Brexit: How tight is it, really?

brexit-ballot-boxWith the official referendum expected in less than two months, the latest polls on Brexit show a narrower than ever gap between both camps. The Financial Times’ Brexit poll tracker shows that the June referendum could go either way. However, as mentioned in an earlier post, bookmakers such as Betfair have barely adjusted their odds over the last few weeks and still predict a victory for the ‘Bremain’ side with a 65% probability – and even closer to 75% following Barack Obama’s visit to the UK last week. How can we reconcile those two facts?

Evolution of implied ‘Bremain’ success odds according to Betfair.

First, to reiterate an argument already developed on that blog, bettors and bookmakers believe that, unconsciously or not, individuals positioning themselves in favour of Brexit do not reveal their real vote intention to pollsters. A similar bias can be observed in voters’ behaviour towards the most extreme parties prior to an election. A share of the self-declared ‘extremist’ electorate will actually revise their intentions just before putting the ballot in the box.

Result of the first round of the 2002 French Presidential Elections

That being said, the reverse trend used to be true in some countries such as France – i.e. individuals planning to vote for the Front National were fearful of revealing their real intentions and hid it to pollsters – and partly explained the 2002 French Presidential Election upset where Front National’s Jean-Marie Le Pen unexpectedly ousted Parti Socialiste’s Lionel Jospin from the second round. Being able to identify and quantitatively assess behavioural biases has become part of survey institutes’ core job, especially in tight contests such as the one we are witnessing today.

Unconscious behaviours nonetheless do not fully explain the discrepancy between polls and bookmakers. Statistics also come into play. In the context of the Brexit referendum, the Bremain camp has indeed managed to maintain a small, although very narrow, lead in most of the polls. As a consequence, the odds of the Bremain camp winning are actually greater than the gap could lead us to believe. To illustrate this fact, let us assume that the distribution of vote shares in favour of ‘Bremain’ follows a normal distribution – the infamous ‘bell curve’.

This distribution is centred around an average of 52% – i.e. on average Bremain wins by a 52-48 margin. Let us also assume that we are almost certain (with a 95% certainty to be perfectly exact) that the Bremain camp will score between 44% and 60% on D-day. The resulting bell curve is drawn below, with the shaded area representing the area sitting above the 50% threshold – i.e. the area where the Bremain camp wins. Although we built the bell curve around a 52% average, the shaded area represents 69% of the total area under the curve, which means that the Bremain camp has a 69% chance of winning. The parameters for this example have not been chosen randomly: 69% is indeed very close to Betfair’s latest estimates.

Bell curve with average of 52% and std deviation of 4%. Shaded area corresponds to p>50%.

This exercise would theoretically give us a lot of confidence on the referendum outcome. In practice, the exercise is unfortunately made much more complicated by the high share of ‘undecided’ voters, standing at roughly 30% of the voting population as of today. Given its size, this group will clearly decide on the referendum’s outcome and can overturn any statistical projection. Being able to predict the behaviour of such a heterogeneous group has therefore become the focus – and the nightmare – of all pollsters – notwithstanding the bookies.

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