UK Conservatives: only 56% have stayed with the party … the gravity model
1 Conservatives lose badly in Kingswood and Wellingborough
2 National polls
Step ratios …
… the staying rates …
… and leaving rates …
… and arrivals …
… the flow model …
… the gravity model …
… the gravitational trajectories model
… a simple ideal model of the Conservative trajectory, 1945-2015
3 What Labour needs
4 More detail about Kingswood and Wellingborough
5 All parties lost badly to George Galloway in 2011 … and in 2024???
6 “Local elections and national polls: modelling change”
7 UK Conservatives in political space, 2010-2024
Links
1 Conservatives lose badly in Kingswood and Wellingborough
“We’ve given up the fight, say Tories as poll defeats loom. … Party has descended into ‘a death spiral’ … byelection losses set to fuel Sunak pressure.”
The Observer, Sunday, February 11, 2024: 1, 5.
“Today, in Kingswood and Wellingborough, the country is likely to give the government a good kicking.”
The Times, Thursday, February 15 2024: 25. James Kanagasooriam.
Sure enough, the Conservatives lost the two by-elections yesterday, at Kingswood and at Wellingborough:
BBC “LIVE. Labour overturn big Tory majorities in by-election wins.”
https://www.bbc.co.uk/news/live/uk-politics-68277176
The Conservative vote was very roughly half what their vote had been at the general election of 2019 … ‘half’ is … in percentage terms, 50% … and in terms of ratios, 0.50.
I shall refer to this ratio as the ‘step ratio’ and I consider that the concept of step ratio is a good starting point for thinking about change in the percentage support for a political party. It is how I shall start my systematic account of changes in national opinion which I shall give in Section 2.
I have used above the phrase “very roughly half”. Let me be more precise. The step ratio for Kingswood was 0. 61; and for Wellingborough was 0.39 – an average of 0.50, ‘a half’.
Local and national: Conservative step ratios
The local step ratios in Kingswood and Wellingborough can be set alongside the national step ratios derived from the eleven opinion polls this past week – and also alongside the local step ratios in six by-elections last year.
Conservative step ratios:
0.26 in Rutherglen, Scotland
0.39 in Wellingborough
0.47 in Frome
0.48 NATIONAL, lowest - this week’s and since January 2023
0.52 in Mid-Beds
0.57 in Selby
0.57 NATIONAL, this week’s median
0.60 NATIONAL, midpoint since January 2023
0.61 in Scotland
0.61 in Kingswood
0.61 in Tamworth
0.67 NATIONAL, this week’s highest
0.73 NATIONAL, highest since January 2023
0.86 in Boris Johnson’s Uxbridge seat in London
The implications of the step ratio
“… more than one recent poll has suggested that Conservative support is falling most in seats where the party was previously strongest …”
The Times, February 17, 2024: 12.
The step ratio has implications for other quantities. In particular, it has implications for “the step difference” – what John Curtice refers to as the ‘fall’.
step ratio = vote in 2024 / vote in 2019
fall = step difference = vote in 2024 - vote in 2019
It follows that
step difference = (step ratio – 1) (vote in 2019)
If the step ratio is less than one, then the step difference will be negative, in other words an actual fall.
If the step ratio is constant, then the step difference will be greater, the greater is the vote in 2019.
“… Conservative support is falling most in seats where the party was previously strongest …”
If the step ratio is not constant, then the step difference will depend on two factors: the step ratio and the vote in 2019. Note that there may be a relationship; between these two factors.
The rationale for step ratios
The rationale for step ratios will become clear in the next section. Briefly, step ratios are related to staying rates. And the expectation for the staying rate for a group is the mean of the staying probabilities for individual voters. In this way the step ratio links in to the basic relationship between individual probabilities and group rates.
2 National polls
Step ratios …
In the 2019 general election, the Conservatives had 43.6% of the vote.
Now in mid-February 2024, they have 25% (the median of eleven recent polls).
Dividing the second number by the first number gives:
the “step ratio” 0.57.
Looking now at the lowest and the highest of the eleven polls,
the lowest vote was 21%, giving a step ratio of 0.48,
and the highest vote was 29%, giving a step ratio of 0.67;
giving a midpoint step ratio of 0.575.
… the staying rates …
Whereas the step ratio just divides two percentages,
the staying rate looks at how individuals voted in 2019 and in 2024:
did individuals stay with the Conservatives, that is voting for them in 2019 and then ‘voting’ for them in 2024 (that is, saying they intended to vote for them)?
One of the polls gave the Conservative staying rate: only 62% stayed with the party.
We shall find that many left the Conservatives and few arrived from other parties. In such circumstances the step ratio and the staying rate are almost equal.
The staying rates for the other two main parties were:
The LibDem staying rate was 52%.
The Labour staying rate was 91%.
Source: Delta poll, 12 February 2024:
https://deltapoll.co.uk/wp-content/uploads/2024/02/Deltapoll-240212_trackers.pdf
… and leaving rates …
If the Conservative staying rate is 62%, the Conservative leaving rate is 38%.
Where did the Conservative leavers (38%) go?
They went 18% to Reform; 16% to Labour; 2% to Green; 1% to UKIP; and 1% to LibDem.
Where did the LibDem leavers (48%) go?
They went 35% to Labour; 8% to Conservative; and 5% to Green.
Where did Labour leavers (9%) go?
They went 3% to Green; 2% to SNP; 2% to Conservative; and 1% to LibDem.
… and arrivals …
The current vote is the sum of stayers and arrivals.
Conservative arrivals were 8% of LibDem; 2% of Labour; and 4% of others.
LibDem arrivals were 1% of Conservative; 1% of Labour; and 6% of others.
Labour arrivals were 16% of Conservative; 35% of LibDem; and 17% of others.
Notes:
[1 The above refers to the highest of the polls. The lowest of the polls gives staying rates of: 50% for the Conservatives; 73% for LibDems; and 88% for Labour.]
[2 The headline 56% is the average of the higher and lower Conservative staying rates, 62% and 50%]
… the flow model …
These various percentages represent how voters have moved from one party to another in the period 2019 to 2024. We can think of it as flows of voters between the parties – with the percentages giving the rates of flow. The flow rates can be put into a matrix – a flow rate matrix (known as a transition matrix). There is a matrix equation: the 2024 party percentages equal the flow rate matrix multiplied by the 2019 party percentages:
. 2024 percentages = flow rate matrix x 2019 percentages
… the gravity model …
There is something special about the flow rates in the matrix. The rates reflect two aspects. The first aspect is the size of the parties. There are bigger flows out of bigger parties; and bigger flows into bigger parties. The second aspect is distance – given that parties have different locations in political space. There are bigger flows between parties that are less distant in political space.
Although political space is multi-dimensional, there is a principal dimension which is somewhat akin to the familiar Left-Right dimension. The flow rates are consistent with the following locations - to some extent:
. Labour Green LibDem Conservative Reform; UKIP
The way the two aspects of size and distance are combined is complicated:
UK 2017: mass and gravity in political space
https://drive.google.com/file/d/1iXCf1AKwseBe3iLb_gM6vg8J6Tdwl6YM/view
Chapter 4 in Values, World Society and Modelling Yearbook 2015
Values, World Society and Modelling Yearbook, 2015.
… the gravitational trajectories model …
So far we have been concerned about the change form 2019 to 2024. Now consider the political trajectory over the period 1945 to 2024. Applying the gravity model over this extended period allows us to observe the parties orbiting around the political centre of gravity.
Time series: UK general elections, 1945-2015
https://drive.google.com/file/d/199eS6bbnJtT0gIscZmX7vCLjcQX2NkZo/view
Chapter 12 in Values, World Society and Modelling Yearbook 2017
Values, World Society and Modelling Yearbook, 2017.
… a simple ideal model of the Conservative trajectory, 1945-2015
The 2015 Yearbook shows the trajectory of the Conservative vote over the period 1945-2015. A simple autoregressive model gives an equilibrium of around 40%. The highest vote was around 50% and the lowest vote was around 30%. The trajectory cycles around the equilibrium in an irregular fashion for two cycles (Figure 12.7, page 260).
Even though the real trajectory is complicated a simple ideal model can help us get a feel for what is happening. Suppose the Conservative percentage vote x has a simple harmonic motion.
. x = 40 + 10 sin t
For a suitable sequence of values for time t, there will be a sequence of Conservative percentage votes:
. 40 50 40 30 40 50 40 30 40
… and there will be corresponding step ratios, depending on the time interval:
. . 1
. . 0.60 1.67 0.60
. . 0.80 0.75 1.33 1.25 0.80 0.75 1.33
Links for Section 2
General election, December 2019:
https://en.wikipedia.org/wiki/2019_United_Kingdom_general_election ;
https://commonslibrary.parliament.uk/research-briefings/cbp-8749/;
Opinion polls:
https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_United_Kingdom_general_election
Current voting intention, eleven polls within 8-14 February 2024; the following site gives links to the individual polls:
The Conservative % vote in the eleven polls: 21, 24, 25, 26, 29, 29, 21, 22, 27, 27,22
[midpt 25 med 25; step ratio 62%]
3 What does Labour need?
The Labour lead now in 2024 – and in 1997
The Labour lead is now +18% whereas in 1997 it was +12.5%.
Table The comparison, 2019-2024 with 1992-1997
Cons Labour Labour Labour
lead swing
1992 GE 41.9% 34.4% -7.5
1997 GE 30.7% 43.2% +12.5
difference 11.2% 8.6% 9.9%
step ratio 0.73 1.26
2019 GE 43.6% 32.1% -11.5
2024 poll 25%* 43%** +18
difference 18.6% 10.9% 15.3%
step ratio 0.57 1.34
,* midpoint and median of nine polls which include Feb 8-
** Opinium 6-9 feb had 25% and 43%
How many seats does the Labour lead give rise to?
The present national polls have some bearing on the future national result. The past week’s polls have shown Labour leads ranging between % and %. Last October it was said that:
“On the basis of a +17 LAB lead over CON, the MRP results show in GB (ex NI) LAB on 426 seats CON: 141 LD: 25 SNP: 36 GRE: 1 Others: 5”
https://politpro.eu/en/united-kingdom/institute/survation
How well have poll leads predicted past election results?
– specifically those carried out in advance of an election by say 10 months?
There have been eighteen elections in the period 1951-2019. A poll lead has correctly predicted the winner on twelve occasions – a prediction success rate of 67%. The six failures were: wrongly predicting a Conservative win on one occasion; and wrongly predicting a Labour win on five occasions. The wrong predictions of Labour wins have occurred for Labour leads of 1% (1951); 6% (1955); 4.5% (1987); 6.7% (1992); and 3.7% (2015). The correct predictions of Labour wins have occurred for Labour leads of: 10.2% (1964); 1.5% (1966); 10.4% (1974); 21.8% (1997); 16.6% (2001); and 2.7% (2005). Double digit leads for Labour have on four previous occasions been followed by Labour wins.
Note that eighteen elections is a small sample size.
“Tories in need of a record swing.” (from now to the election)
The Times, February 3, 2024: 17.
Source: PollBase, Mark Pack, https://www.markpack.org.uk/opinion-polls/
“We know we need a 12.7% swing …”
“… cautionary talks from the Labour pollster Deborah Mattinson about the electoral mountain the party has to climb:
“We know we need a 12.7% swing and in 1997 we got a 10.6% swing – so we need a 20% bigger swing than in ’97.” (36)
The Observer, 28 January 2024: 33-36. Toby Helm and Michael Savage.
I find this statement puzzling. If a 12.7% swing is needed, then it has already been achieved and indeed exceeded – see again the table below showing a 14.8% swing – and so “the mountain” has already been climbed.
But is it true that a 12.7% swing is needed? In order for Labour to be equal with the Conservatives, only a 5.8% swing is required. I can certainly imagine that there are various factors which require Labour to be more than equal to the Conservatives – but surely not by as much as seems to be being suggested.
Table The comparison, 2019-2024 with 1992-1997
Cons Labour Labour Labour
lead swing
1992 GE 41.9% 34.4% -7.5
1997 GE 30.7% 43.2% +12.5
difference -11.2% 8.6% 9.9%
step ratio 0.73 1.26
2019 GE 43.6% 32.1% -11.5
2024 poll 25%* 43%** +18
difference -18.6% 10.9% 14.8%
step ratio 0.57 1.34
,* midpoint and median of nine polls which include Feb 8-
** Opinium 6-9 feb had 25% and 43%
From ‘order’ to ‘crisis’
A fortnight ago:
“Order versus chaos. Labour’s iron discipline exposes Tory disarray.
… In the week when a former Conservative minister was calling for the ousting of his own prime minister, the opposition was working to create a level of party uniformity not see since the Blair years. (33)
… Tories feud as Labour enforces discipline (36)”
The Observer, 28 January 2024: 33-36. Toby Helm and Michael Savage.
Now:
“Labour in crisis after a second suspension.”
The Times, February 14, 2024: 1.
4 More detail about Kingswood and Wellingborough
As we noted in Section 1:
“We’ve given up the fight, say Tories as poll defeats loom. … Party has descended into ‘a death spiral’ … byelection losses set to fuel Sunak pressure.”
The Observer, Sunday, February 11 2024: 1, 5.
“Today, in Kingswood and Wellingborough, the country is likely to give the government a good kicking.”
The Times, Thursday, February 15 2024: 25. James Kanagasooriam.
Sure enough, the Conservatives lost the two by-elections yesterday, at Kingswood and at Wellingborough:
BBC “LIVE. Labour overturn big Tory majorities in by-election wins.”
https://www.bbc.co.uk/news/live/uk-politics-68277176
Kingswood byelection 2024
https://en.wikipedia.org/wiki/2024_Kingswood_by-election
Wellingborough byelection 2024
https://en.wikipedia.org/wiki/2024_Wellingborough_by-election
The step ratios for the Conservatives and for other parties
Consider the step ratio, in other words the ratio of the vote now to the vote in 2019.
How do the two local step ratios compare with one another?
How do the two local step ratios compare with the national step ratios?
Conservatives
The local and the national step ratios for Conservatives are very roughly similar: 0.61 and 0.39… giving midpoint 0.50; and 0.55. The local midpoint is quite close to the national. The Wellingborough result is a good bit lower than the national figure.
Step ratio: Conservative vote now / Conservative vote in 2019
Local, Kingswood: 0.61; … (34.5% now / 56.2% in 2019)
Local, Wellingborough: 0.39; … (24.6% now / 62.2% in 2019)
National: 0.55; … (24% now / 43.6% in 2019)
All parties
“Reform and Greens channel desire for change. Both the Tories and labour are vulnerable to small partis luring dissatisfied voters and not just in this election year.”
The Times, Thursday, February 15 2024: 25. James Kanagasooriam.
Reform shows an advance at both local and at national levels. The Kingswood step ratios for Labour and Greens are similar to the national step ratio. In Wellingborough Labour do better than the national but Greens do worse than the national. LibDem locally do worse than at the national – possibly due to tactical voting for Labour at Conservative expense.
The local and the national step ratios for each of the other parties:
Labour 1.34 and 1.73; and 1.34.
Lib Dem 0.51 and 0.59; and 0.95.
Green 2.42 and 0.97; and 2.69.
Reform/Brexit infinite and infinite; and 5.00.
Step ratios: all parties now / all parties in 2019
Local, Kingswood: Cons 0.61; Lab 1.34; LibDem 0.51; Green 2.42
Local, Wellingborough: Cons 0.39; Lab 1.73; LibDem 0.59; Green 0.97
National: Cons 0.; Lab 1.34; LibDem 0.95; Green 2.69; Reform/Brexit 5.00
In detail:
Local, Kingswood: Cons 0.61; Lab 1.34; LibDem 0.51; Green 2.42
(% now: Cons 34.5%; Lab 44.9%; LibDem 3.5%; Green 5.8%; Reform 10.4%; UKIP 0.5%)
(% in 2019: Cons 56.2%; Lab 33.4%; LibDem 6.9%; Green 2.4% …)
Local, Wellingborough: Cons 0.39; Lab 1.73; LibDem 0.59; Green 0.97
(% now: Cons 24.6%; Lab 45.9%; LibDem 4.7%; Green 3.4%; Reform 13.0% …)
(% in 2019: Cons 62.2%; Lab 26.5%; LibDem 7.9%; Green 3.5%)
National: Cons 0.; Lab 1.34; LibDem 0.95; Green 2.69; Reform/Brexit 5.00
(% now: Cons 25%; Lab 43%; LibDem 11%; Green 7%; Reform 10%; UKIP %)
(% in 2019: Cons 43.6%; Lab 32.1%; LibDem 11.6%; Green 2.6%; Brexit 2.0%; UKIP %)
https://twitter.com/OpiniumResearch/status/1756407689570132235/photo/1
Questions commonly asked
The following questions are commonly asked:
Q1 How does this local result compare with the local result at the last election in 2019?
The local step ratios show that grow and that shrink.
Q2 How does this local result compare with the national polls?
Similar but different: the national step ratios show that grow and that shrink.
. Cons Lab LibD SNP Green Brexit/Reform
step ratio
Q3 How does this compare with last year?
The national slump in the Conservative vote has been long-standing: their support has ranged between 20% and 32% since January 2023 – the corresponding step ratios ranging between 0.46 and 0.73 – giving a mid-point of 0.60.
This was reflected last year in local step ratios in the five most recent by-elections in England: 0.47 in Frome, 0.52 in Mid-Beds, 0.57 in Selby, and 0.61 in Tamworth … although higher at 0.86 in Boris Johnson’s Uxbridge seat in London. The range between 0.47 and 0.86 gives a midpoint of 0.67.
5 All parties lost badly to George Galloway in 2011 … and in 2024???
Now in 2024:
“Galloway capitalises on rival’s antisemitism row. … The populist calling himself ‘Gaza George’ has become Rochdale’s by-election front runner”
The Times, February 14, 2024: 9.
Then in 2011:
“Galloway hails a ‘Bradford spring’ while Labour licks its wounds.”
The Guardian (2011) Saturday 31 March, pp, 1, 4, 5.
In 2011, all the three main parties lost badly to George Galloway. The step ratios were 0.27 for Conservatives, 0.39 for Lib Dem and 0.55 for Labour.
See “7.1 George Galloway and Bradford West, March 2011”, a subsection of “Local elections and national polls …”.
6 “Local elections and national polls: modelling change”
Throughout 2023, local elections and byelections were studied with a view to gauging how successful Rishi Sunak was being in rescuing the fortunes of the Conservatives. An analysis of the local elections by Rob Ford, set me thinking and led to me producing a report:
Local elections and national polls: modelling change
W5 Local elections and national polls: modelling change
[W5.1 PART 1 The first two sections]
[W5.3 PART 3 The main part, Section 7.2]
PART 1 The first two sections (5 pages)
Abstract
1 Introduction
2 A simple account
2.1 This week’s by-elections: the headlines
2.2 Six recent by-elections
2.3 A simple model
2.4 Beyond the simple model
2.5 Conditional statements about the next general election
PART 2 Sections 3 to 8 (12 pages)
3 Regions and constituencies: density-dependent survival rates?
4 How the vote changes: percentage change, step ratio or change in z-score?
5 Scotland parliamentary elections: SNP and LibDem step ratios, 2007 - 2011
6 Local government elections, 4th May 2023 … step ratios
7 Local by-elections
7.1 George Galloway and Bradford West, March 2011
7.2 The main part … England: the ‘historic’ by-elections, 20th July 2023
… see Part 3
7.3 Scotland: SNP loses Rutherglen, 5th October 2023
7.4 England: another two losses, 19th October 2023
8 Conditional statements for the next election
PART 3 The main part, Section 7.2 (19 pages)
England: the ‘historic’ by-elections, 20th July 2023 …
1 Introduction
Part 3.1 Statics - the situation at one point in time: 2019
Part 3.2 Change
Part 3.3 Flow
Part 3.4 Political space (not yet available)
Part 3.5 The distribution of size (not yet available)
Part 3.6 Gravitational flow (not yet available)
7 UK Conservatives in political space, 2010-2024
The Conservative Party has long been dominant in UK politics. It has been in government since 2010 … but these past fourteen years have seen tensions between centre and right, both within the party and outside it. The coalition with the Liberal Democrats (2010-2015) and the continued premiership of David Cameron (2015-2016) empowered the centre of the party, dissatisfying the right. Labour moved left: Gordon Brown had lost in 2010, Ed Miliband had lost in 2015 and Jeremy Corbyn became leader.
The triumph of UKIP in the European elections of 2014 led to the Brexit referendum of 2016 and the attempted implementation of Brexit in the period 2016-2019 under the premiership of Theresa May … all this exacerbated the tensions between centre and right. May defeated Labour’s Jeremy Corbyn in the 2017 election – but with a reduced majority. The Brexit Party continued to flourish under the leadership of Nigel Farage, drawing voters away, mostly from the Conservatives and it was the decision by Farage not to contest all of the seats that allowed Boris Johnson to win the 2019 election, a second defeat for Labour’s Jeremy Corbyn. Corbyn was replaced by Keir Starmer.
Boris Johnson ‘got Brexit done’ in 2020, with strong personal and party ratings in the polls. Support for the Brexit Party dwindled. Yet tensions continued between centre and right.
Also, COVID had arrived in the UK in January 2020 (and possibly earlier, at the end of 2019), and there was a second wave in the Autumn of 2020 and a third wave in the summer of 2021 …
The year 2022 was a disaster for the Conservatives. Conservative MPs and Conservative party members voted first to remove Boris Johnson as leader and replace him with Liz Truss; and then they voted to remove Liz Truss as leader and replace her with Rishi Sunak – in October 2022. Three prime ministers within a year. This was against a backdrop of low support in opinion polls, poor local election results and by-election losses. The Queen died.
Since then, into 2023 and now in 2024, the key question has been whether or not Rishi Sunak can rescue the party. Sadly for the Conservatives he has not been able to do so. Poll ratings for the Conservatives have remained below 32%, the results in the local elections in 2023 were poor, and there have been a string of by-election defeats -
the most recent of which were yesterday: Conservatives lost the Kingswood and the Wellingborough by-elections.
8 Links
Wellingborough byelection 2024
https://en.wikipedia.org/wiki/2024_Wellingborough_by-election
Kingswood byelection 2024
https://en.wikipedia.org/wiki/2024_Kingswood_by-election
General election, December 2019:
https://en.wikipedia.org/wiki/2019_United_Kingdom_general_election ;
https://commonslibrary.parliament.uk/research-briefings/cbp-8749/;
Opinion polls:
https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_United_Kingdom_general_election
Local elections and national polls: modelling change
W5 Local elections and national polls: modelling change
[W5.1 PART 1 The first two sections]
[W5.3 PART 3 The main part, Section 7.2]
UK 2017: mass and gravity in political space
https://drive.google.com/file/d/1iXCf1AKwseBe3iLb_gM6vg8J6Tdwl6YM/view
Chapter 4 in Values, World Society and Modelling Yearbook 2015
Values, World Society and Modelling Yearbook, 2015.
Time series: UK general elections, 1945-2015
https://drive.google.com/file/d/199eS6bbnJtT0gIscZmX7vCLjcQX2NkZo/view
Chapter 12 in Values, World Society and Modelling Yearbook 2017
Values, World Society and Modelling Yearbook, 2017.
THE END