Jump then slump: the trajectory for the UK Liberal Democrats, 1945-2019
The Liberal Democrat conference, Autumn 2023
The headlines
The polls
No parties … Whigs, Liberals and Liberal Democrats (notes)
The three main parties: the hexagon of orderings
The constituency orderings, 2019 to 2024
The Nadine Dorries Mid-Bedfordshire by-election, 19 October 2023
Modelling the 1945-2019 trajectory
The hierarchy of competition … the Lib Dem share of the three main party vote
In what state are the Liberal Democrats now?
An appetite for the middle ground?
The Liberal Democrat conference, Autumn 2023
https://www.libdems.org.uk/conference/papers/autumn-2023
The headlines
The Times; The Observer on Sunday:
September
22nd: “Lib Dems are looking like kingmakers again. Of the 91 seats in which the party came second in 2019, 80 are Tory held – it’s time to start paying attention to Ed Davey. Davey has won nearly 1,000 new councillors, mostly from the Tories.”
24th: “No Tory seat is safe: Davey vows to take an axe to the thin blue wall. … The health service is a dividing line. This is a thread through all our byelection campaigning … fears have opened up the door to the party in the most unlikely places.” 10-11.
“Before we get to the election, Lib Dems need to raise their sights and up their game.” 49
25th: “Lib Dems attack the blue wall to win over home counties voters.” 6
“Lib Dens must lead the way on blunting Brexit. The damage from leaving the EU is growing and opposition parties need to catch up with voters. For the Tories any backtracking is viewed as betrayal.” 24
26th: “Lib Dems vote for vacuous vow to build 380,000 homes a year” 8
27th: “Davey: No one should lose parents to cancer as I did.” 8
“Matt Chorley’s Conference Diary” 8
“Not the Tory party. Liberal Democrats must say what they stand for, not just what they are against.” 27
12/83
A
The polls
The Liberal Democrats have polled at around 12% (7%-16%) throughout 2023.
https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_United_Kingdom_general_election;
No parties … Whigs, Liberals and Liberal Democrats (notes)
Parliament
England 1238-1707
Great Britain 1707-1800
UK 1801-1922
UK & Northern Ireland 1922
https://en.wikipedia.org/wiki/Parliament_of_England
Political parties in England
“In England, rival political grouping, reflecting an intensifying conflict between court and country interests, can be detected from the mid-1660s through the 1670s, although these are normally thought of as factions rather than parties.”
embryonic parties: Whigs and Tories
1678-1859: Whigs
https://en.wikipedia.org/wiki/Whigs_(British_political_party)
1859-1988: Liberal Party
https://en.wikipedia.org/wiki/Liberal_Party_(UK)
1922-2019
https://en.wikipedia.org/wiki/United_Kingdom_general_elections_overview
https://en.wikipedia.org/wiki/List_of_United_Kingdom_general_elections
A century of elections
Research Briefing
Published Wednesday, 09 August, 2023
See the first graph in Section 2.1 on page 7 of the full report.
https://commonslibrary.parliament.uk/research-briefings/cbp-7529/
full report: https://researchbriefings.files.parliament.uk/documents/CBP-7529/CBP-7529.pdf
Liberals and Liberal Democrats, 1983-2019
“The Liberal Party contested the 1983 and 1987 elections in alliance with the Social Democratic Party (SDP), before the two parties merged in 1988 to form the Liberal Democrat Party. The SDP had been established in January 1981 and by March 1982 it had 29 MPs, most had defected from Labour.
The Alliance received a quarter of votes in the 1983 election but won just 23 seats.
62 Liberal Democrat MPs were elected in 2005, the highest number for the Party and its predecessors since 1923 (when the Liberals won 158 seats). In 2010, there were 57 Liberal Democrat MPs, but their number fell to 8 in 2015. In 2017 the number of Liberal Democrat MPs rose to 12, before decreasing to 11 in 2019.”
The three main parties: the hexagon of orderings
The Conservative party was the winner in the 2019 general election, Labour was next and the Liberal Democrats third. Let us denote this ordering: *C>L>LD.
Restricting our attention to these three main parties, in all there are six possible orderings. The orderings can be arranged in a hexagon – see below. Adjacent orderings in the hexagon differ by an adjacent pair transition in the ordering. The Liberal Democrats come second in two orderings: ^L>LD>C and ^C>LD>L.
. L>C>LD *C>L>LD
^L>LD>C ^C>LD>L
. LD>L>C LD>C>L
The constituency orderings, 2019 to 2024
Liberal Democrats are keen to hold constituencies they won in 2019 and keen to win constituencies which they did not win in 2019. Their best chances are in constituencies where they came second, namely ^L>LD>C and ^C>LD>L. The latter constituency orderings greatly outnumber the former, 80 to11. So the Liberal Democrats are particularly keen to target constituencies where they came second to the Conservatives in 2019.
In terms of voting percentages … how do constituencies differ from one another? … how do changes in voting percentages differ from one constituency to another? Will the change be the same across all the constituencies? Will the swing be the same? Will the step ratio be the same? Will the transition matrix be the same? ...
… these questions will be addressed in a forthcoming analysis of recent by-elections.
The Nadine Dorries Mid-Bedfordshire by-election, 19 October 2023
Which party is second in Mid-Bedfordshire? Table 1 shows the general election results for Mid-Bedfordshire in the period 2001-2019. The Conservative percentage has had an increasing trend. The Labour percentage had a trough in 2010 and 2015. Note also the slump in the Lib Dem vote from 2010 to 2015 and the substantial UKIP vote in 2015.
Table 1 Results for Mid-Bedfordshire, 2001-2019
2001 2005 2010 2015 2017 2019
Conservatives 47.4 46.3 52.5 56.1 61.6 59.8
Labour 30.1 22.5 14.8 15. 28.4 21.7
Lib Dem 19.7 23.8 24.9 7.2 6.0 12.6
UKIP 2.7 2.7 5.1 15.4 0 0
https://members.parliament.uk/constituency/3603/election/397
“Dorries told: quit as MP, you’ve failed your voters.” The Times, July 28, 2023, p. 6.
The by-election is due to be held on 19th October.
‘Prediction’: the Conservatives will have 35.7%. In 2019 the Conservatives obtained 59.8% of the vote. Assuming the national polls stay the same, and applying the national transition matrix*, we can predict the Conservatives gaining 35.7% of the vote.
*(see forthcoming: The ‘historic’ by-elections, 20th July 2023: a modelling approach)
‘Prediction’: the Conservatives will have 29%. A small-sample Survation poll in Mid-Bedfordshire in mid-September gives Conservatives 29%; Labour 29%; Lib Dem 22%; Reform 7%; Independent 6%; True and Fair 4%; and Green 2%. Note: this is just one poll.
https://www.survation.com/mid-bedfordshire-by-election-update/
The national ‘prediction’ of the Conservative vote is not far away from the local poll – both are far away.
“Tory vote is collapsing in Dorries’ old seat – but divided rivals could let victory slip away.” The Observer, September 17 2023.
The local poll suggests a gain of 7.3% for Labour and a gain of 9.4% for Lib Dem. This suggest that former Conservatives are splitting fairly evenly but with a small advantage to the Lib Dems. This small advantage may not be enough for the Lib Dems to replace either of the other two parties.
Modelling the 1945-2019 trajectory
The UK general election in 1945 was held on 5th July (two months after victory in Europe - but a month before Hiroshima on 6th August 1945 and the defeat of Japan). The Liberal Party gained 9% of the vote (having gained 6.7% in 1935).
For the next three decades the percentage vote for the Liberal Party varied between 2.5% (in 1951) and 11.2% (in 1964). Then there was a jump to 19.3% in February 1974. Between then and 2010 the percentage vote varied between 13.8% (in 1979) and 25.4% (in 1983). In 2015 there was a slump to 7.8%. In 2017 the vote was 7.4% and in 2019 it was 11.5%. Thus the jump was from 7.5% in 1970 to 19.3% in Feb 1974; and the slump was from 23.0% in 2010 to 7.8% in 2015.
https://en.wikipedia.org/wiki/1945_United_Kingdom_general_election
https://en.wikipedia.org/wiki/Atomic_bombings_of_Hiroshima_and_Nagasaki
A common approach is to look at the numbers and look at the graphs and finding patterns. A different approach is to hypothesise models that would generate the numbers and test how good that model was.
We now consider how we might model the time series for these percentages. A detailed analysis has been carried out for the 1945-2015 period:
(Chapter 12: Time series: UK general elections, 1945 to 2015. pp. 244-265. 258
Burt, Gordon. Values, World Society and Modelling Yearbook 2015. 2017. Cambridge Scholars.)
Let us consider a number of models starting with the simplest models and progressing to more complex models. Note that there have been only twenty-one general elections in the period we are studying and this is rather a small sample size to draw definite conclusions.
.(1) Constant
The simplest model is that the percentage stays constant over time. Clearly this model is false.
.(2) Independent … the mean
There is a distribution of percentages and the percentage in one election is a random event selected from the distribution and is independent of the percentages in the other elections. An estimate of the mean of the distribution is given by the mean of the percentages over the period (1945-2015), namely 13.8% [actually the equilibrium
in (4) below].
.(3) Independent … bimodal
As in (2). However, noting that the distribution may be bimodal, one can think of a lower mode and an upper mode.
.(4) Dependent … autoregressive model, AR(1)
Each election percentage may depend on one or more of the previous election percentages … possibly with some random error. The simplest such model is a linear dependence on just the previous percentage. The linear model may correspond to a weighted sum of the previous percentage and the equilibrium percentage, namely 13.8%. This model explains 40% of the variation.
.(5) Dependent … binary state equilibria
Party support can be in one or two states, low or high. Below 13.8% it is low; and above 13.8% it is high.
There is a strong probability that the current state is the same as the previous state (only one change of state in each direction in the period under study). The current percentage is the equilibrium percentage for the previous state plus a random error. There are two equilibria: a low equilibrium of 8.3 and a high equilibrium of 18.5. Note that this is a binary version of (2). This model explains 52% of the variation.
.(6) Dependent … binary autoregressive model, AR(1) … binary equilibria
As in (5), but also dependent on the previous percentage. The current percentage is a weighted sum of the previous percentage and the equilibrium percentage for the previous state. Thus there are two equilibria: a low equilibrium and a high equilibrium.
The equation for the percentage x at time t+1 depends on the percentage x at time t; it depends on the state b at time t with b=0 if the state is low and b=1 if the state is high; and it depends on a random error.
.(7) Orbiting binary equilibrium models
Catastrophe theory and complexity theory offer a variety of models for switches in the orbiting of binary equilibria.
The hierarchy of competition … the Lib Dem share of the three main party vote
Rather than looking at the straightforward percentage Lib Dem vote, LD, we can consider the Lib Dem share of the combined three main party vote, LD/(C+L+LD). The trajectory is similar. Here too there are two equilibria, a low equilibrium of 9% share and a high equilibrium of 20% share. Note that this is a binary version of (2). Here, the binary state equilibrium model explains 57% of the variation. In terms of this criterion, 57% is better than models (4) and (5) above.
[Current polls give the Lib Dem three-party share at maybe somewhere between 11% and 17% … based on 9/82 and 14/84 respectively.]
In what state are the Liberal Democrats now?
In view of the binary models it is relevant to ask in which binary state are the Liberal Democrats now? Following their slump from 2010 to 2015 the Liberal Democrats have been in a low state in the last three general elections. The binary model notes that the jump from a low state to a high state has happened on just one out of eight occasions. So a jump has a small chance of occurring. Separate from this are the opinion polls which give no sign of a jump.
However this low state for the Liberal Democrats has co-existed with a low state for the Conservatives. The Liberal Democrats have won several byelections and may defeat the Conservatives in constituencies where they were second in 2019.
An appetite for the middle ground?
Distaste for Trump and Johnson has given some people an appetite for the middle ground. This might be promising for the Liberal Democrats. However the middle ground is contested by the centre right and the centre left as well as by the centre:
“Why I still believe in the political centre. Populists of recent years have suggested governing is easy yet it’s centrists on the left and right who embrace its true complexity.” Daniel Finkelstein. The Times, September 27th 2023.
Gordon Burt, 28 September 2023
THE END