Hurry or you Will Lose: David Cameron and the Brexit Referendum

No wonder David Cameron is in a hurry to hold the EU referendum. If he waits until next year he will lose the vote. This is the conclusion of a paper I have just published in Political Quarterly.

It is also not surprising the Prime Minister wants the vote to take place in the summer when everybody is planning their holiday and have little time for politics. And he is well advised to get the vote out of the way as soon as possible

Why? Referendums are won when the governments have been in office for a short time – and when the turnout is low. And turnout will be low if the vote is held during the summer.

So, if the turnout is the same as in the General Election in 2015, Cameron will squeeze through with 56.1 per cent if the vote is held in May.

However, if Cameron waits until next year – and if the turnout is as high as in the 2014 Scottish referendum (not an unreasonable assumption given the passion Europe arouses), then David Cameron will only get 49 per cent. In other words, he will lose.

This explains why he is in a hurry to get a deal with the other European leaders on the 18th of February.

Statisticians and economists often use so-called econometric models to forecast the rate of inflation, unemployment and sundry other macroeconomic indicators.

The same type of equation can be developed for political events. The American political scientist Michael S. Lewis-Beck developed a model that could predict US presidential election with a margin of plus/minus two point five per cent.

In 2012, I used this model to correctly predict that Barack Obama would win the US presidential election. The prediction was more accurate than the opinion polls.

Based on all the 44 referendums on the EU (or EEC) held since 1972 we can come up with a similar equation that accounts for the factors, which statistically are associated with a no-vote.

All other things being equal, EU referendums tend to be won if there is a leading question on the ballot. Voters tend to vote for the Governments’ propositions if so-called ‘emotive’ words, like ‘agree’ and ‘approve’ are on the ballot.

Further, if there is a low turnout and if the government has taken office recently, the yes-vote is likely to be high.

All of this can be summed up in an equation of the type developed by Michael S. Lewis-Beck. The equation looks like this:

Yes = 74 + 13* Emotive Word – 0.25*Turnout -1.4*Years in Office

Let’s do the math!

The 74 is a base line – or a constant, that need not worry us. The emotive word variable is also of little concern. The ballot-question in the EU referendum will be a bland one. (The question on the ballot is ‘Should the United Kingdom remain a member of the European Union or leave the European Union? Leave/Stay’). So the value for this variable is zero.

Assuming the turnout in the referendum is 66 (like in the General Election in 2015) and assuming David Cameron has been in office for one year, when the referendum is held, we get: 74 –(0.25*66) – (1.4*1), which is 74-16.5 – 1.4 = 56.1.

However, if the turnout is higher – like in the Scottish referendum – he is in trouble. Let’s assume, for the sake of the argument, that the turnout is 85 per cent and the vote is delayed to 2017. If so, we get 74 -21.25- 2.8= 49 per cent.

Of course, everything is not statistics and there are many unique and idiosyncratic factors that are we need to take into account. But many of the factors we usually associate with referendums have little statistical effect, as I show in my article.

Factors such as campaign spending, control over the media and trust in the government have little impact on EU referendums. In fact, in Romania – one of the countries with the lowest levels of trust in the Government – more than 90 per cent endorsed EU membership. Conversely, in Norway and Sweden – countries where more than 80 per cent of the voters trusted the respective governments, three out of four referendums were lost.

So why the turnout and the years the government has been in office?

The tenure is easy. Governments break promises and disappoint if they have been in office for a long time. The sins of commission are a positive function of the number of years a government has been in office. In Denmark in 1992 – the conservative Poul Schlüter- Government was worn out after ten years in power and lost the referendum on the Maastricht Treaty. A year later, a new government – headed by the Social Democrat Poul Nyryp Rasmussen - was able to capitalize on the honeymoon feeling in the country and won a referendum on the same Treaty.

That a high turnout is correlated with a high yes vote is more surprising. From countries with compulsory voting – such as Australia – we know that voters with little political interest often are more sceptical than voters who have a greater interest in politics (see here for more info). It seems that the same is at play in EU referendums.

Of course, there is more to referendums than statistics. However, the tendency is clear: low turnout and a government that has recently taken office are associated with a high yes-vote.

David Cameron and his staff are well advised to hold the referendum as soon as possible – and at a time when as few citizens as possible will vote.