Stephen Fisher and Alan Renwick have developed a method for forecasting the outcome of the EU referendum based on current vote intention polling and analysis of opinion polling from previous referendums in the UK and across Europe. Their final forecast, taking account of polls published up to yesterday evening, suggests that Remain will win 52-48. However, there is a lot of uncertainty and a Leave victory can certainly not be ruled out.

The polls this week have been better for Remain than they were last week. Since this is our final forecast it makes sense for us to restrict our sample of polls to include in our polling average just the most recent poll from each company (or company-mode combination) over the last week. If we do this then our polling average finds Remain at 51 per cent after setting aside don’t knows. This is up two points from our polling average on Sunday. The two-point difference is partly due to restricting the sample from two weeks to just one, partly rounding error and partly to the fact that more of the polls than previously include Northern Ireland. So it is not clear whether the apparent movement towards Remain is real or not.

Our forecast share of the vote is 52 per cent for Remain, 48 per cent for Leave. This reflects an expectation of a 1.5-point rise in support for the status quo, based on the change that is visible on average between the final polls and the actual result in previous referendums in Britain or on the EU elsewhere. While this reflects the average historical experience we have explained here and here why the average may not be a very reliable guide.

The unreliability means there is a lot of uncertainty in our forecast. The 95 per cent prediction interval is considerably narrower than it was at the beginning of the week. But at ±10 points it is still very wide. So wide that Remain could reasonably be expected to get anywhere between 42 per cent and 62 per cent of the vote. Neither a comfortable Remain victory nor a comfortable Leave victory can be ruled out.

That said not all the possible outcomes in this range are equally likely. Our forecast probability that Remain will win the referendum is 64 per cent.

The methods behind our forecast

The method behind this forecast is based on the historical experience of referendum polls and referendum outcomes in the UK and on the EU elsewhere, as discussed here.

As mentioned above, our polling average for the final forecast is constructed by taking the most recent poll from each company within the last week. If a company uses both phone and online modes then both the most recent phone poll and the most recent online poll are used. This applies just to BMG this time. The current average is based on the results of nine polls from eight companies, of which four were conducted by phone and five online. All polls are adjusted to account for the tendency for phone polls to be more favourable to Remain. This is done by adding 1.35 to the Remain share for online polls and subtracting the same amount for phone polls. This reflects a further diminution in our estimate of the mode difference.

Note that the polling average would be the same to one decimal place had we included the last two polls from each company within the last week and increased the sample to twelve.

About the authors

Dr Stephen Fisher is an Associate Professor in Political Sociology and the Fellow and Tutor in Politics at Trinity College, Oxford.

Dr Alan Renwick is the Deputy Director of the Constitution Unit.