After the difficulties the polls had in estimating Conservative and Labour support in last year’s general election, it might be thought that little attention would be paid to them during the current EU referendum. But that is proving to be far from the case – even though their message is far from being an unambiguous one.

There is one obvious reason why this is happening. Although the polls do not agree on how quite how close the contest is, if they are to be believed at all, it looks as though the result of the referendum is likely to be relatively close.

Polls of voting intentions in the referendum are being conducted in one of two ways – either over the phone or via the internet. The latter have consistently suggested the race is very close indeed; on average (after leaving Don’t Knows to one side) they give Remain 50%, Leave 50%. Indeed, this the picture they have painted ever since the question that will appear on the ballot paper was unveiled last September.

In contrast, all but a handful of the polls conducted by phone have put Remain ahead – though not necessarily by much. On average they have credited Remain with 55%, Leave with 45%. That is not enough of a lead to suggest the result is a foregone conclusion, but represents a sufficiently different picture to raise important questions about which set of polls – if either – is right.

Various attempts have been made to try and account for the difference between the results obtained by the two kinds of polling, but so far no one has managed to come up with a clear, well evidenced explanation. Most likely the answer lies in the very different ways in which the two ways of polling obtain the people they manage to interview – but quite why one approach should find more Leave supporters than the other is not obvious.

That said, the polls have reported some clear and consistent messages. The first concerns the kind of person who is more likely to vote to Remain and who is more likely to vote to Leave.

Younger voters and those who have been to university are keenest on remaining in the EU, while older voters and those with few, if any, educational qualifications are most likely to say they wish to leave.

At the same time, whereas the polls suggest that the outcome in England and Wales will be close, they also suggest that in Scotland and in Northern Ireland there will be around a two to one vote in favour of remaining.

The polls’ second key message is that both sides have arguments that many voters find persuasive. A plurality of voters agree with Remain that Britain will be economically worse off if she leaves the EU. But equally a majority reckon that immigration will increase if Britain stays in the EU – and most do not find that an alluring prospect.

Britain’s future in Europe looks as though it will turn on which voters eventually regard as the more important consideration  – the economy or immigration.

John Curtice is Professor of Politics, Strathclyde University, and Senior Research Fellow, NatCen Social Research, and ‘The UK in a Changing Europe’ initiative. You can read more of his analysis at http://whatukthinks.org/eu/