by Dr Adrian Worton
Having got our General Election probability model underway and unveiled our Constituency Profile tool, we are now going to do a series of articles on the various parties to look at the different narratives of this election.
We are starting with Labour, and we are going to look at the plausible range of majorities they could end up with. From a Labour point of view, the question is "What size majority can be achieved?", from a Conservative (or anti-Labour) point of view, it is "How much can Labour's majority be limited?".
Having got our General Election probability model underway and unveiled our Constituency Profile tool, we are now going to do a series of articles on the various parties to look at the different narratives of this election.
We are starting with Labour, and we are going to look at the plausible range of majorities they could end up with. From a Labour point of view, the question is "What size majority can be achieved?", from a Conservative (or anti-Labour) point of view, it is "How much can Labour's majority be limited?".
A quick note on majorities:
Majorities are calculated by counting the difference between the seats won by the largest party and the other parties combined. As there are 650 seats in the House of Commons, this is given by:
Majorities are calculated by counting the difference between the seats won by the largest party and the other parties combined. As there are 650 seats in the House of Commons, this is given by:
( [number of seats won] - 325 ) x 2
At the time Parliament broke up for the election, the Conservatives held 330 seats. So using the formula above, their majority was (330 - 325) x 2 = 10.
In practice, because the Speaker does not vote and Sinn Féin do not take up their seats, a party's majority will be greater than this. But we will just be using the standard method shown above.
In practice, because the Speaker does not vote and Sinn Féin do not take up their seats, a party's majority will be greater than this. But we will just be using the standard method shown above.
Probability distributions
Because our model provides a probability of each party winning each constituency, we can use this to calculate the probability of a specific party winning a given number of seats.
So for Labour, here is our probability distribution for the upcoming election (using the probabilities from the 14th of June):
Because our model provides a probability of each party winning each constituency, we can use this to calculate the probability of a specific party winning a given number of seats.
So for Labour, here is our probability distribution for the upcoming election (using the probabilities from the 14th of June):
The chances of any specific seat count is quite low. The most likely seat count is 423, but that only has a 5.22% chance of occurring. Instead, we take a range of seat counts to give a more tangible probability estimate. This is called a confidence interval.
The 50% confidence interval (dark red above) gives the central range of seat counts that is as likely to happen as not. The 95% confidence interval (red) is the range that we would be 95% confident that the final count is within. 95% is the standard level used in statistics.
Here are those two confidence intervals:
The 50% confidence interval (dark red above) gives the central range of seat counts that is as likely to happen as not. The 95% confidence interval (red) is the range that we would be 95% confident that the final count is within. 95% is the standard level used in statistics.
Here are those two confidence intervals:
Confidence interval |
Seat range |
Majority range |
50% |
418-427 |
186-204 |
95% |
409-438 |
168-226 |
I have to say I am surprised how narrow these ranges are. To illustrate this, our last update had Labour as favourites in 437 seats, but our probability distribution above has Labour as having just a 3.87% chance of ending up with that many seats.
Is it reasonable to assume Labour's seat tally will be in this range? To see, we can look at our data on previous elections. Below are the same probability distributions for the Conservatives and Labour for the past three elections, with an additional marker (yellow line) for the number of seats they ended up with:
Is it reasonable to assume Labour's seat tally will be in this range? To see, we can look at our data on previous elections. Below are the same probability distributions for the Conservatives and Labour for the past three elections, with an additional marker (yellow line) for the number of seats they ended up with:
Remarkably, in every single instance the final seat count is nowhere near our probability distribution. In fact, the only election where it is anywhere close is 2019, and even there both parties ended up outside the 95% confidence interval.
This points to a key problem with using our individual constituency odds to predict a range for overall performance: the constituency votes are not independent events.
Imagine if you rolled a standard dice 100 times, and you won if you rolled a 1, 2, 3 or 4. You would be the favourite to win each roll, but you would also expect to lose a third of the rolls. Over the 100 rolls you would expect to end up with around 67 wins, and the more rolls you do the more likely it will converge on that figure.
However, those rolls are independent of each other - one roll does not affect the outcome of the next. This is not the case for General Election constituencies. Say Labour win a seat they were rated as 25% likely to take, they would probably become more likely to win a seat where they were previously 75% likely.
Outcome by seat probability
Let us have a look at how the two parties did in the three previous elections by looking at their chances of winning each seat and which of those they actually won:
This points to a key problem with using our individual constituency odds to predict a range for overall performance: the constituency votes are not independent events.
Imagine if you rolled a standard dice 100 times, and you won if you rolled a 1, 2, 3 or 4. You would be the favourite to win each roll, but you would also expect to lose a third of the rolls. Over the 100 rolls you would expect to end up with around 67 wins, and the more rolls you do the more likely it will converge on that figure.
However, those rolls are independent of each other - one roll does not affect the outcome of the next. This is not the case for General Election constituencies. Say Labour win a seat they were rated as 25% likely to take, they would probably become more likely to win a seat where they were previously 75% likely.
Outcome by seat probability
Let us have a look at how the two parties did in the three previous elections by looking at their chances of winning each seat and which of those they actually won:
For each plot you could find a point where the party:
Taking the Conservatives' 2019 performance as an example, we draw the line at 40%:
- Loses nearly every seat out to the left of the line
- Wins nearly every seat out to the right of the line
- Wins roughly half of the seats near to the line
Taking the Conservatives' 2019 performance as an example, we draw the line at 40%:
On the graph above, the Conservatives:
We can draw similar lines for the other charts:
Remember, a low percentage is good as it means the party is winning seats that it was considered unlikely to take.
We will call this value the success level of a party. Because the seats near the success level roughly cancel each other out, we can say that the success level is the percentage at which a party wins all seats it had a greater probability of winning, and loses all the ones it has a lower percentage of winning.
Using the success rate
We can use this method on our General Election 2024 data to find a perhaps more realistic range of outcomes for the upcoming election.
Below is Labour's seat probability chart:
- Lost nearly every seat that was over 15% to the left of the line
- Won every seat that was over 15% to the right of line
- Won roughly half of the seats within 15% either side of the line
We can draw similar lines for the other charts:
- Conservatives 2015: ~ 13%
- Labour 2015: ~ 80%
- Conservatives 2017: ~ 85%
- Labour 2017: ~ 13%
- Labour 2019: ~ 60%
Remember, a low percentage is good as it means the party is winning seats that it was considered unlikely to take.
We will call this value the success level of a party. Because the seats near the success level roughly cancel each other out, we can say that the success level is the percentage at which a party wins all seats it had a greater probability of winning, and loses all the ones it has a lower percentage of winning.
Using the success rate
We can use this method on our General Election 2024 data to find a perhaps more realistic range of outcomes for the upcoming election.
Below is Labour's seat probability chart:
Based on the 2015-2019 elections, let us say that the realistic range for the success level is between 10-90%. Below is the number of seats Labour would win for every success level in that range:
The three areas on the graph above are:
Perhaps there is a glimmer of hope for the Conservatives after all, as a success level higher than 84% (remember, high is bad) would see Labour somehow fail to gain a majority. Given the narrative of this election this seems out of the question, but in fact the Conservatives had a success level of 85% in 2017. There are still weeks of campaigning to go, and Labour's position in the model may weaken by then.
But from a (positive) Labour point of view, it is striking that the majority of scenarios above see Labour breaking Stanley Baldwin's 1924 record majority. Just as likely as Labour failing to reach a majority is that they have a success level of 15%, which would earn them exactly 500 seats, a stratopheric majority of 350! A majority so big that it itself would have a majority.
Summary
Our model is consistent with every other General Election forecast in that it pointing towards a very heavy Labour victory, with a record win a very plausible outcome.
However, our predictions for previous elections were largely off the mark. Considering the inherent issues with combining hundreds of constituencies into a wider probability model, we have used a new measure to hopefully give a better way of give a plausible range for Labour's seat count.
Under this method, a 2017-size shock at the polls could see Labour fail to get a majority at all. But it is noteworthy that there was a pollster (YouGov) who did correctly predict a hung parliament. If there are no such predictions this year, a repeat feels unlikely.
We will continue this series looking at individual parties next time with the Conservatives.
- Dark red: Labour end up with a majority greater than the record of 210
- Red: Labour end up with a non-record majority
- Gray: Labour fall short of a majority
Perhaps there is a glimmer of hope for the Conservatives after all, as a success level higher than 84% (remember, high is bad) would see Labour somehow fail to gain a majority. Given the narrative of this election this seems out of the question, but in fact the Conservatives had a success level of 85% in 2017. There are still weeks of campaigning to go, and Labour's position in the model may weaken by then.
But from a (positive) Labour point of view, it is striking that the majority of scenarios above see Labour breaking Stanley Baldwin's 1924 record majority. Just as likely as Labour failing to reach a majority is that they have a success level of 15%, which would earn them exactly 500 seats, a stratopheric majority of 350! A majority so big that it itself would have a majority.
Summary
Our model is consistent with every other General Election forecast in that it pointing towards a very heavy Labour victory, with a record win a very plausible outcome.
However, our predictions for previous elections were largely off the mark. Considering the inherent issues with combining hundreds of constituencies into a wider probability model, we have used a new measure to hopefully give a better way of give a plausible range for Labour's seat count.
Under this method, a 2017-size shock at the polls could see Labour fail to get a majority at all. But it is noteworthy that there was a pollster (YouGov) who did correctly predict a hung parliament. If there are no such predictions this year, a repeat feels unlikely.
We will continue this series looking at individual parties next time with the Conservatives.