PR in the UK: Mixed Member Proportional

Joe C
6 min readSep 29, 2022

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On Monday, attendees of the UK Labour Party conference voted in favour of including a pledge to introduce proportional representation into its manifesto for the next general election. Of course, Proportional Representation can mean many things, so in this series of articles I’ll be looking at the effect of different variations of PR on the UK Parliament.

Today, I’ll look at Mixed Member Proportional Representation, which combines constituency MPs with party list MPs, and exploring how the ratios between these groups of MPs affects proportionality. Earlier I looked into thresholds for entering Parliament and how seats are allocated, and after this I’ll look into the impact of different sizes of regions.

For these examples, I’ll be using the results of the 2019 election as the inputs to these calculations, with an acknowledgement that many voters would vote differently under PR than under the current First Past The Post system. I’ll be treating the UK as a single electoral region, with no explicit minimum threshold for getting into Parliament. I’ll be using d’Hondt’s method to allocate seats, and I’ll also be making a simplifying assumption that, whatever the number of constituencies are used, the ratio of constituency seats between the parties will mirror the actual 2019 election results.

Mixed Member Proportional: A Recap

One of the common criticisms of proportional representation is the lack of connection between MPs and their local areas. A Parliament elected using Mixed Member Proportional representation aims to address that by having MPs elected in two different ways, generally using two different ballot papers. A share of MPs will be elected to represent individual constituencies, usually using First Past The Post. The remainder will be allocated between parties, with names submitted on lists in advance, so that the total representation is proportional to the party vote. This can be done across the entire electorate as is done for the London Assembly, or within regions as is done for the Scottish and Welsh Parliaments.

With MMP, one of the big questions is how many of these MPs are elected in each of these ways. Too few constituency MPs will mean the link between MPs and constituents isn’t established in the way that’s intended; too many constituency MPs means there won’t be enough proportional MPs to make the result fully proportional.

Start with 50:50

Germany’s starting point is to have the same number of constituency MPs as proportional MPs. In the UK, this would mean 325 constituencies elected through single-member constituencies, and 325 members from party lists allocated to create full proportionality.

CON 290 (184+106), LAB 213 (102+111), LD 76 (5+71), SNP 25 (24+1), GRN 17 (0+17), BREX 13 (0+13), DUP 5 (4+1), SF 3 (3+0), PC 3 (2+1), SDLP 2 (1+1), APNI 2 (0+2), UUP 1 (0+1)
What the 2019 result would have been using MMP, with a 50:50 split between constituency and list MPs

In order to ensure proportionality, a party that wins in a large number of constituencies will win a smaller number of list seats. However, even on a 50:50 allocation, the SNP wins only a single list seat, due to the fact that they win nearly all constituencies in Scotland, while Sinn Féin wins no list seats at all for a similar reason.

Most places that use MMP, however, put greater weight on constituency MPs; if we were to do so here, we’d be in a tricky situation where the SNP and Sinn Féin have won more constituency MPs than they should have in total.

Overhangs? Balances?

There are a few approaches that can be taken when a party wins more constituencies than their proportional vote share suggests that they should have. This comes up very clearly when we reach 60% of MPs being from constituencies, which is the level used in New Zealand. One option that is off the table is to remove the excess seats from that party, as those MPs are directly elected by constituents.

For the Scottish and Welsh Parliaments, the number of seats is fixed. This means that, if a party wins excess constituencies, list seats have to be taken away from other parties to compensate. This produces a result that is most predictable for Parliament’s staff to manage (they know exactly how many MP offices they’ll need), but the overall shape of Parliament would be furthest away from pure proportional. In this case, it’s the Conservative and Labour Parties that happen to lose seats as a result of this, but there is no guarantee that a smaller party won’t be the among those losing seats.

CON 287 (222+65), LAB 211 (122+89), LD 76 (6+70), SNP 29 (29+0), GRN 17 (0+17), BREX 13 (0+13), DUP 5 (4+1), SF 4 (4+0), PC 3 (2+1), APNI 2 (0+2), SDLP 2 (1+1), UUP 1 (0+1)
MMP with a 60:40 split, with the number of seats being fixed

In New Zealand, the number of seats produced by the allocation formula represents a minimum for the Parliament. If a party wins constituencies in excess of that minimum, then these become “overhang” seats, and additional seats are created in Parliament to accommodate those overhangs. This party will still be over-represented overall, but slightly less so as seats aren’t being taken away from other parties, meanwhile the number of additional seats should be manageable for Parliamentary authorities.

CON 290 (222+68), LAB 213 (122+91), LD 76 (6+70), SNP 29 (29+0), GRN 17 (0+17), BREX 13 (0+13), DUP 5 (4+1), SF 4 (4+0), PC 3 (2+1), APNI 2 (0+2), SDLP 2 (1+1), UUP 1 (0+1), Total overhang seats: 5
MMP with a 60:40 split, with the SNP and Sinn Féin keeping their overhang seats

Finally, to Germany, where maintaining proportionality is valued above all else. If a party wins more constituencies than proportionality says they should have in total, not only are overhang seats created to accommodate those mandates, but “balance” seats are also created and allocated to other parties to restore overall proportionality. The number of balance seats necessary to achieve this, however, can be very large; for every additional constituency a party like the SNP wins in Scotland, an additional 25 balance seats would need to be created to ensure proportionality, while a single Sinn Féin constituency would need 200 more seats to fully balance. This would make planning difficult for those who organise Parliamentary logistics.

CON 386 (222+164), LAB 284 (122+162), LD 101 (6+95), SNP 33 (29+4), GRN 22 (0+22), BREX 17 (0+17), DUP 6 (4+2), SF 4 (4+0), PC 3 (2+1), APNI 2 (0+2), SDLP 2 (1+1), UUP 1 (0+1), Total overhang and balance seats: 211
MMP with a 60:40 split, with balance seats created to restore full proportionality

The German system doesn’t quite do a full balance, though; they do allow a party to have a small excess in order to prevent the size of the Parliament from expanding beyond what can by physically accommodated. If we were to allow a party to have up to one more seat than proportionality would demand, it would reduce the number of balance seats significantly; up to three seats excess of proportionality (which is still under 0.5% of the total), and the number of balances seats reduces even further.

CON 324 (222+102), LAB 238 (122+116), LD 85 (6+79), SNP 29 (29+0), GRN 19 (0+19), BREX 14 (0+14), DUP 5 (4+1), SF 4 (4+0), PC 3 (2+1), APNI 2 (0+2), SDLP 2 (1+1), UUP 1 (0+1), Total overhang and balance seats: 76
MMP with a 60:40 split, with balance seats created to restore near proportionality (up to 1 excess)
CON 301 (222+79), LAB 221 (122+99), LD 79 (6+73), SNP 29 (29+0), GRN 17 (0+17), BREX 13 (0+13), DUP 5 (4+1), SF 4 (4+0), PC 3 (2+1), APNI 2 (0+2), SDLP 2 (1+1), UUP 1 (0+1), Total overhang and balance seats: 27
MMP with a 60:40 split, with balance seats created to restore near proportionality (up to 3 excess)

Mixed Member Proportional introduces some additional challenges. Having more directly elected members is a desirable thing, as is keeping the Parliament proportional; as we can see, these goals are in conflict with each other. Getting the balance right, both in terms of the share of constituency seats and the handling of excessive constituency mandates, is just one more thing that requires additional thought.

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Joe C

I am Joe. I am a techy at heart, a self-taught psephologist (political number cruncher), a pleasure cyclist, and someone who just calls things as he sees them.