Tomorrow the voters of Eastleigh go to the polls to select a new MP following the resignation of Chris Huhne. The eyes of observers of British politics are keenly trained on the outcome of the by-election because it might give us some early clues to some serious questions about the next election: How are voters going to respond when faced with two incumbent government parties? Is Liberal Democrat support going to evaporate? What is the effect of UKIP going to be?

As is normal in the run up to an election, the press have used a combination of over interpretation of polling and pure speculation to try and divine the outcome of the election. I found myself wondering whether past by-elections could tell us what is likely to happen tomorrow. Predicting electoral outcomes is a precarious game, and as the sage of American electoral prediction, Nate Silver, will tell you, this is especially true for British elections. By-elections are also renowned for throwing up spectacular results which might make them even more difficult to predict. Regular readers of Politics in Spires might remember I’ve dabbled in election prediction before, and so I decided to turn my hand to trying to predict the outcome of the Eastleigh by-election.

In order to do so I gathered a dataset of previous English by-elections and changes in public opinion and ran a series of regression models (statistically minded readers can see a brief rundown of my data and methodology here). My model takes into account five things: the vote share a party received in the by-election constituency at the preceding general election; changes in public opinion towards the party since the last general election; whether the party won the seat at the last election; whether the party is in government; and whether there are ‘party effects’ on by-election outcomes.  Due to the absence of easily available  data, I took no account of ‘campaign effects’ but this is less cause for concern than some might think. Previous research on by-elections has found that they are largely determined by feelings about national level politics and not by local campaigning.

What does my model show? In short, for a very simple model, it fits the data remarkably well, explaining 88.5% of the variance in English by-election results (an R² of 0.885 in stats parlance). There are a number of interesting general findings which are worth pointing out:

• Governments get punished at by-elections. Holding all other factors (including public opinion towards government parties) constant, government parties receive 6.5% fewer votes than non-governing parties.
• The Liberal Democrats are better at fighting by-elections than other two main parties. Holding all other factors constant the Liberal Democrats receive 2.4% more votes than the Conservatives and 5.2% more votes than Labour. Labour appears to be particularly bad at fighting by-elections, fairing 2.8% worse than the Conservatives.
• There is no clear seat incumbency or size of majority effect – without taking the size of majority into account the incumbent party receives a 1.7% boost in vote share. Taking the size of a majority into account, however, this effect disappears – as the size of a party’s majority increases they actually start to lose votes, perhaps indicating that party supporters feel safe in their party winning the by-election and not bothering to turn out. Holding everything else constant, when a majority is more than about 4.5%, the incumbent bonus is outweighed by the effect of the size of a majority.

Before I move to what my model actually predicts there are several important caveats about why the Eastleigh by-election might be particularly difficult to predict.

• This is the first by-election the Liberal Democrats have faced as the seat incumbents whilst in government. It remains to be seen whether they will face a ‘standard’ government incumbency effect or something else.
• This is the first by-election where both Coalition parties face each other as the parties that finished first and second in the constituency at the preceding election. It’s not clear how voters will respond to a choice that, given that Labour have little chance of winning, many will see as being between two governing parties.
• Although I tried a variety of methods, I found no way of dealing with the ‘UKIP effect’ which might change the outcome of the Eastleigh by-election (simply because there aren’t enough cases where UKIP has played a prominent role in the outcome of a by-election).

This last factor is probably the most important factor that I couldn’t take into account. As Tom Chivers points out, unless the polling has been poorly carried out, there is almost no chance UKIP will win the Eastleigh by-election. But the fact that they are polling around 20% of the vote does mean that they are going to have an impact on the final result.

With the caveats in mind then, here are the predictions my model generates (with 99% confidence intervals):

• Liberal Democrats: 37.6% (±0.4)
• Conservatives: 32.5% (±1.5)
• Labour: 10% (± 3.5)

As a result of the UKIP effect I highly doubt the final result will fall within my predicted ranges. But they are nonetheless very interesting numbers. First because they predict the Liberal Democrats will hold Eastleigh by about 5% of the vote, which is very similar to what the last opinion polls were showing. Secondly because if we make some crude adjustments for the UKIP effect, the results are very similar to what polls suggest is going to happen. The last poll of Eastleigh voters suggest that 10% of previous Liberal Democrat voters, 14% of Conservative voters and 13% of Labour voters are going to vote for UKIP. Approximating from the 2010 election, results  in a 4.65%, 5.5% and 1.25% drop in vote share respectively. Adjusting my predictions accordingly yields:

• Liberal Democrats: 32.95% (±0.4)
• Conservatives: 27% (±1.5)
• Labour: 8.75% (± 3.5)

Only the final vote count will show whether or not these predictions are accurate. At the very least, though, they provide a yardstick by which we can measure the outcome of the Eastleigh vote. If the Liberal Democrats lose the seat it suggests that they will seriously struggle at the next general election (as those who don’t understand the drawbacks of Universal National Swing are already fond of predicting). If their vote share is close to what I’ve predicted here it might indicate that they not quite facing the electoral annihilation many expect. If Labour receives fewer votes than UKIP political commentators will no doubt discuss their ‘humiliating defeat’ – however if their vote share is similar to what I’ve predicted (as polling indicates they might) then they will have done exactly as well as we should expect, indeed if they win more than 12.25% of the vote they will have done better than expected, regardless of where UKIP finish.

Chris Prosser is a Dphil student in Politics at St Catherine’s College, Oxford, a lecturer in Politics at Christ Church, Oxford, and a graduate deputy editor of Politics in Spires. You can follow him on twitter @caprosser.

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