The candidates in 2024
All parties lost badly to George Galloway in 2012
Rochdale, general election 2019
Rochdale, by-election 2024
Result scenarios (before the result is known)
The result
Local and national: Conservative step ratios
Step ratio and step difference: the equation
The regression equation: the vote in 2019 and the vote in 2023/4
National opinion
Probability and event: voting Conservative
Deriving the equation from the staying and arrival rates
The variables and their relationships
The equation of a straight line … difference and ratio
Books, online, draft … Israel & Palestine … Local elections and national polls
“Save Britain from mob rule, Sunak tells police. PM orders end to ‘intimidatory’ Gaza protests.” The Times, February 29, 2024: 1.
And after the result, outside 10 Downing Street:
“Prime Minister labels George Galloway’s Rochdale win ‘beyond alarming’.”
Bolton News, March 1, 2024: https://www.theboltonnews.co.uk/news/24157529.prime-minister-labels-george-galloways-rochdale-win-beyond-alarming/
“Galloway prepares for comeback as honourable member for Gaza. Rochdale’s frontrunner is vowing to return ‘like a tornado’ after tapping into Muslim anger.”
The Times, February 24, 2024: 8.
“‘We don’t deserve this’: Rochdale’s voters left cold by campaign chaos. Disappointment in the candidates is palpable in the town, where people feel let down and neglected by the main parties.” The Observer, February 25 2024: 6-7.
Last Saturday, visiting family up in Inverness, I found myself on the High Street, in conversation with a complete stranger, discussing the distinction between ‘genocide’ and ‘military urban devastation’. There is sympathy and criticism, concern and emotion and tension in Britain about the war in Gaza. Every day there are articles in the paper about events in Britain relating directly or indirectly to the war. The UK Parliament is in turmoil about it. And it was at the centre of yesterday’s by-election in Rochdale.
The candidates 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.
The candidate parties were:
Labour: but the name on the ballot paper, Azhar Ali, has been suspended from the party over allegations of antisemitism (relating to Israel-Palestine);
Conservative: off on holiday;
Reform UK: forced to apologise for inappropriate text messages;
LibDem: one of its campaigners suspended for canvassing for a different party;
Green: but the name on the ballot paper has withdrawn after making Islamophobic comments;
“one name is left and it is that of one of the most controversial figures in British politics - George Galloway … the bookies’ favourite to win the seat. … he wants to see one state called either Israel-Palestine or Palestine-Israel where every person, Muslim, Christian, Jews [would be] an equal citizen.”
The Times, February 24, 2024: 8.
All parties lost badly to George Galloway in 2012
In 2012:
“Galloway hails a ‘Bradford spring’ while Labour licks its wounds.”
The Guardian (2012) Saturday 31 March, pp, 1, 4, 5.
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 …”.
https://www.theguardian.com/politics/2012/mar/30/george-galloway-bradford-spring-labour
Step ratio:
The step ratio for a party is the ratio of two percentages. It is the percentage in [2024] divided by the percentage in [2019].
Rochdale, general election 2019
In the 2019 general election, Labour won Rochdale gaining half the votes, well ahead of the Conservatives who gained 31%. The 2019 election was the Brexit election and the Brexit Party gained 8%. The Liberal Democrats were fourth with 7% (“We’ve been LibDem for a long time, back to Cyril Smith.”)
Note for later that the vote for the two main parties sum to 82.8%.
. Labour Cons Brexit LibD Green
2019 51.6 31.2 8.2 7.0 2.1
Rochdale byelection 2019
https://electionresults.parliament.uk/election/2019-12-12/Results/Location/Constituency/Rochdale/
Rochdale, by-election 2024
The by-election was called because of the death of the sitting Labour MP, Tony Lloyd. There were eleven candidates. Labour, Conservative, LibDem and Green were all on the ballot paper. So was the Reform UK party, successor to the Brexit Party. So was the Workers Party, with its leader, George Galloway as candidate (see link below). The remaining five candidates were three Independents, ‘no description’, and the ever-present Monster Raving Loony Party.
(https://en.wikipedia.org/wiki/Workers_Party_of_Britain).
Result scenarios (before the result is known)
In recent by-elections the result has been ‘known’ in advance: the Conservatives would do badly and either Labour or LibDem would win, depending on which party was the main opposition to the Conservatives in that locality. Not so this time. There are so many unusual features involving so many of the candidates that it is quite unclear what will be the outcome. In such a situation it is sensible to consider a wide variety of possible scenarios.
Labour, Conservative and George Galloway’s Workers Party are the main contenders. Nationally the Conservatives are down and Labour are up on their 2019 results. Locally the Labour vote (on the ballot paper) is likely to be reduced because the Labour Party has disowned their own candidate.
Let us start by considering orderings. The six possible orderings of the three candidates are:
Gall Cons Lab
Cons Gall Lab
Cons Lab Gall
Lab Cons [Gall] The 2019 result
Lab Gall Cons
Gall Lab Cons
Now let us consider percentages.
Dividing the 2019 Lab-plus-Cons vote equally amongst the three main parties gives 27.6% to each party.(Sum equals 82.8%). This would arise if Labour lost 24%, Cons lost just 3.6% and Galloway gained 27.6%. It seems likely that the Conservative vote will be down by much more than that …
Dividing just the 2019 Labour vote between Labour and Galloway gives 25.8% to each of Labour and Galloway.
Suppose the step ratio for Labour and Conservatives was the same: p. Suppose Labour and Galloway each have the same percentage. Then Labour and Galloway have 31.8%; and Conservatives have 19.2%. The step ratio is p=0.616. (It so happens that this value for the step ratio is almost identical with the national step ratio.)
Calculations:
[0.828(1-p)=0.516p
0.828=1.344p
p=0.616
0.516p=0.318
0.312p=0.192]
Or might it be possible that moderates converge upon the LibDems, giving them victory?
The result
BBC “LIVE.
“This is for Gaza” says George Galloway.
George Galloway only won because Labour did not stand, party claims
https://www.bbc.co.uk/news/live/uk-politics-68402672
https://www.bbc.co.uk/news/politics
The Guardian:
https://www.theguardian.com/politics/2024/mar/01/george-galloway-wins-rochdale-byelection
The Spectator:
Times of Israel:
“This is for Gaza George Galloway wins UK seat after campaigning against Israel.”
Board of Deputies:
George Galloway won easily with 39.7% of the vote, ahead of the combined total of 34.4% for the five parties who contested Rochdale in 2019. The vote for Labour in 2019 all but disappeared, most of it going one assumes to Galloway. The Labour vote in 2019 was 51.6%, whereas the combined Labour and Galloway in 2024 was 47.4%.
Coming second was David Tully, an Independent, with 21.3%. The vote for Conservatives fell dramatically, most of it going one assumes to Tully. The Conservative vote in 2019 was 31.2%, whereas the combined Conservative and Tully vote in 2024 was 33.3%.
LibDem retained its share while Brexit and Green lost a third of their vote. The four other candidates gained a combined total of just 5.3%.
Note that turnout was a low 31%.
. Labour Cons Brexit/ LibD Green Gall Tully Indep Indep Indep MR
Reform Indep
2019 51.6 31.2 8.2 7.0 2.1 0 0 0 0 0 0
2024 7.7 12.0 6.3 7.0 1.4 39.7 21.3 1.7 1.5 1.4 0.7
step r. 0.15 0.38 0.77 1.00 0.67
My scenarios? It turns out that it was only me that didn’t ‘know’ the result in advance – the bookies and the columnists were right! The scenario that caught one aspect of what was happening was:
“Dividing just the 2019 Labour vote between Labour and Galloway gives 25.8% to each of Labour and Galloway.”
Being to the left of Labour might well have suggested that Galloway would only attract Labour voters.
Rochdale byelection 2019
https://electionresults.parliament.uk/election/2019-12-12/Results/Location/Constituency/Rochdale/
Rochdale byelection 2024
https://en.wikipedia.org/wiki/2024_Rochdale_by-election
Local and national: Conservative step ratios
The local step ratio for the Conservatives in Rochdale 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 the two by-elections a fortnight ago and six by-elections last year. Rochdale has the second lowest step ratio.
Conservative step ratios:
0.26 in Rutherglen, Scotland
0.38 in Rochdale
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
* ‘this week’ is actually the second week in February 2024. However the Conservative vote in the last fortnight has been in the same range as previously – see next section.
Step ratio and step difference: the equation
“… 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.
step difference = (step ratio – 1) (vote in 2019) true in each case*
step difference = –0.39 (vote in 2019) [A] using national step ratio of 0.61
y = -0.39 x [A]
*See W13.2 UK Conservatives: only 56% have stayed with the party … the gravity model
The following table gives more detail. There is indeed a tendency for the difference in the vote to be larger if the 2019 vote is larger. The correlation between the two columns is -0.7, supporting the validity of equation [A] in this situation. A graph also supports equation [A].
Table Measuring change from 2019 to 2023
Locality vote vote differ. step regional
. 2019 2023 pcent ratio survival rate*
x y
Tamworth 66.3 40.7 -25.6 0.61 61
Wellingborgh 62.2 24.6 -35.6 0.39 61
Selby 60.3 34.3 -26.0 0.57 72
Mid-Beds 59.8 31.1 -28.7 0.52 61
Kingswood 56.2 34.5 -21.7 0.61 60
Frome 55.8 26.2 -29.6 0.47 60
Uxbridge 52.6 45.2 - 7.4 0.86 81
[UK] 43.6 26 -17.6 0.60 61
Rochdale 31.2 12 -19.2 0.39 72
[Scotland] 26.1 16 - 9.9 0.61 80
Rutherglen 15.0 3.9 -11.1 0.26 80
. P1 P2 P2-P1 P2/P1
*See section 3 in W5.2 PART 2 Sections 3 to 8
The table below shows how the model provides a good fit to the actual step difference – see second and third columns. As noted above the correlation is 0.7 between actual and model (and -0.7 between x and y).
Table The step difference: the actual and the model
Locality vote differ. model
. 2019 2023 y=-0.39x
x actual model
Tamworth 66.3 -25.6 -25.9
Wellingborgh 62.2 -35.6 -24.3
Selby 60.3 -26.0 -23.5
Mid-Beds 59.8 -28.7 -23.3
Kingswood 56.2 -21.7 -21.9
Frome 55.8 -29.6 -21.8
Uxbridge 52.6 - 7.4 -20.5
[UK] 43.6 -17.6 -17.0
Rochdale 31.2 -19.2 -12.2
[Scotland] 26.1 - 9.9 -10.2
Rutherglen 15.0 -11.1 - 5.9
. P1 P2-P1
The regression equation: the vote in 2019 and the vote in 2023/4
The previous section has looked at the relationship between the step ratio and the step difference. We now take a more direct approach, looking at the relationship between the 2019 and the 2023/4 voting percentages.
The correlation between the vote in 2019 and the vote in 2023 is 0.84. A linear regression gives a beta-coefficient of 0.62, significant at the 0.001 level. The constant coefficient is very insignificant, p=0.7. So the regression equation is approximately proportional. (Note though that the standard error of beta is 0.13.)
. vote(2023/4) = -2.9 + 0.62 vote(2019)
Uxbridge, Boris Johnson’s old set in London, is an outlier. Removing this outlier gives an even stronger result. The correlation between the vote in 2019 and the vote in 2023 is 0.92. A linear regression gives a beta-coefficient of 0.59, significant at the 0.0002 level. The constant coefficient is very insignificant, p=0.5. So the regression equation is approximately proportional. (Note though that the standard error of beta is 0.09.)
. vote(2023/4) = -3.1 + 0.59 vote(2019)
Links
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, sixteen polls within 15-27 February 2024; the above site gives links to the individual polls:
The Conservative % vote in the sixteen polls:
29, 24, 23, 27, 26, 28, 23, 27, 20, 24, 25, 27, 26, 23, 23, 28
[range 20-29; midpt 25, median 25.5; step ratio 62%]
National opinion
Probability and event: voting Conservative
After you have tossed a coin the outcome event is either a head or a tail. Before you toss the coin the probability is a half.
After you put your cross on the ballot paper the outcome event is either a vote for the Conservatives or it is not. Before you put the cross, there is only a probability that the vote will be for the Conservatives.
This week YouGov asked the question:
“On a scale of 0 to 10, where 0 means you would never consider voting for them, and 10 means you would definitely consider voting for them, how likely are you to consider voting for the following parties at the next election?” February 26, 2024.
One interpretation of the scale is that the numbers on the scale correspond to probabilities – for example 7 on the scale corresponds to a probability of 0.7.
The results are given in the table below: 41% said ‘never’; 10% gave a middling response; and 7% said ‘definitely’. For each of the other points on the eleven-point scale there were just a few percent opting for it.
Overall, 23% gave a response of 0.6 or above. We can calculate the expectation of considering the Conservatives and that gives 0.281 (summing the products of probability of event and percentage of people).
prob % prob x %
0 41 0
0.1 6 .006
0.2 6 .012
0.3 6 .018
0.4 4 .016
0.5 10 .05
0.6 4 .024
0.7 5 .035
0.8 4 .032
0.9 2 .018
1.0 7 .07
. 100 .281
Deriving the equation from the staying and arrival rates
Party percentages – the percentages of voters supporting each party – change over time. How does the percentage at one point in time relate to the percentage at a previous point in time? A simple notion is that the later percentage is a linear function of the earlier percentage:
p(2) = u + b p (1) [1]
A simple case is that if u=0, then the two percentages are in proportion, and b is what we have called the step ratio.
p(2) = b p (1) [2]
We now show how equation [1] can be derived. In what follows percentages and proportions are equivalent: 50% corresponds to 0.5; and 100% corresponds to 1.
We are interested in those (the population S) who are making a definite choice in 2024 … and amongst those, the percentage C(2) choosing Conservative. The population S comprises three parts: those voting Conservative in 2019, as a percentage C(1); those voting other than Conservative in 2019, as a percentage (1-C(1)); and the rest, a proportion R (those in population S who did not vote in 2019). The total of these three parts is (1+R).
Within each of these three parts, a certain percentage votes Conservative in 2024, percentages/proportions s, a and n, respectively – stayers, arrivals and newcomers. So the percentage/proportion C(2) is given by:
C(2) = [ s C(1) + a (1-C(1)) + n R ] / (1+R)
= [ (a + n R) + (s-a) C(1))] / (1+R) [3]
Note that equation [3] is in the form of equation [1].
If there are no newcomers, R=0, then we have:
C(2) = [ a + (s-a) C(1))] [4]
If in addition there are no arrivals then a=0, and we have:
C(2) = s C(1) [5]
In this case s, the staying rate, is equal to the step ratio.
It so happens that equation [4] can arise in a different way. Consider n, the proportion of newcomers who are Conservatives. The simplest assumption would be that this is the same as the current proportion, C(2). So n=C(2). From equation [3] we get:
C(2) +R C (2) = (a + C(2) R) + (s-a) C(1)
And from this we get equation [4].
Application
The information reported about a survey by Opinium 21-23 February 2024 gives estimates of s and a: s=0.6 and a=0.02. So we get:
C(2) = 0.02 + 0.58 C(1) [4]
This is approximately equal to the equation we used when looking at step ratios and step differences in an earlier section:
C(2) = 0.61 C(1) [6].
The link to Opinium 21-23 February 2024 is in:
https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_United_Kingdom_general_election
The variables and their relationships
Four sections of this report look at the variables and their relationships:
Local and national: Conservative step ratios
Step ratio and step difference: the equation
The regression equation: the vote in 2019 and the vote in 2023/4
Deriving the equation from the staying and arrival rates
The two basic variables are the vote in 2019 and the vote in 2023/4. The step ratio and the step difference are two different ways of describing the change in the basic variables. There are various relationships between these four variables. The regression equation looks directly at the empirical relationship between the vote in 2019 and the vote in 2023/4. Another approach involves deriving the equation from the staying and arrival rates. The coefficient in each of these equations is almost the same as the national step ratio. There is an equation expressing the step difference in terms of the step ratio and the voting percentage.
The equation of a straight line … difference and ratio
In abstract terms, our discussion goes back to what we all learned in school mathematics. We learned about graphs with an x-axis and a y-axis and about the equation of a straight line:
. y = m x + c
Consider the difference d between x and y:
. d = y – x = (m-1) x +c
Consider the ratio r between x and y:
. r = y / x
The relationship between difference and ratio is:
. d = r x – x = (r-1) x
Books, online, draft … Israel & Palestine … Local elections and national polls
B1 Israel and Palestine: self and other, positive and negative; 2023
Israel and Palestine: self and other, positive and negative; 2023
B2 Local elections and national polls
Local elections and national polls
Online book in preparation, 53 pages, 1 March 2024.
1 Local elections and national polls, 2023
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]
2 Kingswood and Wellingborough: Conservatives lose badly
W13.2 UK Conservatives: only 56% have stayed with the party … the gravity model
3 Rochdale: George Galloway wins with 40%; Labour 8%
W14 Rochdale: an Israel-Palestine UK by-election
THE END