Voting Systems: Additional Member System / Mixed Member Proportional explained
using the Scottish parliament as an example
The Additional Member System (AMS) (also known as Mixed Member Proportional or MMP) is the voting system used to elect the Scottish Parliament, the Welsh Senedd, and the London Assembly.
Variations of the same system are also used in other countries, including elections to Germany's Bundestag, and New Zealand's parliament. Outside the UK, AMS is usually referred to as Mixed Member Proportional.
I'll describe the system as it is implemented in Scotland, then I will talk about differences in how it is used elsewhere. I’ll also discuss problems with AMS, and how they might be fixed.
AMS in Scotland
The Scottish Parliament has 129 members. To elect them, Scotland is divided into 8 electoral regions. Each electoral region elects 9 constituency MSPs and 7 list MSPs (the exception being North East Scotland, which has 10 constituency seats).
Each constituency seat is elected in a FPTP election. The 7 list seats are top-up seats allocated to the parties to make the result more proportional.
Note that a party might win more list seats than they would get proportionally considering both constituency and list seats together. For example, a party might win 40% of the vote and win all 9 constituency seats. Then they would hav 9/16 = 56.25% of the total seats. This is called an overhang.
How to vote in Scottish AMS elections
Here is a ballot paper from the 2007 election in Banff and Buchan:
To vote you put an X in one of the boxes for the constituency vote (on the right), and an X in one of the boxes for the regional list vote (on the left). For historical reasons the constituency vote is sometimes known as the "1st vote" and the list vote as the "2nd vote".
The constituency votes are counted, and 9 (or in NE Scotland, 10) constituency MSPs elected. Then the list seats are allocated, using d'Hondt. List seats are sometimes called top-up seats because they top-up the constituency seats the parties got, to make the result more proportional.
d'Hondt explained
The d'Hondt method was invented by the Belgian lawyer Victor d'Hondt in 1878, but is equivalent to the method invented by Thomas Jefferson a century earlier. Maybe we should call it the Jefferson method?
D'Hondt works by allocating seats, a seat at a time, to the most "deserving" party. Deservingness is calculated by:
deservingness = votes / (seats+1) where:
votes = the number of votes the party got
seats = the number of seats the party has already been allocated
When used in AMS, votes means the number of list votes, and seats includes the constituency seats that a party has already won.
Seats are allocated one at a time. When a party has been allocated a seat, its deservingness therefore falls, so another party may be more "deserving" of the next seat.
In the Scottish system, the top-up seats are allocated by closed party lists: each party gives a list of its candidates to the election authorities, and if they win N top-up seats, the top N people on their list are elected. Note that "closed list" means the voters have no way to choose between individuals on a party's list: the only thing a voter can do is vote for a list, and accept it as it is, or vote for another list (or not vote at all).
A worked example of d'Hondt allocation
We'll use the 2016 election in the Lothian region for our example.
First we'll establish our starting data: what we care about is the number of constituency seats each party got and the number of list votes.
Leaving out some small parties, who didn't win any seats or affect the result of the election, here is the number of list votes and constituency seats each party got:
Party Votes Seats
===== ===== =====
SNP 118546 6
Con 74972 1
Lab 67991 1
Grn 34551 0
LD 18479 1 Based on this, we can calculate the deservingness of each party to win the 1st list seat:
7 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 1 2 37486 YES
Lab 67991 1 2 33995
Grn 34551 0 1 34551
LD 18479 1 2 9239 The Conservatives are the most deserving, so they are allocated the 1st list seat. They now have 2 seats (which reduces their deservingness) and there are 6 more seats to allocate:
6 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 2 3 24990
Lab 67991 1 2 33995
Grn 34551 0 1 34551 YES
LD 18479 1 2 9239 The Greens are now the most deserving, and get the 2nd list seat. Notice how the Conservatives' deservingness has gone down.
Going to to the next seat:
5 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 2 3 24990
Lab 67991 1 2 33995 YES
Grn 34551 1 2 17275
LD 18479 1 2 9239 Labour win this time. Note that at the start their deservingness was only just behind the Conservatives and Greens, but now those parties have each been allocated a seat, Labour has the most deservingness.
Now let's allocate the rest of the seats:
4 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 2 3 24990 YES
Lab 67991 2 3 22663
Grn 34551 1 2 17275
LD 18479 1 2 9239
3 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 3 4 18743
Lab 67991 2 3 22663 YES
Grn 34551 1 2 17275
LD 18479 1 2 9239
2 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 3 4 18743 YES
Lab 67991 3 4 16997
Grn 34551 1 2 17275
LD 18479 1 2 9239
1 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 4 5 14994
Lab 67991 3 4 16997
Grn 34551 1 2 17275 YES
LD 18479 1 2 9239
0 seats left to allocate
Party Votes Seats Divisor Deserve Extra?
===== ===== ===== ======= ======= ======
SNP 118546 6 7 16935
Con 74972 4 5 14994
Lab 67991 3 4 16997
Grn 34551 2 3 11517
LD 18479 1 2 9239
No more seats to allocate, finished So our final result is:
Const List Total
Party Seats Seats Seats
===== ===== ===== =====
SNP 6 0 6
Con 1 3 4
Lab 1 2 3
Grn 0 2 2
LD 1 0 1 Note that even though the SNP got more list votes than anyone else, they got no list seats, because they had already won 6 constituency seats.
AMS in the Senedd Cymru
The Senedd Cymru elects 60 members in 5 regions. Each region elects 8 constituency seats and 4 top-up seats. The top-up seats come from closed lists.
Because the total number of seats per region (12) it less than in Scotland (16), it is less proportional in Wales than in Scotland.
Also, because the proportion of seats which are top-ups is lower than in Scotland, overhangs are more likely.
AMS in the London Assembly
The London Assembly elects 25 members, 14 in FPTP constituencies and 11 top-up members. The top-up members come from closed lists.
There is a threshold applied to the London Assembly, in that a party has to get at least 5% of the list votes, otherwise it is barred from winning any seats.
MMP in the German Bundestag
The Bundestag has 598 seats: 299 constituency seats, and 299 list seats. List seats are allocated using closed party lists.
The 299 constituency seats are elected by FPTP, as in other AMS/MMP systems.
The 299 lists seats has a 5% threshold, so if a party gets less than 5% of the total list votes, they get no top-up seats, unless they won at least 3 constituency serats.
If there is an overhang, extra seats are created to ensure proportionality. The current Bundestag has 111 of these extra seats.
The Bundestag uses Sainte-Laguë instead of d'Hondt. Sainte-Laguë is like d'Hondt but uses a different formula which favours small parties:
deservingness = votes / (seats+0.5) MMP in New Zealand
The New Zealand Parliament, also known as the New Zealand House of Representatives, elects 120 MPs, of which 72 are constituency MPs and 48 top-up lists MPs. If there is an overhang, more list MPs are created to compensate. New Zealand used to use FPTP but moved to MMP in 1996.
There is a threshold of 5% of the list vote or winning 1 constituency seat; parties that fail to meet the threshold get no list MPs.
List MPs are elected from party closed lists.
Criticisms of AMS, and proposed fixes
While AMS is clearly more proportional (and therefore responsive to voters' desires) than FPTP, it has still been criticised. Here are some criticisms, with proposed solutions.
AMS allows tactical voting
That is to say, voters can sometimes get a result more to their liking if they vote other than honestly.
There are two parts to this. The constituency seats are FPTP, so suffer from all its shortcomings. One fix would be to elect the constituency seats by a different system, for example AV. This is what Roy Jenkins proposed in his AV+ system.
Decoy lists
Tactical voting issues with the top-up seats are more serious. Going back to our worked example above, the SNP won more list voters than anyone else, but got zero list seats, because they had already won lots of constituencies. Some people have suggested that pro-independence voters should vote for the SNP in the constituencies but for a different pro-independence party (that only contests lists) for their list vote. This is the idea behind Alex Salmond's recently created Alba Party.
Could the Alba Party work? I ran my simulation again, with all the SNP's list votes going to the Alba party, and they won 4 seats:
Party Votes Seats Divisor Deserve Diff
===== ===== ===== ======= ======= ====
SNP 0 6 7 0
Alb 118546 4 5 23709 (+4)
Con 74972 2 3 24990 (-2)
Lab 67991 2 3 22663 (-1)
Grn 34551 1 2 17275 (-1)
LD 18479 1 2 9239 In this scenario, Alba win 4 seats, gaining 2 from the Tories, and 1 each from Labour and the Greens. Since the Greens are also a pro-independence party, that's a net gain of 3 seats for pro-indy parties. That's in 1 of Scotland's 8 electoral regions, so across the whole of Scotland it could amount to about 8*3=24 extra seats for pro-indy parties.
In this scenario, the Alba Party is functioning as a decoy list that changes AMS from being a top-up system into a de facto parallel voting system.
How to fix decoy lists? Instead of a 1st (constituency) and 2nd (list) vote, every voter only has only one vote, which would be for their constituency MSP and would also be a vote for their constituency candidate's list.
AMS is insufficiently proportional
Continuing with our discussion of the Alba party, it's clear that not every SNP voter will switch to them. What if only 4% of the electorate in every region switches from SNP to Alba? 4% isn't enough to win Alba any regional seats, but probably is enough to lose the SNP some, so pro-indy parties face a net loss in that scenario.
So if a voter cares for nothing other than maximising the number of pro-indy MSPs (and obviously many voters care about other issues), then whether it makes sense for that voter to vote Alba depends on their assessment of how many other voters are likely to do so.
In the current Scottish system you need about 5.5% of the vote to get elected. This isn't very proportional. To be fully proportional, if a parliament elects 129 members, then a party should be able to get elected with 1/129th of the vote.
For example, in the 2011 election there were 1’990’836 list votes, and 129 MSPs elected so that’s an average of 15’432 votes needed to elect an MSP. But 5 parties got greater than that number of votes, without getting a single MP:
Party Votes Seats
===== ===== =====
SSCUP 33253 0
UKIP 18138 0
ScoChr 16466 0
SocLab 16847 0
BNP 15580 0It’s undemocratic, and morally wrong, that these voters should all be descriminated against.
If they can't, then their votes aren't being counted equally, and it's a basic principle of democracy that votes should have approximately equal value.
This lack of proportionality could be fixed in the Scottish system in two ways:
by abandoning regional lists and having one nationwide list electing all 56 top-up members.
or, by keeping the regional lists and adding another 10 nationwide top-up members, allocated by d'Hondt using the parties' total list votes for all the regions.
Either of these reforms would make it a lot easier for smaller parties to get elected, and would mean a lot less voters would be saying to themselves "I want to vote for X but they'll probably get only 1% of the vote so it'll be a wasted vote and I'll vote for Y instead".
Closed lists put parties in charge, not voters
The idea behind representative democracy is that the voters chose the representatives. But if list seats are allocated using closed party lists, that puts the parties in charge, not the voters. It means that MSPs will need to keep on good terms with the party hierarchy to keep their seats, and so they will care more about what the party hierarchy thinks than what the voters think. This isn't democracy! Democracy is where the representatives are responsible to the voters, not to the parties.
One fix would be for a party's list MSPs be chosen from their best placed non-winning candidates. So if a party got 0 constituency MSPs and 1 list MSP in a region, their list MSP would be whichever of their candidates got the highest vote share, or highest number of votes, or some other measure of their popularity.
This might mean that a party might run more than one candidate in a constituency, because if there are 9 constituencies and they only run one in each they can win at most 9 of the 16 constituency seats.
Note: NZ also uses StLague. See onthethreshold.nz for ideas on threshold problems and solutions. Cheers Ed