13 seats to compensate for parties B and C's seat deficits under the New Zealand type 'MMP', and by 65 (which allows parties A, B and C to receive more seats) under a flexible amount of additional leveling seats.

The additional member system might provide [[proportional representation]] when there are no overhang seats that would need to be compensated; in this case it would have the same outcome as other 'MMP' systems, if the results of the FPTP elections were completely proportional (which is almost never the case in reality). If decoy lists and tactical voting were used (see below), the results under the AMS would be the same as under parallel voting.

In all other cases the AMS is more proportional than parallel voting, but sometimes less proportional than 'MMP' in New Zealand.
{| class="wikitable"
! colspan="4" rowspan="3" |
! colspan="2" rowspan="2" |Constituency seats only
([[First-past-the-post voting|FPTP]])
! colspan="2" |[[Mixed-member majoritarian representation|Mixed-member majoritarian]]
! colspan="6" |Broadly [[Mixed-member proportional representation|mixed-member proportional]] type of system (MMP)
|-
! colspan="2" |[[Parallel voting]] 
(supplementary member system)
! colspan="2" |Additional member system (AMS)
! colspan="2" | Overhang seats re-added
! colspan="2" | True MMP (with leveling seats)
|-
| colspan="2" |[[File:AMS fptp seats.svg|frameless]]
| colspan="2" |[[File:AMS example parallel total seats.svg|frameless]]
| colspan="2" |[[File:AMS total seats.svg|frameless]]
| colspan="2" |[[File:AMS example MMP overhang only total seats.svg|frameless]]
| colspan="2" |[[File:AMS example MMP total seats.svg|frameless]]
|-
! colspan="2" |Party
!Popular vote (%)
!Constitu&shy;encies won
!Seats
!Share (%)
!Seats
!Share (%)
!Seats
!Share (%)
!Seats
!Share (%)
!Seats
!Share (%)
|-
| style="background:#D10000" |
|Party A
|43%
|54
|54
|77%
|67 (54+13)
|67%
|54 (54+0)
|54%
|54 (54+0+0)
|48%
|71 (54+0+17)
|43%
|-
| style="background:#0008A5" |
|Party B
|41%
|11
|11
|16%
|24 (11+13)
|24%
|34 (11+23)
|34%
|41 (11+23+7)
|36%
|68 (11+23+34)
|41%
|-
| style="background:#03AA00" |
|Party C
|13%
|0
|0
|0%
|3 (0+3)
|3%
|7 (0+7)
|7%
|13 (0+7+6)
|12%
|21 (0+7+14)
|13%
|-
| style="background:#820084" |
|Party D
|3%
|5
|5
|7%
|5 (5+0)
|5%
|5 (5+0)
|5%
|5 (5+0+0)
|4%
|5 (5+0+0)
|3%
|-
|
|TOTAL
|100%
|70
|70
|100%
|100 (70+30)
|100%
|100 (70+30)
|100%
|113 (70+30+13)
|100%
|165 (70+30+65)
|100%
|-
| colspan="4" |Index of disproportionality
([[Gallagher index|Gallagher]])
| colspan="2" |31.55 (highly disproportional)
| colspan="2" |22.01 (disproportional)
| colspan="2" |10.25 (moderately disproportional)
| colspan="2" |4.97 (considered proportional)
| colspan="2" |0.25 (highly proportional)
|-
| colspan="4" |'''Method used'''
| colspan="2" |Only first-past-the-post
| colspan="2" |Independent PR tier
| colspan="2" |Fixed number of compensatory seats
| colspan="2" |Number of (extra) leveling seats = 
number of overhang seats
| colspan="2" |As many leveling seats as needed
|-
| colspan="4" |'''This type of system used in'''
| colspan="2" |United Kingdom, among others
| colspan="2" |Russia, among others
| colspan="2" |Scotland, London
| colspan="2" |New Zealand, Germany (until 2009)
| colspan="2" |Germany (2013, 2017)
|}

=== Threshold ===
{{see also|Election threshold}}

As in many systems containing or based upon [[party-list]] representation, in order to be eligible for list seats in some AMS models, a party must earn at least a certain percentage of the total party vote, or no candidates will be elected from the party list. Candidates having won a constituency will still have won their seat. In almost all elections in the UK there are no thresholds except the "effective threshold" inherent in the regional structure. However the elections for the [[London Assembly]] have a threshold of 5% which has at times denied seats to the [[Christian Peoples Alliance]] (in [[2000 London Assembly election|the 2000 election]]), the [[British National Party]], [[Respect – The Unity Coalition]] (both in [[2004 London Assembly election|the 2004 election]]), and the [[Women's Equality Party]] (in [[2016 London Assembly election|the 2016 election]]).