Additional-member system

The first vote is used to elect a member from their constituency under the first past the post (FPTP) 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. Parties receive additional seats to match the voting percentages which they received, making the legislature more representative of voters' preferences.

In the model of AMS 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 list votes a party got with the number of FPTP seats it won, with the result then being divided by 2.[4]

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 FPTP 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	Constituency 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	Additional seats	Total seats
	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

If the 30 additional seats in the example were allocated independently by list-PR the system would be called parallel voting or a supplementary vote system. This would be a mixed-member majoritarian system, under which even party A received additional seats, even though it is overrepresented even without getting any.

Mixed-member proportional systems, like the ones used for electing the national parliaments of Germany and New Zealand, compensate for overhang seats as well, by adding seats to the assembly if needed. In the most basic implementation, like that used in New Zealand (and until 2013, also in Germany), only the parties with a seat deficit are given the additional seats, and only to compensate for their deficit, which is not a perfect correction for the disproportionality. An implementation with leveling seats, like the one used in Germany from 2013, adds even more additional seats (called leveling seats) to the assembly to ensure full proportionality.

In this example, the assembly size is increased by 13 to compensate for parties B and C's seat deficits under the basic implementation, and by 65 (which allows parties A, B and C to receive more seats) under the leveling seats implementation.

The additional member system sometimes provides proportional representation (when there are no overhang seats that would need to be compensated), in which case it the same as MMP, if the results of the FPTP elections were completely proportional (which is almost never the case in reality). If decoy-lists and tactical voting are used (see below) the results under AMS would be the same as under parallel voting.

In all other cases AMS is more proportional than parallel voting, but less proportional than MMP.

			Parallel voting (MMM)		Additional member system (AMS)		Mixed-member proportional (MMP)
							with overhang seats only		with overhang and leveling seats
Party		Popular vote (%)	Seats	Share (%)	Seats	Share (%)	Seats	Share (%)	Seats	Share (%)
	Party A	43%	67 (54+13)	67%	54 (54+0)	54%	54 (54+0+0)	48%	71 (54+0+17)	43%
	Party B	41%	24 (11+13)	24%	34 (11+23)	34%	41 (11+23+7)	36%	68 (11+23+34)	41%
	Party C	13%	3 (0+3)	3%	7 (0+7)	7%	13 (0+7+6)	12%	21 (0+7+14)	13%
	Party D	3%	5 (5+0)	5%	5 (5+0)	5%	5 (5+0+0)	4%	5 (5+0+0)	3%
	TOTAL	100%	70+30	100%	70+30	100%	70+30+13	100%	70+30+65	100%

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).

AMS was also incorrectly used as another term to mean mixed-member proportional representation (MMP),[5] but (as the term additional member system is used here) AMS, unlike some MMP systems, does not compensate for the disproportionate results caused by a leading 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 some MMP systems, leveling seats (extra additional members) are filled in such a way as to ensure parties have proportional representation.

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 a 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 by the term mixed member proportional representation (in the broader sense) coined by New Zealand's Royal Commission on the Electoral System (1984–1986).[6]

Ways to make the UK elections using AMS more proportional are discussed below. Also discussed are ways for voters to cast votes for individual candidate and not just for parties. The MMP systems used in Bavaria and elsewhere in Germany are discussed below for example.

The Scottish elections are divided into two tiers.

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 past the post, and thus the available top-up seats could be used to produce more proportional overall chamber composition.

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.

For instance in the 2001 Italian general election, where a system in many respects similar to AMS was used, one of the two main coalitions (the House of Freedoms coalition, which opposed the scorporo system) linked many of their constituency candidates to a decoy list (liste civetta) in the proportional parts, under the name Abolizione Scorporo. As a defensive move, the other coalition, Olive Tree, felt obliged to do the same, under the name Paese Nuovo. The constituency seats won by each coalition would not reduce the number of proportional seats they received. Between them, the two decoy lists won 360 of the 475 constituency seats, more than half of the total of 630 seats available, despite winning a combined total of less than 0.2% of the national proportional part of the vote. In the case of Forza Italia (part of the House of Freedoms), the tactic was so successful that it did not have enough candidates in the proportional part to receive as many seats as it in fact won, missing out on 12 seats.

Although a theoretical possibility, decoy lists are not used in Scotland, Wales, or most other places using AMS, 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.

For the 2020 South Korean legislative election the electoral system was changed and a partial use of AMS was implemented. In response, there were two satellite parties that only ran in the proportional part, the Future Korea Party (controlled by the United Future Party) and the Platform Party (controlled by the Democratic Party of Korea). Both merged with the parent party after the election.

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.[7]

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.[10] However, in 2011, the Scottish National Party won 69 seats, a majority of four.[11]

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 fuelled a misconception that the constituency vote should be a first preference and the regional vote a second one. That misconception was not helped by the Green Party's tactic of running only regional candidates and appealing for "second votes".

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.