- \n
- The most accurate forecaster of the 2019 general election<\/a> – I was independently assessed as the most accurate forecaster beating even Sir John Curtice’s exit poll.<\/li>\n
- Keir Starmer’s Train to Downing Street<\/a> – My assessment in 2021 of what Labour needed to do to win the next election.<\/li>\n
- My election forecasting Track Record 2010 to 2024<\/a> – A list of all election forecasts I have made for General, European and Local elections, how I made them, how they turned out and what lessons I learned.<\/li>\n
- How Accurate are Voting Intention Polls (Revised)<\/a> – A recent article which explains why I now think the polls are accurate when before they would often underestimate the Conservative lead over Labour.<\/li>\n
- Going Beyond the Swing in 2024<\/a> – A preliminary look at the 2024 general election at the start of the year.\u00a0 I give probabilities for 10 specific outcomes.<\/li>\n<\/ol>\n
<\/p>\n
Data used in this article<\/strong><\/span><\/h5>\n
All electoral data I display and use in this article comes from the House of Commons Research Library<\/a>.\u00a0 The PDF file I use most of the time is this one UK Election Trends 1918-2019<\/a>.<\/p>\n
All polling data prior to April 2024 comes from Mark Pack’s invaluable Pollbase<\/a>.\u00a0 For data since April, I am using the BBC poll tracker<\/a>.\u00a0 For a summary of what the polls are saying at the time of this article, see this X\/Twitter thread<\/a>.<\/p>\n
I’ve created a spreadsheet GB General Election Data 1918-2019 – votes and seats<\/a> which contains all the data used to build my models.\u00a0 The table below lists the key data I refer to in this article which are Seat Share, National Vote Share and Average Vote Share by party.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2024\/06\/GB-Vote-Seat-Share-1922-2019-Data.png\")
<\/p>\nFor clarity –<\/p>\n
- \n
- Seat Share<\/strong> is the percentage of seats in Great Britain won by each party.<\/li>\n
- National Vote Share<\/strong> is the percentage of all votes cast in Great Britain for each party.<\/li>\n
- Average Vote Share<\/strong> (per Seat) is the average of the vote share in each British constituency the party stands in.<\/li>\n<\/ul>\n
I first explained the national and average vote share concepts in my article “How accurate are voting intention polls? – Revised<\/em><\/a>“.<\/p>\n
<\/p>\n
Why I did not use data before 1955<\/strong><\/span><\/h5>\n
I spent a long time trying to decide if I could use data for all elections since 1918 in my model.\u00a0 In the end, I concluded my model should be built using data for elections between 1955 & 2019, a total of 18<\/strong> elections.\u00a0 My reasons for excluding the earlier 10<\/strong> elections were –<\/p>\n
- \n
- Uncontested seats<\/strong> – these were common in the interwar years and did not die out until 1950.\u00a0 Uncontested seats distort the national vote share.<\/li>\n
- National Coalition parties<\/strong> – The interwar years were marked by frequent splits in the main parties.\u00a0 As a result, many MPs stood and were elected on labels such as National Liberal\/Conservative\/Labour or Independent Liberal\/Conservative\/Labour.\u00a0 The historical records on who took what whip are not reliable which can affect the seat share estimates.\u00a0 By 1955 the only remaining such party was the National Liberals who took the Conservative whip until 1970 when they merged with the Conservatives.<\/li>\n
- Multi-member seats<\/strong> – these are still common in local elections today where one has more than one vote and each ward elects two or more councillors.\u00a0 Multi member seats in Parliament were abolished in 1950 but they existed before then.\u00a0 This can distort both seat and vote shares.<\/li>\n<\/ul>\n
As will be seen later, most of the excluded 9<\/strong> elections between 1922 (first election without Irish seats) and 1951 still fit my 1955-2019 model quite well.\u00a0 For the sake of greater certainty over the historical data, I am happy for my model to be confined to elections since 1955.<\/p>\n
<\/p>\n
FPTP Outcomes = f(Sum & Difference of CON & LAB votes)<\/span><\/strong><\/h5>\n
The UK uses First Past The Post<\/strong> (FPTP) as its general election system.\u00a0 To me, this name is incomplete since it doesn’t tell you what the Post<\/strong> is.\u00a0 The full name should be First Past The Post Set By Party Coming Second<\/strong> (FPTPSBPCS) since the party coming second sets the threshold for winning a seat.\u00a0 Therefore it should be no surprise that to forecast FPTP outcomes, we need to know which two parties will come first and second.<\/p>\n
Since 1922, the top two parties across Britain have always been the Conservative (CON<\/strong>)<\/span> and Labour<\/span> (LAB<\/strong><\/span>) parties.\u00a0\u00a0With the exception of 1923, 88%<\/strong> or more of all seats contested in every election over last 100 years have been won by a Labour or Conservative candidate.<\/p>\n
By following this logic, it turns out we can forecast the number of CON<\/strong><\/span> & LAB<\/strong><\/span> seats using the Sum<\/strong> and Difference<\/strong> in CON<\/strong> <\/span>& LAB<\/strong><\/span> vote shares.\u00a0 I will use the following shorthand notation at various times in this article –<\/p>\n
- \n
- vCON = CON Vote Share,<\/strong>\u00a0 percentage of those voting who voted Conservative<\/span><\/li>\n
- vLAB = LAB Vote Share,<\/strong>\u00a0percentage of those voting who voted Labour<\/span><\/li>\n
- sCON = CON Seat Share,<\/strong>\u00a0percentage of seats won by the Conservatives<\/span><\/li>\n
- sLAB = LAB Seat Share,<\/strong>\u00a0percentage of seats won by Labour<\/span><\/li>\n<\/ol>\n
Rather than using vCON<\/strong><\/span> to predict sCON<\/strong><\/span> and vLAB<\/strong><\/span> to predict sLAB<\/strong><\/span>\u00a0which is how I made my forecast in the 2010 general election<\/a>, for 2024, I will use the sum and difference of these four variables –<\/p>\n
- \n
- vCLs<\/span> = vCON<\/span> + vLAB<\/span><\/strong> = sum of CON<\/strong><\/span> vote share and LAB<\/span><\/strong> vote share<\/li>\n
- vCLd<\/span> = vCON<\/span> – vLAB<\/span><\/strong> = difference between CON<\/strong><\/span> vote share & LAB<\/strong> <\/span>vote share, also known as the Conservative lead over Labour.<\/li>\n
- sCLs = sCON<\/span> + sLAB<\/span><\/strong> = sum of CON<\/strong> <\/span>seat share and LAB<\/span> <\/strong>seat share<\/li>\n
- sCLd = sCON<\/span> – sLAB<\/span><\/strong> = difference between CON<\/span><\/strong> seat share & LAB<\/strong><\/span> seat share<\/li>\n<\/ol>\n
My 2024 models uses vCLs<\/span><\/strong> to predict sCLs<\/strong> and vCLd<\/strong><\/span> to predict sCLd<\/strong>.\u00a0 Once I have my estimates of the sum and difference of the CON<\/strong><\/span> & LAB<\/span><\/strong> seat share, I can solve the simultaneous equations as follows to estimate the seat share for CON<\/strong><\/span> and LAB<\/strong><\/span> separately –<\/p>\n
- \n
- sCON<\/strong><\/span> = ( sCLs<\/strong> + sCLd<\/strong><\/span> )\/2 = sum plus difference divided by two<\/li>\n
- sLAB<\/span><\/strong> = ( sCLs<\/strong> – sCLd<\/strong><\/span> )\/2 = sum minus difference divided by two<\/li>\n<\/ol>\n
<\/p>\n
The Relationship between Vote & Seat Share under FPTP<\/strong><\/span><\/h5>\n
The four scatter plots here show the vote & seat share relationship since 1955.\u00a0 The plots on the left are for the sum of seat share vs sum of vote share, the plots on the right are for the difference in seat share vs difference in vote share.\u00a0 The plots at the top use national vote share, the plots at the bottom use average vote share.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2024\/06\/GB-Vote-Seat-Share-1955-2019-Natl-Avg.png\")
<\/p>\nMy observations are –<\/p>\n
- \n
- For sum seat share, there was a step change in 1997 which splits the data into two eras.<\/li>\n
- Up to 1992 (the black era), 3rd parties only won between 1%<\/strong> and 4%<\/strong> of seats but from 1997 (the green era), they won 8%<\/strong> to 12%<\/strong> of seats.<\/li>\n
- The fit between sum seat share and sum vote share appears to be linear in both eras.<\/li>\n
- The fit between sum seat share and sum vote share appears to be almost identical whether national vote share or average vote share is used.<\/li>\n
- The lowest ever sum vote share was in 2010 at 66.6%<\/strong>.<\/li>\n
- For the difference in seat share, history shows two distinct lines and three eras.<\/li>\n
- From 1955 to 1979, we are in the black era, from 1983 to 2010, we are in the green era and from 2015 to 2019, we returned to the black era.<\/li>\n
- The fit between seat share difference and vote share difference appears to be linear in all eras.<\/li>\n
- The fit appears to be better if average vote share is used.<\/li>\n
- Seat share difference has varied between +14.4%<\/strong> in 1983 and -15.6%<\/strong> in 1997 using average vote share.<\/li>\n<\/ol>\n
It turned out observation 9 was correct, the fit with average vote share (adjusted r^2 of 0.983<\/strong>) is better than with national vote share (adjusted r^2 of 0.963<\/strong>).\u00a0 This is very good news given I recently realised voting intention polls are better estimators of average vote share<\/a> than national vote share.\u00a0 It means I can plug poll data directly into my model to estimate number of seats won without having to worry about turnout differentials between Conservative and Labour seats.<\/p>\n
<\/p>\n
My GE2024 Model for Great Britain<\/strong><\/span><\/h5>\n
I built a linear model with an additional constant to account for the step from the black to green eras as shown here –<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2024\/06\/GB-Vote-Seat-Share-1955-2019-GE24-Model-B.png\")
<\/p>\nThe coefficient of 0.164<\/strong> for vote seat share implies the sum of CON<\/strong><\/span> & LAB<\/strong> <\/span>vote shares has to fall by 6<\/strong> points for 3rd parties to gain an extra 1<\/strong> point of seat share.\u00a0 This is the incumbency advantage of being one of the top two parties under FPTP.<\/p>\n
I used R to build my model and the model summaries are below.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2024\/06\/GB-Vote-Seat-Share-1955-2019-GE24-Model-R-Code-Output.png\")
<\/p>\nThe standard errors shown are for the sum and difference of CON<\/strong><\/span> & LAB<\/strong> <\/span>seat shares.\u00a0 In the end, what people want to know is how many seats the Conservatives and Labour (and others) are going to win.\u00a0 Using the simultaneous equation approach the standard error for estimates of CON<\/strong> <\/span>seat share is 1.3%<\/strong><\/span> and for LAB<\/strong><\/span> seat share is 1.2%<\/strong><\/span>.\u00a0 With 632<\/strong> seats in Great Britain, this works out as +\/-8<\/strong> seats which is good enough for my purposes.<\/p>\n
As would be expected from statistical theory given my forecasting model, the errors for the party seat shares are highly negatively correlated at -0.91<\/strong> i.e. if one party is overestimated, the other is very likely to be underestimated.\u00a0 This is shown by the largest historical errors which occurred in 2005 when the CON<\/strong><\/span> seat share was overestimated by 3.1%<\/strong><\/span> and the LAB<\/strong><\/span> seat share was underestimated by 2%<\/strong><\/span>.<\/p>\n
<\/p>\n
Critiquing my GE2024 Model<\/strong><\/span><\/h5>\n
An immediate issue with my model is whilst it can forecast how many seats the Conservatives and Labour will win, it doesn’t forecast how many seats smaller parties such as the Liberal Democrats, SNP, Plaid Cymru, Greens, Reform, etc will win.\u00a0 To address this, I’ve built an England only model based on the same approach as described above.\u00a0 The difference between the number of seats other parties are expected to win in Great Britain and in England will provide a good starting point for the number of seats to be won by the SNP and Plaid Cymru.\u00a0 Within England, the Liberal Democrats can be expected to win the bulk of the other seats though I will need to think of a way to account for Reform and the Greens.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2024\/06\/ENG-Vote-Seat-Share-1955-2019-GE24-Model.png\")
<\/p>\nThat leaves two main points to address here which are connected.\u00a0 They are –<\/p>\n
- \n
- Is the assumption of linear model fit appropriate?<\/li>\n
- Is the model fit for purpose given the polls so for the 2024 general election?<\/li>\n<\/ol>\n
It should be obvious that the fit cannot be linear for the sum seat share model.\u00a0 What if the sum vote share was 100%<\/strong> i.e. everyone votes CON<\/strong><\/span> or LAB<\/strong><\/span>?\u00a0 Then the sum seat share must be 100%<\/strong> (in the absence of uncontested seats) but at the moment, the green era sum seat share model would predict 94%<\/strong> and the black era model would predict 99.9%<\/strong>.\u00a0 Likewise, the linear fit for the seat share difference does not in theory prevent a forecast greater than 100%<\/strong> or less than -100%.\u00a0<\/strong> This would only happen if the vote share difference exceeded +39%<\/strong><\/span> (black era) or was less than -39%<\/strong><\/span> (green era).<\/p>\n
These extremes have not happened since 1955 but did they happen in the 9<\/strong> elections between 1922 & 1951?\u00a0 The chart below show my black and green era linear fits based on 1955-2019 for both sum seat share and seat share difference along with the earlier elections added as brown markers.\u00a0 To the sum seat share chart, I have added two extra lines of which I explain the point later –<\/p>\n
- \n
- A dashed brown line which is parallel to the green and black lines but differs from the green era fit by the same margin as the green fit differs from the black fit.<\/li>\n
- A dashed green curved line which is almost identical to the green era fit for the most part but curves away at the ends.<\/li>\n<\/ul>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2024\/06\/GB-Vote-Seat-Share-1922-1951.png\")
<\/p>\nThere is no question the 9<\/strong> earlier elections fit the seat share difference chart on the right very well.\u00a0 Importantly this includes the 1931 general election<\/a> which was a disaster for the Labour party where they lost 235<\/strong><\/span> seats to end up on 52<\/strong><\/span> to the Conservatives 470<\/strong><\/span>.\u00a0 In my 1955 onwards model, the maximum vote share difference was +14.4%<\/span><\/strong> in 1983 whereas 1931 was +30.3%<\/span><\/strong>.\u00a0 \u00a0This will be a vital observation for later on when I discuss if my model is fit for purpose for 2024.<\/p>\n
The other observation I make on the seat share difference chart is why 1945 & 1929 are the only elections on the green era fit whereas the other 7<\/strong> sit on the black era fi.\u00a0 I think the answer is both elections saw big swings from the Conservatives to Labour (6.1%<\/strong><\/span> swing in 1929,
- sLAB<\/span><\/strong> = ( sCLs<\/strong> – sCLd<\/strong><\/span> )\/2 = sum minus difference divided by two<\/li>\n<\/ol>\n
- vCLd<\/span> = vCON<\/span> – vLAB<\/span><\/strong> = difference between CON<\/strong><\/span> vote share & LAB<\/strong> <\/span>vote share, also known as the Conservative lead over Labour.<\/li>\n
- vLAB = LAB Vote Share,<\/strong>\u00a0percentage of those voting who voted Labour<\/span><\/li>\n
- National Coalition parties<\/strong> – The interwar years were marked by frequent splits in the main parties.\u00a0 As a result, many MPs stood and were elected on labels such as National Liberal\/Conservative\/Labour or Independent Liberal\/Conservative\/Labour.\u00a0 The historical records on who took what whip are not reliable which can affect the seat share estimates.\u00a0 By 1955 the only remaining such party was the National Liberals who took the Conservative whip until 1970 when they merged with the Conservatives.<\/li>\n
- National Vote Share<\/strong> is the percentage of all votes cast in Great Britain for each party.<\/li>\n
- Keir Starmer’s Train to Downing Street<\/a> – My assessment in 2021 of what Labour needed to do to win the next election.<\/li>\n