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18 June 2016: New batch of polls suggest result is in the balance
A series of of new referendum polls released on Saturday evening suggest that the result still hangs in the balance.
Online polls by Opinium and YouGov suggest the two sides are neck and neck.
Opinium for the Observer has both remain and leave on 44%.
YouGov has published two polls. For the Sunday Times it has Remain one point up; for ITV it has Leave two up.
Survation has published the only telephone poll of the evening for the Mail on Sunday. It has Remain up by three points.
It's difficult to say with any confidence whether these new polls represent a significant change.
But perhaps they suggest that the momentum enjoyed by Leave over the last couple of weeks has, for the time being at least, stalled.
How does it feel?
ComRes has also published an interesting poll for the Independent and Sunday People, although not with referendum voting intention figures.
It asked people about the emotions they would feel depending on the referendum outcome.
Significantly more people said they'd be delighted if Leave wins (44%) than if Remain wins (28%).
A Leave victory would also disappoint fewer people.
However, it would also make more people anxious.
Some 41% of people said a Leave victory would cause them anxiety compared to 33% for a Remain victory.
16 June 2016: Leave trend continues
Two more polls published today confirm the trend of a significant shift to leave.
And they're particularly striking because they're both telephone polls conducted by companies who have previously had remain ahead - sometimes with substantial leads.
Ipsos MORI now give leave a 6 point lead. Survation have them 3 points ahead.
Two further polls - one internet, one telephone - are expected overnight tonight.
14 June 2016: TNS and ComRes continue pattern
New polls were published on Tuesday from TNS and ComRes. Both followed the pattern we've seen in other recent poll of a marked shift to Leave.
In TNS's online poll that gave Leave a 7 point lead. For ComRes, who conduct fieldwork by phone, Remain were in the lead, but only by 1 point compared with 11 points last month.
So the long-established gap between phone and internet polls still seems to be in place - with the exception of ICM - but for both methods the centre of gravity has shifted to Leave.
14 June 2016: Clear shift to leave
After weeks of uncertainty about whether the polls were moving one way or another there now seems to be a clear picture: there has been a shift to leave.
Four polls were published yesterday evening: two by ICM for the Guardian, one by YouGov for the Times, and one by ORB for the Daily Telegraph.
All of the pollsters are showing leave in a stronger position than they were a fortnight ago. And both of ICM's polls - phone and internet - now have leave ahead by 5 points. In the YouGov poll the lead is 7 points.
The ORB figures in the referendum tracker are their 'turnout weighted' ones. They show remain ahead but by a narrower margin than they have found in recent phone polls.
More polls to come
Before leave campaigners get ahead of themselves, though, they might want to wait until further polls are released by some of the other companies.
Phone polls from Ipsos MORI, ComRes and Survation are all anticipated. They've all tended to show remain in a stronger position than ICM or YouGov.
That said, Ipsos MORI have already announced that they'll be making a change to their methodology to take educational background into effect, which they say would have reduced the lead for remain in their last poll.
It would be surprising if the shift to leave wasn't reflected in the next set of polls from these three.
But we'll have to wait and see whether it's enough to put leave ahead.
12 June 2016: Where are all the polls?
With less than two weeks to go, interest in referendum polls is reaching a climax. So it's perhaps surprising that there have been very few published in the last week.
There are two polls in the Sunday papers - both online - which continue to show a very close race, as most online polls have done for months. YouGov in the Sunday Times has leave one point in the lead. Opinium in the Observer has remain two points up.
On Friday night there was one other poll which reported a clear lead for leave. The ORB/Independent online poll put leave on 55% and remain on 45% in its "turnout weighted" figures.
Like previous ORB online polls, it doesn't appear in the BBC poll tracker because it doesn't allow a "don't know" option. Up to now, they've generally been in line with other online polls, with the two sides neck and neck.
In the coming days more polls are anticipated, including some telephone polls. So perhaps we might get a clearer picture.
Labour voters crucial?
There have been numerous reports in recent days about pro-remain Labour MPs worrying that their supporters are switching to leave.
A lot of this is supposedly based on their reception on the doorstep when they're out canvassing.
Looking at the polls, though, it's hard to find much evidence for it.
Pollsters always publish a demographic breakdown of how different groups have responded to their polls. You have to be even more cautious with these than with the headline numbers. But looking at a large number of polls, clear trends emerge.
In the referendum, one trend is that Labour voters say they back remain over leave in a ratio of approximately 2:1.
That's only budged very slightly over the course of the campaign.
Friday's ORB poll suggested a different picture, but it still had a clear majority of Labour supporters for remain. And the other weekend polls had Labour voters supporting remain by a little over the 2:1 ratio.
So if a lot of Labour voters have switched to leave, the polls aren't really picking it up.
But they do suggest that the Labour Party, whose MPs overwhelmingly support remain, has not convinced a substantial portion of its supporters.
6 June 2016: Leave ahead?
Two weeks ago some people thought they'd identified a decisive shift in the polls towards remain. That now looks wide of the mark.
Most of the polls over the last fortnight have shown leave with a small lead. And many of the pollsters have reported a swing away from remain.
We've also had a rare telephone poll with leave in the lead - only the third such poll since the question was fixed last September. (ICM 27-29 May)
Can we say then that leave is now definitely on course to win? It's still probably too early to say.
For one thing, we've had very few phone polls recently and, with the exception of the ICM poll, they've still tended to show remain ahead, albeit by smaller margins than previously.
Secondly, some people have suggested that there could be a 'bank holiday effect' or 'half term effect'.
With a lot of people away for the half term it might have been even more difficult than usual for pollsters to find samples who represent the country as a whole.
The evidence on that is pretty patchy. There are some cases of polls conducted over holidays producing what later look like skewed results.
But in other cases it doesn't seem to make any difference.
One area of referendum polling which has shown a pretty clear trend over a long period of time is about turnout.
The number of people who say they are certain to vote, or who rate their likelihood of voting at 10 out of 10, has increased.
It's notoriously difficult to estimate turnout from polls because, as a group, the people who take part almost always over-estimate how likely they are to vote.
But there has been a marked increase in people saying they will vote, and that could point to a high turnout.
24 May 2016: Bookies vs Pollsters
Ipsos Mori's latest poll gave remain a 55-37 lead, with 8% saying they were undecided or wouldn't vote. That's the biggest gap between the two sides we've seen since February.
On the other hand, ICM's online poll showed a 47-44 lead for leave, with 9% saying don't know.
Some observers argue that betting odds provide a better clue to the outcome of elections and referendums than opinion polls.
If that's true then Remain looks the most likely result.
The referendum is expected to be the biggest ever political betting event in the UK. Millions of pounds have already been gambled on the outcome.
Last week several bookmakers cut their odds for a vote to remain to 1/6. That means people would have to risk £6 for a potential profit of £1.
Ladbrokes reported that there were lots of people prepared to back Remain despite the short odds.
Most bookmakers have the odds for leave at 7/2. A £2 stake would return a profit of £7.
Perhaps an easier way to track the bookmakers' odds over time is to look at what they imply about the chances are of each side winning. If both sides were at evens they'd both have an implied probability of 50%.
On the Betfair betting exchange, the probability they suggest of a remain vote has risen from about 65% a month ago to nearly 80% now.
Another market that's very sensitive to news about the referendum is the currency market.
After the publication of the Ipsos Mori poll last week, with its large lead for remain, the value of the pound jumped by almost two cents against both the US dollar and the euro.
That's because many currency traders expect that the uncertainty caused by a vote for Brexit would lead to a sharp drop in the value of sterling - at least in the short term.
We're always told not to pay too much attention to individual polls but clearly some traders think there's been a decisive shift.
16 May 2016: Phone v internet
There's a consistent pattern: in telephone polls remain tends to be in the lead; in internet polls the two sides are neck and neck.
The discrepancy between the two types of poll has narrowed in the last few months.
The lead for remain in phone polls is now about 8-12% when people who respond "don't know" are eliminated, down from about 20% last year. Internet polls have been suggesting a virtual dead heat for months.
There's been a lot of discussion about why the two types of poll are different and which is more accurate.
One theory is that the internet polls get more "don't know" or "undecided" responses because they offer it as an option on the screen. In phone polls, "don't know" is not usually offered as an option although respondents can choose not to back either side.
The theory is that more people who say "don't know" in internet polls are likely to vote remain than leave when push comes to shove.
Martin Boon at ICM has suggested that the samples in phone polls may contain too many Labour voters, as they did at the general election, and that the samples in internet polls may contain too many UKIP voters.
That would skew the phone polls in remain's favour - Labour voters tend to break for remain by at least two to one - and skew the internet polls in favour of leave, suggesting that the true balance of opinion is somewhere in between.
My colleague Chris Cook has looked at this issue in more depth.
Most important issue
Pollsters have also reported some interesting results beyond straightforward voting intention.
Several have asked people which issue would be most important in their decision about how to vote.
ICM found that 45% of people said that immigration into the UK was the most important, followed by the impact on the UK's economy on 36%. (Sample: 2,029, 27-29 April)
Similar polls by ComRes and Ipsos MORI have put the same two issues at the top of the list but in reverse order.
Interestingly, the division between internet and telephone polls is noticeable here too: ICM's poll was conducted by internet, the other two by phone.
Referendum a turn-off?
ComRes also asked whether people were bored by the referendum. Sixty-three percent said they weren't, which is probably a good thing because there are still many weeks to go.