# Additional-member system

The additional-member system (AMS) is a two-vote seat-linkage-based mixed electoral system used in the United Kingdom in which most representatives are elected in single-member districts (SMDs), and a fixed number of other "additional members" are elected from a closed list to make the seat distribution in the chamber more proportional to the votes cast for party lists. It is distinct from using parallel voting for the list seats (also known as the supplementary-member system) in that the "additional member" seats are awarded to parties taking into account seats won in SMDs (referred to as compensation or top-up) – these are ignored under parallel voting (a non-compensatory method).
AMS is the name given to a particular system used in the United Kingdom that aims to provide proportional representation. However, in theory it can fail to be proportional, a situation called a seat overhang. In practice, the proportionality of AMS depends on the number of additional ("top-up") seats and the votes cast in a specific election. In parts of the United Kingdom where it is or was used, it has produced results closer to mixed-member proportional rather than mixed-member majoritarian representation.
This article focuses on the use of the AMS in the United Kingdom. The AMS is used to elect the Scottish Parliament (in a regionalized top-up system) and the London Assembly (with at-large top-up seats), and up until the 2026 election, the Senedd in Wales.

## How AMS works

In an election using the additional member system, each voter casts two votes: a vote for a candidate standing in their local constituency (with or 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 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.

### Counting votes and allocating seats

The first vote is used to elect a member from their constituency under the "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, 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).

#### 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 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.
| Party | Popular vote (%) | Constituency seats | Additional seats | Total seats |
| Party A | 43% | 54 | ? | ? |
| Party B | 41% | 11 | ? | ? |
| Party C | 13% | 0 | ? | ? |
| 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.
| Party | Popular vote (%) | Constituency seats | Additional seats | Total seats | Overhang seats | Seats deficit |
| Party A | 43% | 54 | 0 | 54 | +11 | |
| Party B | 41% | 11 | 23 | 34 | | 7 |
| Party C | 13% | 0 | 7 | 7 | | 6 |
| 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 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 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 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.
| | | | | Constituency seats only (FPTP) | Constituency seats only (FPTP) | Mixed-member majoritarian | Mixed-member majoritarian | Broadly mixed-member proportional type of system (MMP) | Broadly mixed-member proportional type of system (MMP) | Broadly mixed-member proportional type of system (MMP) | Broadly mixed-member proportional type of system (MMP) | Broadly mixed-member proportional type of system (MMP) | Broadly mixed-member proportional type of system (MMP) |
| | | | | Constituency seats only (FPTP) | Constituency seats only (FPTP) | Parallel voting (supplementary member system) | Parallel voting (supplementary member system) | Additional member system (AMS) | Additional member system (AMS) | Overhang seats re-added | Overhang seats re-added | True MMP (with leveling seats) | True MMP (with leveling seats) |
| Party | Party | Popular vote (%) | Constitu­encies won | Seats | Share (%) | Seats | Share (%) | Seats | Share (%) | Seats | Share (%) | Seats | Share (%) |
| | Party A | 43% | 54 | 54 | 77% | 67 (54+13) | 67% | 54 (54+0) | 54% | 54 (54+0+0) | 48% | 71 (54+0+17) | 43% |
| | Party B | 41% | 11 | 11 | 16% | 24 (11+13) | 24% | 34 (11+23) | 34% | 41 (11+23+7) | 36% | 68 (11+23+34) | 41% |
| | Party C | 13% | 0 | 0 | 0% | 3 (0+3) | 3% | 7 (0+7) | 7% | 13 (0+7+6) | 12% | 21 (0+7+14) | 13% |
| | 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% |
| Index of disproportionality (Gallagher) | Index of disproportionality (Gallagher) | Index of disproportionality (Gallagher) | Index of disproportionality (Gallagher) | 31.55 (highly disproportional) | 31.55 (highly disproportional) | 22.01 (disproportional) | 22.01 (disproportional) | 10.25 (moderately disproportional) | 10.25 (moderately disproportional) | 4.97 (considered proportional) | 4.97 (considered proportional) | 0.25 (highly proportional) | 0.25 (highly proportional) |
| Method used | Method used | Method used | Method used | Only first-past-the-post | Only first-past-the-post | Independent PR tier | Independent PR tier | Fixed number of compensatory seats | Fixed number of compensatory seats | Number of (extra) leveling seats = number of overhang seats | Number of (extra) leveling seats = number of overhang seats | As many leveling seats as needed | As many leveling seats as needed |
| This type of system used in | This type of system used in | This type of system used in | This type of system used in | United Kingdom, among others | United Kingdom, among others | Russia, among others | Russia, among others | Scotland, London | Scotland, London | New Zealand, Germany (until 2009) | New Zealand, Germany (until 2009) | Germany (2013, 2017) | Germany (2013, 2017) |

### 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 the 2000 election), the British National Party, Respect – The Unity Coalition (both in the 2004 election), and the Women's Equality Party (in the 2016 election).

## Definitions and variations of AMS
### AMS vs. MMP

AMS is used by some as another term to mean the broadly same type of system called mixed-member proportional representation (MMP) in New Zealand. As the term additional member system is used here, AMS is unlike some MMP systems more true to its name, because it does not compensate for the disproportionate results caused by a party taking so many district seats that the fixed number of top-up seats cannot compensate. Such is the case where the leading party takes overhang seats and the legislature has a fixed number of seats. In 'true' MMP systems, leveling seats (extra additional members) are filled in such a way as to ensure parties have proportional representation, but not in the AMS as used in the UK.
Due to the problem of district contests electing too many members for leading parties (overhang), the AMS systems discussed here, instead of producing fully proportional results, often produce only semi-proportional representation. However, even semi-proportional representation is a considered by some a great advance on an electoral system that uses only the first-past-the-post voting system, where the number of seats a party takes only vaguely reflects the number of votes that party receives.
The term additional member system, as introduced by the Hansard Society, has been confused in the literature with the term mixed member proportional representation (in the broader sense) coined by New Zealand's Royal Commission on the Electoral System (1984–1986). The term AMS has been conflated also with parallel voting, which is not a compensatory system and in New Zealand was offered under the name supplementary member system. AMS has also been used to mean any system with additional members (both parallel voting and compensatory systems), therefore any two-tiered mixed system with first-past-the-post and additional list members. This is also why some unconventional systems, such as scorporo have also occasionally been described as 'additional member systems', although with compensatory systems this was also reinforced by the conflation of compensatory mixed systems and mixed-member proportional representation in general.

### Variations of AMS

The Arbuthnott Commission recommended that Scotland change to a model where the voter can vote for a specific regional candidate as well (called an open list), but this has not been implemented. A similar system is used in Bavaria, where the second vote is not simply for the party but for one of the candidates on the party's regional list and both votes count for party and candidates so that every vote counts twice (Bavaria uses seven regions for this purpose). In Baden-Württemberg there are no lists; they use the "best near-winner" method (Zweitmandat) in a four-region model, where the regional members are the local candidates of the under-represented party in that region who received the most votes in their local constituency without being elected in it, but this model has not been copied in the United Kingdom.
To produce more proportional results without increasing the number of seats in the chamber, reforms might include changing the way district members are elected. If STV or SNTV is used, the district elections are likely to be more proportional than if districts seats are filled through first-preference plurality (FPP), and thus the available top-up seats could be used to produce more proportional overall chamber composition.

## Strategic manipulation and tactical voting
### Decoy lists

So-called "decoy lists" are a trick to unhinge the compensation mechanisms contained into the proportional part of the AMS, so to de facto establish a parallel voting system.
Although a theoretical possibility, decoy lists are not used in Scotland, Wales, or other places using AMS in the UK, where most voters vote for candidates from parties with long-standing names. In the run up to the 2007 Scottish election, the Labour party had considered not fielding list candidates in the Glasgow, West of Scotland, and Central Scotland regions, as their constituency strength in the previous two elections had resulted in no list MSPs; instead they proposed to support a list composed of Co-operative Party candidates. Before this the Co-operative party had chosen not to field candidates of its own but merely to endorse particular Labour candidates. However the Electoral Commission ruled that as membership of the Co-operative party is dependent on membership of the Labour party they could not be considered distinct legal entities.
In contrast, in the 2007 Welsh Assembly election, Forward Wales had its candidates (including sitting leader John Marek) stand as independents, to attempt to gain list seats they would not be entitled to if Forward Wales candidates were elected to constituencies in the given region. However the ruse failed: Marek lost his seat in Wrexham and Forward Wales failed to qualify for any top-up seats.
In the 2021 Scottish Parliament election, former SNP leader, Alex Salmond announced his leadership of the newly formed Alba Party, with the stated aim of winning list seats for pro-independence candidates. At the party's public launch, Salmond quoted polling suggesting the SNP would receive a million votes in the forthcoming election but win no regional seats. He said that having Alba candidates on the regional lists would end the "wasted votes", and the number of independence supporting MSPs could reach 90 or more.

## Use

The AMS is used in some elections in the United Kingdom
* Scotland: the Scottish Parliament
* London: the London Assembly
In 1976, the Hansard Society recommended that a mixed electoral system in a form different from the German be used for UK parliamentary elections, but instead of using closed party lists, it proposed that seats be filled by the "best runner-up" basis used by the German state of Baden-Württemberg, where the compensatory seats are filled by the party's defeated candidates who were the "best near-winner" in each of the state's four regions. It was the way that compensatory seats were allocated that made their report the origin of the additional member system, the term which the report also invented, which was then applied along with the much older "mixed system" by English-speaking writers on voting systems to West Germany's system and similar models until the term mixed member proportional (MMP) was coined for the adoption of the German system proposed for New Zealand in a royal commission report in 1986, which would explain why "AMS" and "MMP" have been used as synonyms. The system the Hansard Society proposed was eventually adopted but with closed lists instead of the "best runner-up" (popularly known in Britain as "best losers") provision for elections to the Scottish Parliament, the Senedd and the London Assembly, but not for that proposed for elections to the House of Commons.
This system was proposed by the Independent Commission in 1999, known as Alternative vote top-up (AV+). This would have involved the use of the Alternative Vote for electing members from single-member constituencies, and regional open party lists. However, contrary to the Labour Party's earlier manifesto promises, no referendum was held before the 2001 general election and the statement was not repeated.
The AMS system in use in the London Assembly would have been used for the other proposed regional assemblies of England, but after the overwhelming No vote in the 2004 North East England devolution referendum, the Government abolished all the regional assemblies in 2008-2010.

### Scotland

Scottish Parliament Election Study 1999 and Scottish Social Attitudes Survey 2003 :
| % answering correctly |||
| Question (and correct response) | 1999 | 2003 |
| You are allowed to vote for the same party on the first and second vote (True) | 78% | 64% |
| People are given two votes so that they can show their first and second preferences (False) | 63% | 48% |
| No candidate who stands in a constituency contest can be elected as a regional party list member (False) | 43% | 33% |
| Regional party list seats are allocated to try to make sure each party has as fair a share of seats as is possible (True) | 31% | 24% |
| The number of seats won by each party is decided by the number of first votes they get (False) | 30% | 26% |
| Unless a party wins at least 5% of the second vote, it is unlikely to win any regional party lists seats (True) | 26% | 25% |
| Average | 45% | 37% |
The system implemented for the Scottish Parliament is known to make it more difficult for any one party to win an outright majority, compared to the first-past-the-post system used for general elections to the UK Parliament in Westminster. However, in 2011, the Scottish National Party won 69 seats, a majority of four.
In the first election for Scotland's new Parliament, the majority of voters surveyed misunderstood some key aspects of the difference there between the "first" (constituency) vote and the "second" (regional list) vote; indeed in some ways the understanding worsened in the second election.
The Arbuthnott Commission found references to first and second votes fueled a misconception that the constituency vote should be a first preference and the regional vote a second one.
To deal with the misunderstanding between "first" and "second" votes, the ballot for the 2007 Scottish Parliament election was changed as recommended by the Arbuthnott Commission. The British government announced on 22 November 2006 that the two separate ballot papers used in the previous Scottish Parliament elections would be replaced for the elections in May 2007 by a single paper, with the left side listing the parties standing for election as regional MSPs and the right side the candidates standing as constituency MSPs.