LAST week, the SNP's Westminster leader Angus Robertson tried to lift the Yes side's spirits by claiming 40% of voters have yet to make up their minds on independence.

At first glance, Robertson would seem to have been over-egging it. Most polls agree the proportion of people who say they do not know how they will vote is around 15%.

That figure is not particularly high. Two or three months before the GB-wide referendum on using the Alternative Vote in Westminster elections, about twice that number did not know what they would do. Even six months before the last UK General Election some polls found one-quarter of voters saying they did not know how they would vote.

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But TNS BMRB puts the proportion of Don't Knows much higher, at around 30%. That seems to be because since the autumn it has been asking what people intend to do next September rather than how they would vote now. At the same time, Ipsos MORI has found around one-quarter of those willing to say which way they would vote now, also say they might change their mind.

So although only around one in seven voters apparently has little or no idea how they will vote, at least as many have an inclination in one direction but are not yet firmly fixed in their views. Between them they probably make up one-third of the electorate, leaving Robertson's estimate looking not so far out.

But how might the SNP persuade these voters to change their minds? The answer seems straightforward - by persuading them of the economics of independence. According to ICM, 97% of those who think independence would be good for Scotland's economy are inclined to vote Yes, while only 4% of those who think it would be bad are inclined to do so. The Yes side's problem is that at the moment pessimists still outnumber optimists.

In contrast, the argument that many in the SNP prefer to emphasise, and which Labour is spending much of its time disputing at its Scottish conference this weekend - that an independent Scotland would be a more equal society - matters much less to voters. Even among those who think independence would have that effect, less than two-thirds say they will vote Yes.

The number of voters who say they are undecided can influence the atmosphere of a campaign, and indeed, that is true of opinion polls in general. If they suggest one side

is well ahead, the media lose interest, politicians get less attention, and some voters decide the result is a foregone conclusion and they might as well stay at home.

If, however, the polls suggest the result will be close, the media get excited, the campaign gets more coverage, and voters are persuaded it might be worthwhile turning out after all.

Until recently there seemed to be a real risk that the polls would dull the atmosphere of Scotland's referendum campaign.

Poll after poll showed the level of support for Yes

and No as largely unchanged. With one much-criticised exception, all pointed to the No side being ahead.

But early in the New Year, it became clear the No lead had narrowed. Once the Don't Knows were set aside, the polls began to settle on an average Yes vote of 42% rather than the pre-Christmas 39%. Hardly a dramatic change, but enough to affect the campaign atmosphere.

Indeed, by the end of last week it seemed the winning post might finally be well within the Yes side's sights.

A Panelbase poll put Yes on 47%, just three points short of victory. The referendum race was apparently well and truly on.

A key feature of referendum polls is, however, that they significantly disagree with each other.

At one end of the spectrum lies Panelbase, which even last year was consistently putting the Yes vote as high as 45% (if Don't Knows were excluded).

It needed no more than the kind of modest increase in Yes support most polls had already seen to push its estimate of the Yes vote close to the 50% mark.

To that extent, last week's poll result should have come as little surprise.

At the other end sits Ipsos MORI.

Its most recent poll gave the Yes side just 36% of the vote, and it has never put Yes support at above 38%.

Other pollsters lie somewhere in between.

Thus, far from making it clear whether the referendum race is close or not, the polls have injected their own note of uncertainty.

They tell us the No side is ahead, but leave us scratching our heads as to how far.

But there are also some big differences in how the polls are conducted.

For example, the three that tend to produce the highest levels of Yes support (Panelbase, ICM and Survation), are done over the internet.

Whether such polls are capable of securing representative voter samples is open to debate.

In contrast, Ipsos MORI polls by phone while TNS BMRB still knocks on doors - and they are getting a lower Yes vote.

In any event, most pollsters (though not Ipsos MORI) try to overcome any risk their samples are biased by adjusting their data.

How someone voted in the past elections - such as the Holyrood 2011 ballot - is quite a good guide to which way they say they will vote in the referendum.

But this common practice has not stopped pollsters disagreeing with each other - not least perhaps because half of Scots failed to vote in 2011, but may still turn out to vote in 2014.

Given all this, perhaps politicians are simply being wise in sometimes ignoring the polls.

l John Curtice is professor of politics, Strathclyde University and is currently running a website on the referendum polls:

l This article is co-published with The Conversation, the news analysis and comment site that brings expert writing by academics to a mainstream audience. This week the site will unveil a panel of Scotland's leading thinkers covering the referendum