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Since the last election resulted in a substantial Conservative majority, many have said that Labour has a mountain to climb to win the next one.  The implication is that the result this time significantly influences the result next time.  The results in 2024 are influenced by the results in 2019.  

But is that true?  In the jargon, do general election results suffer from serial autocorrelation – that bane of second year graduate students in statistical fields?  

Serial autocorrelation defined

If I a roll two fair dice, I might get any value, from a two to a twelve, though the middle values (seven, eight, nine) are the most likely.  Then I roll them again.  Again, I might get any result.  And so on, ad infinitum.  But the first result tells you nothing at all about the second – I am as likely to roll a seven this time if I rolled a two last time, or a twelve.  

But if I take many economic statistics, there is often a correlation between one result and its predecessor.  For example, if you know last year’s that GDP was £2 trillion, you can be almost certain that next year’s will be between £1.8 trillion and £2.2 trillion.  So GDP is serially autocorrelated, but the roll of two fair dice is not.  

Are general election results serially autocorrelated?

So are British general election results more like a roll of two dice, or like GDP statistics?

My intuition has always been that any influence would be weak or non-existent. First, I’ve always thought that, unlike in the United States, the advantages of incumbency to individual candidates are limited. Second, there is substantial churn in the electorate as the old stop voting and the young start. Third, four or five years is a long time, and many going to vote in 2024 may not even remember, much less care, who they voted for in 2019. I’ve never thought that there is NO advantage to the current governing party if it has a substantial majority.  For one thing, new MPs seem to enjoy a slight first-time incumbency basis, and for another, governments with small majorities can seem pretty chaotic, and may be liable to be punished at the next election.  But, equally, I’ve never thought that any benefit is large.

Recently, I got around to testing my prejudice. The most widely used test for serial autocorrelation is the Durbin-Watson (DW) statistic. I have applied it to the Conservative seats in Parliament since the introduction of universal male suffrage in 1918. To those with no interest in detailed statistical testing, my result is that there is no convincing evidence of serial autocorrelation between general election results over the last century, i.e. losing after a landslide victory could be just as likely as losing a majority of 2.  

In case the relationship has shifted over time, I have also applied the same test to three political eras since 1918:

• 1918-1945
• 1950-1992
• 1997-2019 

The result held true.  In fact, for two of those time periods, the DW statistic was greater than two, which implies, if anything, that a good general election result this time may mean a slightly weaker one next time (though the correlation was not significant). 

I have put the results at the end of the thread, for those into statistics.

Implications

Most relevant for this site, these results have important implications for those making long term bets as to the result of the next election.  The current Betfair odds are 4/6 that the Conservatives will win the most seats, compared to 6/5 for Labour.  If the general election result from last time does not influence the result next time, this could be slightly overstating the Conservatives’ chances and understating Labour’s.  (Of course, many other factors, such as punters’ appraisals of the qualities of the leaders, could influence the odds).

These results might also influence how we assess past leaders.  For example, some have praised David Cameron for winning more than a hundred seats from Labour in 2010, while others have criticised him for failing to win an overall majority against a lacklustre Labour government with a poor economic record.  If the 2005 result does not significantly influence what happens in 2010, as this research indicates, then the latter view is much more convincing.

For the future of the country, then, although no-one should deny that Sir Keir Starmer has a difficult task ahead of him, it’s all to play for in 2024. That Labour has to overturn forbiddingly huge majorities in Tory seats is less important than many think. The Conservatives can’t be complacent and Labour shouldn’t despair.

(Thanks to those other PBers who have checked and commented on my result.  Any errors or omissions are my own).

Fishing

Detailed results

For those with nerdier inclinations, the time series I tested was the Conservative share of seats won at general elections, to allow for changes in the number of seats in the Commons. The data source was the parliament.uk site. The null hypothesis was no serial autocorrelation. The results are as in the table below.

As will be seen, there is no evidence for serial autocorrelation in any of the time periods surveyed.

Table: DW statistics for Conservative general election seat share (1918-2019)

Time period	n	k’	Critical DW (5% sig.)	Observed DW	Result
1918-2019	27	1	1.469	1.682	Do not reject
1918-1945	7	1	1.356	2.264	Do not reject
1950-1992	12	1	1.331	1.413	Do not reject
1997-2019	6	1	1.400	2.346	Do not reject