By-elections are not good predictors

3 August 2023

Some readers of Electoral Calculus have written in recently to ask why we don't use by-election results in our predictions, or to demand that we should.

But historically, by-elections are a poor guide to the result at the next general election.

Let's look at a bit of history. Between 2010 and 2019, there were 36 by-elections. They are listed in the table below as a jog to the memory. The table shows the winner of the seat at the previous general election, the winner at the by-election, and the winner at the subsequent general election. The seven by-election gains, where the by-election winner is different from the previous general election winner, are highlighted in bold.

Of the seven by-election gains, five of them reverted to the original party at the next general election. In other words, the by-election gain was temporary and the by-election result was not a good guide to the subsequent general election. There were two seats which bucked that trend, where the by-election gain was retained at the next general election:

• Clacton, where Douglas Carswell the incumbent Conservative MP, changed party to UKIP and triggered a by-election in October 2014. He won the seat for UKIP, and went on to hold the seat for UKIP at the general election in May 2015.
• Copeland, where the governing Conservatives gained a seat from the opposition Labour party at a by-election in February 2017 and held it at the subsequent general election four months later.

We can see why by-elections are a poor guide to predicting general elections. Suppose we ignore national swings for a moment, and try to predict seats just on the basis of either the previous general election or by-election result. For the 29 seats where there wasn't a by-election gain, the two methods would give the same result and would correctly predict 26 out of 29 seats, with only three seats mis-predicted.

But for the seven seats which had a by-election gain, the two methods would be very different. Betting on the previous general election would be correct for five seats out of seven, and only wrong for two. But using the by-election result as a prediction would have the opposite result – with only two correct seats and five seats mis-predicted.

Going further back in time

We can go even further back in time and look at all by-elections since 1979. That's forty years of by-elections, and there were 166 by-elections in that time. Of those, most of them were held by the incumbent party, but there were 45 where the by-election winner was different.

Of these 45 by-election gains, the majority (26) were regained by the original incumbent party at the subsequent general election, and only 19 were held by the by-election winner.

The table below shows all 45 of those by-election gains from 1979 to 2019.

Most by-election gains were overturned at the subsequent general election. This means that purely using the by-election result as a predictor would be worse than just using the previous general election result as a predictor.

But the fraction of by-election gains which are retained, which is 42%, is not that small. That suggests a hybrid approach where we could take, say, the average of the previous general election result with the by-election result. If we do that on the 45 by-election gains from the historical data, then the hybrid predictor is correct 30 times out of 45. And that's a bit better than just using the previous general election, which was correct 26 times.

The message of these data is clear. Both in the short-term and long-term, by-election results are not a great guide to the result of the next general election. More often than not, by-election gains are overturned at the next general election. But taking a mixture of the previous general election and the by-election result could be a better predictor than either on its own.