House of Commons Composition Model

Following the 2017 General Election, under the Fixed Term Parliaments Act 2011 the next general election would be in 2022. Final recommendations for new boundaries for a reduced number of constituencies are due to be made in September 2018. A statutory instrument will then be debated in Parliament to approve or reject the changes. An election held before this would be on the basis of the current constituencies.

If there was an early election what could the result be? To help answer this question the House of Commons Library has produced mathematical models which calculate the number of seats that might be won by each party assuming certain levels of support.

Note: the model is purely mathematical and rests on a number of assumptions. It is intended to be illustrative only.

How the model works…

The basic model:

The simple model takes the 2017 General Election as a baseline and allows users to enter Conservative, Labour and Liberal Democrat party vote shares in Great Britain at the next general election, and then calculates the composition of the House of Commons based on an assumption of uniform national swing from the June 2017 General Election.

631 constituencies in Great Britain are included. 19 constituencies are excluded and are assumed to remain ‘Others’ – these are the 18 constituencies in Northern Ireland and the seat of Buckingham currently held by the Speaker. Calculations focus on the Conservatives, Labour and Liberal Democrats because they have the largest GB-wide vote share. The vote share for all other parties/independents in Great Britain is assumed to remain the same as in 2017.

The advanced model:

The advanced model is similar to the basic version, although it allows users to enter party vote share estimates for the Conservatives, Labour, Liberal Democrats, Sottish National Party, and Plaid Cymru for each country in Great Britain. The model calculates the composition of the House of Commons based on an assumption of uniform national swing from the June 2017 General Election for each party within each country.

631 constituencies in Great Britain are included. 19 constituencies are excluded and are assumed to remain ‘Others’ – these are the 18 constituencies in Northern Ireland and the seat of Buckingham currently held by the Speaker.

What the model doesn’t do…

Because the model is based on uniform national swing it ignores possible local effects in how parties may perform in individual constituencies. It’s likely that changes in vote share in individual constituencies will differ from the national average, for historic or other reasons.

Depending on the vote share estimates entered by the user the model may predict impossible outcomes. If we thought that the Conservatives and Labour would both receive 45% of the GB vote, the model would calculate that the Liberal Democrats would receive 2.2% of the vote – this would be a 5.4 percentage point fall. When the model applies this reduction to all constituencies in some places, such as Aberavon in Wales, the Liberal Democrat vote share would be calculated as negative 3.6% because the Liberal Democrat vote share was already small in the 2017 General Election. The model informs the user if constituencies have a negative vote share based on their estimates.

A worked example…

Assume vote share estimates from the most recent YouGov voting intention poll (10 December 2017) which showed the Conservatives on 42% and Labour 41%. In the model the Liberal Democrat’s share would increase from 7.6% to 9.2% based on the automatic calculation.

Under this scenario we are assuming the Conservative vote share falls by 1.5 percentage points, Labour falls by 0.1% points, and the Liberal Democrats’ share increases by 1.6 percentage points. The model applies these national changes to each constituency and based on these new vote shares the model calculates how many constituencies each party would win, which would be the largest party and their theoretical majority (if any).

The model also shows how many (and which) constituencies would change hands based on the estimates. In this example 13 seats are expected to change party.