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 different formulas for allocating seats between parties in the House of Commons. Yesterday I looked at getting into Parliament, and later in the week I’ll be looking at the use of mixed-member proportional representation and the size of individual 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.
d’Hondt Method
The d’Hondt Method is the most common allocation formula for proportional representation, including in the UK for the Scottish and Welsh Parliaments. Seats are allocated to parties one by one based on the ratio between the number of votes and the number of seats they have thus far (V/(S+1)), with the party having the highest ratio getting the next seat.
This method tends to favour larger parties at the expense of smaller parties, with parties in the middle being most fairly represented and the smaller parties being under-represented. That’s because a party needs to reach the mean vote/seat ratio before getting another seat; for the Ulster Unionists in particular, the size of the Parliament would need to grow by another 50 seats or so for the UUP to get a second seat.
Sainte-Laguë Method
The Sainte-Laguë Method is a slight variation on d’Hondt, with countries using it including Latvia and Sweden. By increasing the denominator more quickly to V/(2S+1), it makes it easier for a party to get their first handful of seats.
Switching to Sainte-Laguë takes six seats away from the two main parties relative to d’Hondt. Three parties (I’m counting Mr. Speaker as a party in this case) would enter Parliament where they would otherwise have missed out, while three other smaller parties would each get an additional seat. It makes it a lot harder for a party to get under-represented based on their vote share, but it does make it easier for a party to get over-represented. For smaller parties, though, it will be impossible to get right.
Largest Remainder Method
The Largest Remainder Method, used in Austria and Lithuania, doesn’t allocate seats one at a time, but in bulk. A quota is calculated based on the votes cast and the total number of seats, and that quota is used to calculate the number of seats. The number of seats is initially rounded down, meaning there will be a shortfall, and so the parties with largest remainders will get an additional seat.
With a quota just under 49,000 votes, the whole number of seats from the division produced 639 seats. Only nine parties had a remainder of more than half, and this allows UKIP, who finished with under half of a quota, would be able to enter Parliament.
There is another option for these remainders, though. Add an element of preferential voting to the mix, and these remainders can be transferred to other parties to get them above a quota. For example, the SNP has around a third of a quota up for grabs, and The Independent Group (remember them?) has around a fifth of a quota; with certain preferences, these could quite easily mean a seat or two (including the one UKIP seat) flipping.
The formula used to allocate seats will inevitably impact the smaller parties the most. When selecting a formula, a choice will have to be made whether to under-represent or over-represent smaller parties, as they won’t have enough seats for true fairness to be possible. While the difference won’t likely have an impact on who forms government, it will have an impact on what voices are heard in the corridors of power.
