The Chancellor “vowed to put “national interest” before “political expediency” ”.

…

Reeves will say it is a “Labour budget” with “Labour values”.

…

  Is it possible for democracy to be rule by the winning party and, at the same time, to be rule for all of the people? This general question is illuminated here by a very specific case study: the analysis of people’s opinions about budget priorities.

  Is a society united or divided? Usually there is variation, a distribution of all of the people, and it may be that the distribution exhibits neither a united nor a divided society.

  How can we avoid exaggerating the differences between the parties? How can we avoid underplaying the differences between parties? Here we compare parties on a variety of different measures: gaps and overlaps, ordering and distancing, grouping, the probability of agreement; and correlations and principal components. Note that the reasoning in Parts 3 and 4 becomes increasingly abstract.

  Part 1 Introduction

Budget speculations and opinion polls

Front page headlines

The parties and all of the people

  Part 2 All of the people

Budget issue priorities – all the respondents

  Part 3 The parties

The parties: the gap and overlap between a pair of distributions

The orderings of the parties and their percentages

The issues and the orderings of parties

Gaps and overlaps: party distributions, similar or different?

Orderings with distances and the grouping of parties

The probability of agreement

  Part 4 Correlations and principal components

The correlation matrix for the five variables

One variable ‘explains’ five

Two variables ‘explain’ five …

… Group A and Group B

… U and V, All and Parties

… the equations for the five variables

… Principal Components I and II, All and Parties

Further details about the principal components analysis

  Part 5 Conclusion

Part 1 Introduction

Budget speculations and opinion polls

Rachel Reeves, the Chancellor of the Exchequer will present her budget to the House of Commons on Wednesday. It has been much discussed and Reeves herself has made a number of comments and speeches. A few weeks ago she seemed to indicate that there would be an increase in income tax but more recently this proposal seems to have been rejected. All proposals have their critics within the cabinet, within the party, within parliament and beyond.

  Alongside all this there have been questions about Reeves’ position and indeed about Prime Minister Keir Starmer’s position, not least in the light of recent opinion polls. Last month an MRP poll conducted in September gave a predicted election result with the percentages given in the table below, alongside which are the range of percentages in the most recent polls conducted since November 5th.

Table 1 UK Opinion polls: MRP in September; polls since November 5

.                               Sept. Nov. 5-

Reform                    36% 25-33

Labour                     21% 15-20

Conservative          15% 16-20

Liberal Democrat    10% 11-15

Green                       7% 11-18

You Party                  4% -

SNP                       3%   2-3

Plaid Cymru           1%   1-2

MIN                       3% -

Others                     -         2-4

combined Cons+Ref   51% 43-51   (Group A)

.                                                              

September 2025: https://www.electoralcalculus.co.uk/blogs/ec_vipoll_20251015.html;

Ongoing: https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_United_Kingdom_general_election ;

Front page headlines

Here are the front-page headlines in The Times and The Observer (on Sundays) for the period leading up to the budget, Wednesday 5th November onwards.

5 Reeves lays ground for 1970s-style tax increase. We will all have to do our bit, says chancellor …

… she vowed to put “national interest” before “political expediency”

6 -

7 Income tax will go up, Reeves tells watchdog. Fear of rises is harming growth, Bank warns

8 Reeves set to announce retirement savings raid. Budget will target salary sacrifice schemes

9 Sunday Generation game … the chancellor’s ‘two-up two-down’ budget for the young

10 Reeves ‘will doom Labour with income tax increase’

11 Reeves hints at lifting two-child benefit cap (as well as taxes)

12 Starmer vows to defend leadership from ‘feral’ Labour MPs

13 PM told to fire top aide as civil war hits Labour

14 Reeves ‘ditches plan to raise income tax’

15 Reeves banks on stealth tax. Threshold freeze to drag pensioners into HMRC’s net.

   U-turn on budget plan spooks market.

16 Sunday -

17 Three in four people paying top-rate tax don’t feel poor

18 Nearly half all Labour voters want Starmer out by next election

19 Reeves ready to protect small businesses from big tax rises (page 2)

20 Reeves gears up to defy Uber with ‘taxi tax’ (page 4)

21 Consumer confidence shaken by jitters over budget tax increases (page 33)

22 Budget will be last throw of the dice for chancellor.

  Reeves: country can’t just keep muddling through. (pages 6-7)

  Reeves: I’m sick of the mansplaining. (Magazine)

23 Sunday, The Observer: Road to the budget. Help with cost of living to make smorgasbord easier to swallow. Minor changes in fiscal forecasts shouldn’t make the weather for the chancellor. (pages 14-15)

24 Middle earners to shoulder £20bn boost to benefits

  CBI warns of ‘Groundhog’ budget (page 8)

25 Reeves tells labour MPs to unite behind her budget. (page 1)

  Reeves will say it is a “Labour budget” with “Labour values”. (page 2)

26 The Budget Day

  Reeves aims at workers, savers and pensioners. ‘Smorgasbord’ budget could cost families £1,600

The parties and all of the people

The Chancellor “vowed to put “national interest” before “political expediency” ”.

  Is it possible for democracy to be rule by the winning party and, at the same time, to be rule for all the people? This general question is illuminated by a very specific case study: the analysis of people’s opinions about budget priorities.

  A newly elected leader will sometimes declare: “our party has won the election but we shall govern for all the people”. The contest between the parties competing in the election may have been bitter and so it is hoped that an attention to all of the people regardless of party will heal the wounds. Society, it is said, has been ‘divided’ and now needs to become ‘united’.

  The distinction between all of the people and the parties is mirrored in quite a mundane way in the results of opinion polls which typically give both the responses given by all of the respondents and also the responses by particular social groups such as the supporters of each party.

  In Part 2 we look at the responses of all of the people; and in Parts 3 and 4 we look at the responses of the different party supporter groups. Part 3 looks at the percentages and Part 4 looks at the correlations and principal components.

Part 2 All of the people

Budget issue priorities – all of the respondents

The MRP poll report (September 2025)

"Ahead of the Autumn Budget coming in November, voters are making their priorities clear, placing the economy, immigration and the NHS at the top of the agenda. Labour now faces a fight for votes, and their ability to act decisively and deliver on these priorities will determine whether the party can defend its leadership or risk falling further behind as Reform seeks to solidify its gains."

Kevin Craig, founder of PLMR

https://www.electoralcalculus.co.uk/blogs/ec_vipoll_20251015.html

Section 3 of the MRP poll report was entitled “most important issues”. Respondents were “asked voters what are the most important issues that they would like the government to prioritise in the upcoming Autumn Budget. Respondents could pick up to three options.” It is the responses to this question that we now discuss in the rest of this report.

  Table 2 below is based on all the respondents and gives the percentage of people prioritising each issue. The issues are listed in order of decreasing percentages.

  Respondents were invited to pick up to three issues. If all of them had picked three issues the total of the percentages would have been 300%. In fact the total is 257%, indicating that the average respondent picked 2.57 issues.

  Which issues are given priority? The top three issues are the economy and the cost of living; immigration and border control; and the NHS. These three issues relate to economic, control and social aspects, respectively. The next most important issue is crime, policing and justice but this has half the percentage given to the top three issues. This issue and the remaining issues also relate to economic, control and social aspects and there is also an issue relating to climate change and the environment.

What is the nature of the distribution of responses? Is the population united or divided? The table shows that a few issues attract many responses while many issues attract fewer responses. Different voters have different priorities: if they were united and all had had the same three top priorities then these three top issues combined would have 257% of the responses (86% each) and the other issues would have 0%. Instead the top three issues combined have 155% - and the other seven issues and two other categories have 102%. Thus the responses do not represent complete consensus – the population is not united - but they do represent a degree of concentration of opinion, contrasting for example with an even spread of opinion which would have given each option under 30% (and three options combined, under 90%).

  This then is the distribution of responses for all of the respondents.

Table 2 All of the respondents: the percentage prioritising each issue; the issue area.

.       Respondents could pick up to three options. September 2025.

Cost of living, economy        59  economic

Immigration, border control     51  control

NHS                                      45  social

Crime, policing, justice         23  control

Social care, elderly, vulnerab    18  social

Cutting taxes                         13  economic

Climate change, environment   12  environment

Education and schools                    8  social

Reducing the budget deficit       8  economic

Public health, illness prevent      7  social

Other                                       3 

Don’t know                           10

Total                                    257

https://www.electoralcalculus.co.uk/blogs/ec_vipoll_20251015.html

Part 3 The parties

Table 2 above gives the distribution of responses for all the respondents. The MRP report also gave the responses for each of the four party supporter groups: Labour, LibDem, Conservative and Reform. We now look at the distribution of responses for each of the parties. Is a party’s distribution similar to or different from the distribution for all the respondents? Do parties have similar or different distributions? These general questions will be addressed by considering a variety of measures:

  the gap and the overlap between a pair of distributions;

The parties: the gap and the overlap between a pair of distributions

“Let me be really clear – every minute that is not spent talking about and dealing with the cost of living is a minute wasted of the political work of this government.”

Keir Starmer quoted in The Times, November 18 2025: 1.

Table 2 above presents the overall responses for “All” of the respondents and all of the issues. Table 3 below gives the responses for just one of the issues, namely the top priority issue, the cost of living and the economy.

The Labour percentage is highest at 68% - in other words 68% of Labour voters mentioned this issue as one of their top three priorities. The LibDem percentage is lowest at 57%, giving a gap of 11% between the two parties. This is quite a small gap.

  Although there is this gap, there is also an overlap between the two parties. The overlap is 89% (=100%-11%), comprising 57% sharing that this is one of their priority issues plus 32% sharing that this is not one of their priority issues. This overlap can be conceived of as a pairing of Labour and LibDem voters who have responded the same way: there are 89% such pairings, leaving 11% of each party unpaired. In this sense the Labour distribution and the LibDem distribution have an extensive overlap.

  For this particular issue Labour and LibDem were the two furthest apart parties. So the gaps between the other parties will be smaller the overlaps bigger.

Table 3 Percentage of a party’s supporters giving the cost of living and economy issue as one of their top three priorities; the largest gap

.

.                                           Lab  All   Cons Ref  LibDem       gap

Cost of living, economy      68    59    59    58    57            -11

The orderings of the parties and their percentages

In Table 3 above the parties have been ordered so that the percentages are in decreasing order. The party ordering for this issue is Labour, All, Conservative, Reform and LibDem.

Note that in what follows we ignore whether the order is a decreasing one or an increasing one.

  In the next section we shall look at all the other issues and we shall find that the order of the percentages leads us to order the parties in different ways. One of the orderings is particularly common and we refer to it as the primary ordering of the parties. It corresponds to our everyday understanding of where the parties are on the Left-Right political spectrum. It is:

         (Labour, LibDem, All, Conservative, Reform)                  [1]

There are other less common, ‘subsidiary’ orderings. One of these switches Labour and LibDem:

         (LibDem, Labour, All, Conservative, Reform)                  [2]

Another switches Conservative and Reform:

         (Labour, LibDem, All, Reform, Conservative)                  [3]

Orderings [2] and [3] involve adjacent switches but another ordering involves  switches that are farther apart: it pairs the extremes (and it pairs the middle parties) that are found in ordering [1]:

         (Labour, Reform, All, LibDem, Conservative)                  [4]

Finally, as we have already noted, the top issue gives the following order:

(Labour, All, Conservative, Reform, LibDem)                  [5]

As is the case for the cost of living issue, equal percentages sometimes occur and we might refer to such a case as a weak ordering [5].

The issues and the orderings of the parties

Table 4 below gives the responses to all the issues for the four parties and also for All the voters. The issues are listed in order of decreasing percentage for All (as in the listing in Table 2 above) – see the middle column. The four parties (and All) are ordered in the table according to the primary ordering [1] – see the row heading. Different parties come top on different issues: Reform comes top on control issues, Conservatives come top on economic issues, Labour comes top on social issues and LibDem comes top on environment issues (note that the Greens are not included in this analysis).

Issues where Reform is the party with the highest priority percentage:

  immigration, crime;

  both issues have the primary ordering [1]

Issues where Labour is the party with the highest priority percentage:

  cost of living, NHS^^, social care^, education,^ public health^^;

  ^^two have the primary ordering [1]; ^two have the weak prime ordering [1];

  cost of living: the weak ordering [5]

Issues where the Conservatives are the party with the highest priority percentage:

  cutting taxes, budget deficit: neither has the primary ordering

  cutting taxes: Labour, LibDem, [All], Reform, Conservative [3]

  budget deficit: Labour, Reform, [All], LibDem, Conservative [4]

Issues where LibDem is the party with the highest priority percentage:

  climate change and environment: this does not have the primary ordering

  ordering: LibDem, Labour, [All], Conservative, Reform [2]

Thus four issues have the primary ordering [1]; two issues have a weak primary ordering [1]; one issue switches the adjacent Reform and Conservatives (cutting taxes) [3]; one issue switches the adjacent Labour and LibDem (environment) [2]; one issue has the ordering Labour, Reform, [All], LibDem, Conservative (budget deficit) [4]; and one issue, cost of living, has ordering [5]. There are ten issues in all.

Table 4 Ten issues. Issue priority profile of parties.

Percentage of a party’s supporters prioritising an issue; the largest gap

.                                           Lab  LD   All   C     R                 gap 

Cost of living, economy      68*  57    59    59    58                -10 (-11)

Immigration, border control   30    36    51    74    90*              60

NHS                                    62*  59    45    39    34                -28

Crime, policing, justice       19    20    23    30    37*              18

Social care, elderly, vulnerab  25*  22    18    18    14                -11

Cutting taxes                         7      8    13    21*  20                13 (14)

Climate change, environment 19    25*  12      6      2                -17 (23)

Education and schools        13*  13*    8      5      3                -10

Reducing the budget deficit     7    10      8    13*    8                1 (6)

Public health, illness prevent  12*  10      7      4      3                -9

Other                                     2      3*    3*    2      2                0 (1)

Don’t know                           4      5    10*    3      2                -2 (8)                                                                                                                               

Gaps and overlaps: party distributions, similar or different?

In Table 4 above the gaps between Labour and Reform are given in the final column. For six of the issues this is the largest of the gaps between the parties. Also, given in brackets, are the gaps between the highest and the lowest percentages, in the cases where the Labour-Reform gap is not the largest gap.

  The gaps vary in size between 0 and 60. However all but three of the gaps are less than 20%. So all but three of the overlaps are more than 80%. The NHS has a gap of 28% and the environment has a gap of (23%). The largest gap by far is the 60% on immigration and border control. With this one exception the overlaps are much larger than the gaps. So it seems reasonable to say that the four parties are more similar than different on all issues other than immigration.

Orderings with distances and the grouping of parties

Consider the ordering for the immigration issue:

.                                           Lab  LD   All   C     R                 gap 

Immigration, border control   30    36    51    74    90                60

The gap between Labour and Reform is 60. This is made up of distances between adjacent parties:

  6 between Labour and LibDem

15 between LibDem and All

23 between All and Conservative

16 between Conservative and Reform

If we ignore the All percentage then the distance between LibDem and Conservative is 38. This is greater than either the distance between Labour and LibDem or the distance between Conservative and Reform. This suggests considering Conservatives and Reform as a group, Group A; and considering Labour and LibDem as a group, Group B. This suggests a hypothesis:

  The distance between groups is greater than the distances within groups.       [H]

Table 5 considers the issues which have the primary ordering [1] and gives the distances between adjacent parties. Let us define the distance between Groups A and B to be the distance between LibDems and Conservatives. In all except one of the cases hypothesis [H] holds. Quite often the distance between the two groups is very much greater than the distance within the two groups.

Table 5 Issues with the primary ordering [1]. Distances between parties. Largest gap

.                                                       distances                                         largest

.                                           L:LD   (LDA) LD:C   (A:C)   C:R              gap 

Immigration, border control   6      (15) 38    (23) 16                60

NHS                                    3      (14) 20      (6)   5                -28

Crime, policing, justice       1        (3)  10      (7)   7                18

Social care, elderly, vulnerab 3        (4)   4      (0)    4                -11

Education and schools        0        (5)   8      (3)   2                -10

Public health, illness prevent  2        (3)   6      (3)   1                -  9

We now consider the other four issues.

One issue switches the ordering within Group A (cutting taxes) to give ordering [3]. The distance LD to R is 12. As with ordering [1], hypothesis [H] holds and the distance between groups A and B is greater than the distances within groups.    

.                                           Lab  LD   All   R     C                 gap

[3] Cutting taxes                   7      8    13    20    21                13 (14)

. adjacent distances               1     5   7     1                                   

Another issue switches the ordering within Group B (climate change) to give ordering [2]. The distance Lab to C is 13. As with ordering [1], hypothesis [H] holds and the distance between groups A and B is greater than the distances within groups.

.                                           LD   Lab  All   C     R                 gap 

[2] Climate change, envt    25    19    12      6      2                -17 (23)

. adjacent distances               6     7   6     4                                   

Another issue brings the two extremes, Labour and Reform together and brings the two centre parties, LibDem and Conservatives together – to give ordering [4]. However the distance between Labour and Conservative is very small: 6.

.                                           Lab  R     All   LD   C                 gap 

[4] Reducing budget deficit   7    8        8    10    13                1 (6)

. adjacent distances               1     0   2     3                                   

Finally, the cost-of-living issue separates Labour from the three other parties which are all close together.

.                                           Lab  All   C     R     LD           gap 

[5] Cost of living, economy 68*  59    59    58    57            -10 (-11)

. adjacent distances               9     0   1     1                                   

In conclusion, although there are five different orderings it is the primary ordering [1] and the separation of Group A from Group B which seem to be the features which stand out most.

The probability of agreement

This section stands somewhat apart from the general line of argument. However here too we are interested in how similar or how different the parties are.

Imagine random encounters between two people. Will the two people agree in the sense of choosing the same option …? From the above percentages in Table 4 we can calculate:

… to the immigration question:

The probability of two Reform people agreeing is 0.82.

The probability of two Labour people agreeing is 0.58.

The probability of a Reform person agreeing with a Labour person is 0.34.

   Here the probability of agreement between parties is lower than the probability of agreement within parties. The probability of agreement about immigration within Reform is exceptional.

… to the NHS question:

The probability of two Reform people agreeing is 0.55.

The probability of two Labour people agreeing is 0.53.

The probability of a Reform person agreeing with a Labour person is 0.46.

   Here the probability of agreement between parties is much the same as the probability of agreement within parties and is about a half.

Part 4 Correlations and principal components

Are the parties similar or different? In particular do their voters have similar or different opinions about which are the priority issues? In quantitative terms are the numbers for one party in Table 4 similar to the numbers for another party? One way to answer this question is to look at the correlations between the columns in Table 4 and then to use the correlations to identify principal components …

  … the five columns in Table 4 give five party/All variables. Table 6 below presents the correlation matrix between these five variables. The patterns in the matrix are suggestive of the factors or components which will be considered in the following sections.

  The correlations were all high, in some cases extremely high. This gives one answer to the question above: the four parties and all of the people are similar in the sense of having similar opinions about the issues. In particular the correlations with All were between 0.89 and 0.94. This suggests a factor which might be called ‘All’.

  The table lists the parties in terms of the primary ordering [1] discussed in a previous section. With this ordering a pattern is revealed: the closer the parties are in the primary ordering, the stronger is the correlation between them. In particular the four correlations between adjacent parties/All are 0.98, 0.91, 0.94 and 0.99 – see the diagonal next to the leading diagonal. This suggests a second factor which might be called ‘Parties’. So two factors are suggested: ‘All’ and ‘Parties’.

  Taking a closer look, and omitting the All variable, the three correlations between adjacent parties are 0.98, 0.76 and 0.99. This suggests a pairing of parties: Group A consisting of Reform and Conservatives; and Group B consisting of Labour and LibDem. This suggests two different factors, Group A and Group B.

Table 6 The correlation matrix for the five variables

         Lab  LD   All   C     R

Lab  1      0.98 0.89 0.72 0.61

LD           1      0.91 0.76 0.66

All                       1      0.94 0.89

C                                     1      0.99

R                                                     1

One variable ‘explains’ five

There are five variables in Table 6 above. These five variables can all be ‘explained’ by just one variable – at least approximately. This variable is the All variable. Its correlations with the other four variables are very high: 0.89, 0.91, 0.94 and 0.89. (And All has a perfect 1.00 correlation with itself.) These high correlations mean that this one variable gives an approximate ‘explanation’ of the five variables. See Table 7 below.

Table 7 One variable correlates with five variables

         All

Lab  0.89

LD   0.91

All   1.00

C     0.94

R     0.91

Two variables ‘explain’ five …

The previous section shows how one variable ‘explains’ the original five variables - approximately. We now show how two variables can provide an even better approximate ‘explanation’. This can be done in a number of different ways. In what follows we consider:

  two variables, Group A and Group B;

  two variables, U and V, All and Parties

  two variables, principal components I and II

Of these three ways it is the third, principal components, approach which is the recognised statistical procedure.

… Group A and Group B

Here the two variables are obtained by combining some of the original five variables. In the correlation matrix, there is an almost perfect correlation between the Conservative (C) and Reform (R) variables. We define the Group A variable as the average of these: A=(C+R)/2. Also, there is an almost perfect correlation between the Labour (L) and LibDem (LD) variables. We define the Group B variable as the average of these: B=(L+LD)/2.

  A correlates almost perfectly with both C and R; and B correlates almost perfectly with both Lab and LD. These high correlations mean that the two variables, A and B, give an approximate ‘explanation’ of the five variables. See Table 8 below.

  The two variables A and B are correlated at 0.69^ (A and B are ‘oblique’); and this is reflected in the correlations of A with Lab and LD; and in the correlations of B with C and R.

^ Note that this number is not in the table.

Table 8 Two variables, A and B, correlate with the five variables

                     * indicates an almost perfect correlation

.       A     B

Lab  0.61 1.00*

LD   0.66 1.00*

All   0.89 0.91

C     0.99*   0.74

R     1.00*   0.64

… U and V, All and Parties

Here the two variables, U and V, are derived from A and B. This is done simply by adding and subtracting A* and B*. U=(A*+B*) and V=(A*-B*). Here

A*=A/25.6; B*=B/20.3 where 25.5 and 20.3 are respectively the standard deviations of A and B.

Notes: (i) This adjustment ensures that the U and V have zero correlation.

(ii) In geometric terms the shift from A and B to U and V represents a rotation of the axes in the same two-dimensional space.

  U correlates very highly with all the variables and can be thought of as relating to All of the people. In contrast V correlates positively with Group A variables and negatively with Group B variables. It might be thought of as relating to Parties aspects. See Table 9 below.

  The two variables U and V have a zero correlation – they are ‘orthogonal’ to one another. (This zero correlation is not part of the table below.)

  Here then the two variables correspond to the distinction that is at the core of this report: the distinction between the parties and All of the people. Note that the variable All is much more powerful than the Parties variable in that its correlations are much higher.

Table 9 Two variables, U and V, All and Parties, correlate with the five variables

.       U     V

.       All   Parties

Lab  0.90 -0.42

LD   0.93 -0.36

All   0.99   0.01

C     0.94   0.32

R     0.89   0.45

The equations for the five variables

Table 9 shows one way in which the two variables explain the original five variables. We can take this further though and find an equation which combines the two variables U and V to explain over 98% of the variation in each of the five variables. This is an almost perfect explanation of each of the five variables. The variable on the left hand side is the column of percentages in Table 4 above.

Labour =                 -0.06 + 0.49 All (U) - 0.54 Parties (V)

LibDem =                0.07  + 0.51 All (U) - 0.45 Parties (V)

All =                     0.04  + 0.54 All (U) + 0.02 Parties (V)

Conservative =        0.03  + 0.52 All (U) + 0.41 Parties (V)

Reform =                 -0.02 + 0.48 All (U) + 0.57 Parties (V)

Notes: (i) none of the intercepts were statistically significant.

(ii) In the equations, ‘All’ is the Table 2 percentage for All; ‘All (U)’ is U as defined above and is an equal weighting of the four party percentages in Table 2.

The coefficients in the above equations are similar to the ‘loadings’ which are obtained in the next section: compare Table 10 below and Table 11 in the next section. (The signs in the second columns of the two tables are simply reversed.)

Table 10 Two variables, U and V, All and Parties: coefficients with the four party variables

.       U     V

.       All   Parties

Lab  0.49 -0.54

LD   0.51 -0.45

C     0.52   0.41

R     0.48   0.57

… Principal Components I and II, All and Parties

Here the two variables, PCI and PCII, are obtained by applying a standard statistical procedure: principal component analysis. The procedure is quite complicated and less intuitive than what we have done so far. Nevertheless, the outcome is somewhat similar to the U and V, All and Parties, model. The outcome is a ‘loading matrix’ where two principal components, PCI and PCII, have ‘loadings’ on the four party variables.

  PCI correlates positively with all the variables and can be thought of as relating to All the people. In contrast PCII correlates negatively with Group A variables and positively with Group B variables. It might be thought of as relating to Parties aspects. See Table 11 below.

  The two variables PCI and PCII have a zero correlation – they are ‘orthogonal’ to one another. (This zero correlation is not part of the table below.)

  Comparing Table 10 with Table 11, the numbers are similar (the signs in the second columns can simply be reversed.)

Table 11 Two variables, PCI and PCII, All and Parties: loadings with the four party variables

.       PCI  PCII

.       All   Parties

Lab  0.43   0.64

LD   0.39   0.49

C     0.54 -0.27

R     0.61 -0.53

Further details about the principal components analysis

Notes:

.(i) We are seeking to ‘explain’ the percentages in Table 4. We do not have data on individual responses and we are not seeking to explain individual responses.

.(ii) We analyse only the four party variables. We exclude the ‘All’ variable from the analysis because it is simply some combination of the four party variables (approximately).

The study of the correlation matrix has suggested two pairs of explanatory variables. We now carry out a principal component analysis to see whether it will produce these explanatory variables as principal components.

  Principal component analysis is a standard statistical procedure. The analysis transforms the original four variables into four principal components. Here it produces two principal components which explain 99.6% of the variation. There are two other principal components but they explain almost none of the variation.

  The first component explains by far the most of the variation, namely 84.5%. All parties have substantial positive loadings on this first component ranging from 0.39 to 0.61. The fact that all the loadings are positive gives some plausibility to the labelling of the component as ‘All’.

Table 12 The loadings on the ‘All’ component

.                   Lab  LibDem       Cons Reform

. loading      0.43 0.39             0.54 0.61

In contrast the loadings on the second component give a strong differentiation between the parties. The Lab and LibDem loadings are substantial and positive and the Conservative and Reform loadings are negative and in the case of Reform substantial. The ordering of the parties according to their loading is the same as the primary ordering discussed earlier. Here too the distances between Group A and Group B is larger than the distance within each group. We refer to this as the Parties component.

Table 13 The loadings on the ‘Parties’ component

.                   Lab  LibDem       Cons Reform

. loading      0.64 0.49             -0.27 -0.53

These are the loadings of the four parties on the two components. We now consider the weights of the twelve issues on the same two components – see Table 14 below. The weights on the first component order the issues in much the same way as the percentages in Table 2. The weights on the second component reflect the parties’ preferences: positive for issues favoured by Group B and negative for issues favoured by Group B.

Table 14

All the voters: the percentage prioritising each issue; the issue area

.                                           I       II

Cost of living, economy        74    18  economic

Immigration, border control     77  -38   control

NHS                                      47    33  social

Crime, policing, justice         10  -13   control

Social care, elderly, vulnerab    -7     7   social

Cutting taxes                         -15 -15   economic

Climate change, environment   -22   15  environment

Education and schools        -29       5   social

Reducing the budget deficit   -26   -  5   economic

Public health, illness prevent  -31       3  social

Other                                   -40   -  6

Don’t know                         -38   -  4

Conclusion

The Chancellor “vowed to put “national interest” before “political expediency” ”.

…

Reeves will say it is a “Labour budget” with “Labour values”.

…

Discussion of the budget raises detailed matters and broad general issues and it is the latter that the present report has considered. There is much debate at present about a divided society and about polarisation between parties. There is a distinction between these two matters. The approach here has been to address the issue of a divided society by looking at the distribution of opinion amongst all of the people. For the very specific situation investigated here the distribution in Part 2 shows substantial variation and so society is not united. However the distribution is graduated rather than sharply divided without evidence of binary polarisation. This makes it inappropriate to talk about society being divided in this sense.

  Might then division be occurring in the sense of differences between parties? This has been investigated extensively in Parts 3 and 4. There is a certain amount of similarity between the parties and a certain amount of difference between the parties and these amounts have been identified in relation to a variety of different measures: gaps and overlaps, ordering and distancing, grouping, the probability of agreement; and correlations and principal components. Broadly the impression is that similarities are greater than differences – although note that these are similarities in the distribution rather than the sameness of individuals. Two components have been identified, ‘All’ and ‘Parties’; and parties have been located along a one-dimensional continuum; Group A and Group B have been defined; but yet there are similarities between the two extremes. The focus of Reform on immigration stands out although there is still some overlap with Labour: the probability of a Reform person agreeing with a Labour person on this issue is 0.34. Clearly what has been investigated here is a very specific situation but the approach adopted here has quite general application.

Gordon Burt, November 2025

THE END