Last week's opinion polls and bookmakers' odds show a much diminished likelihood of a UK exit from the European Union.

The average of the last six opinion polls show that, excluding Don't Knows, Remain is on 55% and Leave on 45%. That is the biggest lead for Remain in three months. The bookmakers' odds have moved even further. At the end of last week they were pricing in just a 22% chance of Brexit, the lowest reading in a year.

The betting odds are widely seen as offering a better guide to the final outcome than opinion polls. The polls are an attempt to create a representative snapshot of how people feel today; the odds are the product of people staking money on the outcome of a future event. In theory, those odds should incorporate all available information, not just the latest polls.

Then there is the problem of which poll to believe. Even polls carried out on the same day, by the same pollster, can show wildly different results on the Brexit question depending on whether it was carried out on-line or by telephone.

Since the Prime Minister announced the date of the referendum on 20th February on-line polls have on average shown Remain and Leave neck and neck. Over the same period telephone polls show Remain ahead by eight percentage points.

One theory is that Eurosceptic opinion may be over-represented in on-line polls, as voters with strong views are more likely to sign up for on-line survey panels. Another is that by asking people to choose between Remain and Leave telephone polls confront people with the choice they will face in the polling booth, avoiding the escape clause of "Don't know" widely offered by on-line polls. Including a Don't Know option seems to siphon support from Remain and, on this theory, provides a misleadingly strong showing for Leave.

History suggests that faced with uncertainty and complexity voters tend, as they did during the Scottish referendum in 2014, to stick with what they know. In the last month the Don't Knows have accounted for between 5 and 25% of those polled, more than enough to shift the result in either direction.

The supposed superiority of telephone polls over on-line polls and of bookies odds over all polls point to a commanding lead for Remain. A spokesman for Ladbrokes told the Financial Times that 90% of the money it has received is for the UK staying in the EU and punters see Remain as, "a rock solid bet".

Yet while Remain is the clear front runner this is still a two-horse race.

The punters are often, but not always, right. In the run up to last year's UK General Election the bookies were offering odds of 7/1 on a Conservative majority, an implied probability of just over 12%. This enabled a Glasgow pensioner to pocket £210,000 on a bet placed ten days before the vote. More recently the bookies got it wrong over Donald Trump's success in the Republican primaries and Leicester City's Premiership triumph.

Undecided voters may tend to favour the status quo, but the evidence of referendums on similar issues suggest the size of the swing from Don't Know to Remain may not be large. Don't Knows are also less likely to turn out to vote on June 23rd.

Then there are also uncertainties about turnout. According to the Financial Times only 200,000 out of several million UK expats have registered to vote. The change from household to individual registration has resulted in the loss of one million people from the voter register, many of them likely to be younger, more pro-EU voters.

My hunch is that the bookies odds, at 22%, are underestimating the probability of Brexit.

But I would be the first to concede that such off the cuff prognostications are no more reliable than the polls or the punters. In March of last year, the London School of Economics asked eleven academic forecasting teams to predict the outcome of last year's UK General Election. Not one predicted the actual outcome, a majority Conservative government.

On the 24th June, as the result comes through, it is not only the Remain and Leave camps which will be celebrating or drowning their sorrows. Pollsters, punters and "experts" will be too.

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