You might remember that when Scotland on Sunday reported a big swing to Yes in their ICM poll at the weekend, I was slightly surprised to learn that the headline numbers showing a No lead of just 7% somehow translated into a Yes vote of 45% with Don't Knows excluded, as opposed to 46%. I assumed that the explanation was that the unrounded numbers were somewhere in the region of Yes 45.4%, No 54.6%. But the datasets have now been published, and we can see that after weighting was applied to the raw numbers there were actually 391 respondents who said they planned to vote Yes, and 468 who said they planned to vote No. By my calculations (which I've now double-checked several times, because initially I assumed that I must be wrong), that works out as -
The Yes figure is clearly closer to 46% than 45%, and the No figure is clearly closer to 54% than 55%, so after rounding the reported figures should really have been -
Yes 46% (+3)
No 54% (-3)
For the avoidance of doubt, I'm not suggesting any sort of conspiracy here - ICM strike me as being scrupulously impartial and professional. The only explanation I can think of is that they must have some kind of quirky rule for how to round their numbers, and that Yes have fallen foul of it on this occasion. But whatever that rule is, it certainly doesn't coincide with the basic arithmetic I was taught at school!
UPDATE : Or another possible explanation is that the summarised number of Yes-voting respondents was itself rounded up after weighting, and the true number was 390.6 or something like that. Either way, the calculation was certainly borderline.