Don't you not want some points or not?The point of QI, if you don't know, is that the questions are all kind of a trick. In this case, the trick is that it's hard to work out what the right answer is, and there's a penalty for a wrong answer.
This question brought about some linguistic chat, all of which ended with Sandi saying that only 'arbitrary pedants' would worry about double negatives, and explaining why the stigma came about in the first place. Gyles Brandreth also took the opportunity to tell us at length how English has half a million words and German only a hundred thousand (I guess it depends how you count them).
But the point here is the difficulty of the piled-up negatives, of course. Let's dispense with the easy one first: the or not at the end caused both Alan Davies and Victoria Coren to claim that it wasn't a yes or no question: it's two questions. WELL. This is technically true, it is two questions, but as I discuss at length in my thesis (and as is generally known; it's not my idea), this is actually one question because yes/no questions are a choice between two alternatives. So that's OK. We can in theory give a yes or no answer to this question. So which is the right one, assuming that you do want points?
WE DON'T KNOW! That's one of the cool things about this question and it's not even because of the double negative! It's because negative questions are inherently ambiguous! Look:
Don't you want some points?We don't always really have a clear sense of what 'yes' means in answer to a negative question. Probably, you feel that it means yes, I do want some points in this case. I do. But it's got to have the right intonation otherwise it doesn't mean anything much, though it can't mean that I don't want points, I don't think.
No (I don't want some points)
Do you not want some points?Again, it's not clear, without a sort of contradictory emphasis, what this means. There's tons of research on this which you can read if you're interested. Kramer & Rawlins use examples like the following to show that in fact, the interpretation is likely to be negative in such questions:
No (I don't want some points)
Is Alfonso not coming to the party?So we've already got an issue with this kind of negation. Adding in a double negation, as in the original question, just adds parsing difficulty to the already ambiguous question. It is a real double negative, so it cancels out, as in I don't not like him... or is it double negation as found in many varieties, where one reinforces the other, as in I didn't do nothing or Didn't you not? We just don't know.
No (=he isn't coming)
Yes (=he isn't coming)
What, you thought I was going to answer this one? Nope. Unsolved problem, my friends.
(The 'correct' answer was yes, which is actually not what I'd have gone for: I'd have said it meant something like Isn't it the case that you don't want some points, or is that wrong?, so I'd have answered No, that's not the case. But maybe they went with yes as in Yes, that's true, it isn't the case that....)