Some people – Yes supporters essentially – are claiming that it is plain that the opinion polls – none of which (so far, at least – I hope I am not tempting fate) have reported a Yes lead – in the Scottish independence referendum are rigged is because they have never been asked.
Well, there is a simple reason for that: polls are small and the electorate is very large.
There are about 4 million electors able to vote in the Scottish independence referendum.
If we assume every elector has an equally random chance of being asked (which is not true for many cases: if you are not on an online panel it just won’t happen), and that each poll asks 1200 electors then the chances of you being asked in any given poll are 1200/4000000 or about 1 in 3,333: a bit better than winning the lottery jackpot I’d admit, but who bets on a 3332/1 chance?
Of course, though, there are multiple polls but to have just a 1 in 100 chance of being asked then 33 polls would have to be taken. To make it more likely than unlikely that you had been polled then 1667 polls would have to be taken.
What Scotland Thinks, at the time of writing, records 80 polls on the referendum question – so the chances of any individual elector being asked are (given all my approximations) about 1 in 42, or in bookies’ odds terms, it’s a 41/1 shot.
If you think a race is fixed because your 41/1 wager never comes home, I’d suggest you weren’t to be trusted in a betting shop.
Update: Should make it clear this is a pretty crude approximation to make a point – opinion poll sample sizes vary and if they are closer to 1000 in sample size then the odds of you being asked go up to about 49/1 (ie., it’s a fair bit less likely).
A further update: My intention on writing this was to demonstrate, in the broad brush terms why an argument based “I have never been polled so therefore the polls are wrong” didn’t hold any water. It seems the article now being touted around as an exact prediction of how likely it was you’d been asked: it’s not. As I say above much (most probably) polling these days is via online panel – if you are not on the panel you cannot be asked to begin with.