(1) Do you mind if I ask you a question?
How do you respond? There's a complexity here, no matter what your opinions about question-asking are. The problem is that (1) has the form of a yes-no question (about what the addressee's sensibilities are) but also conveys a request (for the addressee to allow the questioner to perform an action). An affirmative response to the yes-no question is a negative response to the request, and vice versa. Oh dear. (Actually, there's more.)
I'm familiar with the phenomenon, from many years back, when I used to teach courses on speech acts and the like. But: when Language Log reader Erick Tejkowski asked me about it a few days ago (he saw sentences like Do you mind if I take another piece of cake? as ambiguous, which I think is not quite right), and when Elizabeth Traugott and (lawyer/linguist) Peter Tiersma and I fell into a breakfast discussion of it a little while back (Peter was in town to talk to Elizabeth's class on forensic linguistics), I realized that I had no sources at my fingertips to recommend to people. Who had discussed it in print? Did the phenomenon have a name? Was there relevant legal literature?
To start: the yes-no question understanding of (1) is the "literal", on-the-face-of-it, understanding. If you mind, the appropriate answer is yes (I do mind), and if you don't, the appropriate answer is no (I don't mind). But the CONVEYED content of (1) is a request. So if you grant the request, the appropriate answer is yes (go ahead), and if you don't, the appropriate answer is no (don't do it).
Now a lack of fit between the form of a sentence and what it conveys is commonplace, as in famous examples like
(2) Can you pass the salt?
This has the form of a yes-no question (about ability to pass the salt), but it serves as a request (to pass the salt), and in this case the request meaning has clearly become CONVENTIONALIZED. Answering (2) as if it were a yes-no question is, in the relevant context, uncooperative and obstructive; if you just say yes and don't pass the salt, you're being an annoying asshole. (In other contexts, of course, can you questions can be straightforward yes-no questions about ability: Can you run a marathon?)
In other words, can you questions are ambiguous, with ability readings in some contexts and request readings in others (and room for uncertainty in still other contexts).
But do/would you mind if questions are different: they come with both understandings, simultaneously. They're in a middle ground between cases where content is conveyed entirely by "conversational implicature" (It's cold in here intended to convey a request to close the window) and cases of conventionalization (the can you cases). Frankly, I've never found it easy to deal with the mind questions myself in real life. The best solutions are to read out the whole answer:
No, I don't mind; I will answer your question.
Yes, you may ask me a question. / Yes, I'm willing to answer your question.
Yes, I mind; I will not answer your question.
No, you may not ask me a question. / No, I'm not willing to answer your question.
But yes or no alone isn't going to work.
I have a feeling that this case has been discussed in the semantic/pragmatic literature, but I don't have references to hand. (Please don't write in with reports of the problem. I assume that it's been noticed again and again. What I'm looking for is analyses.)
The next level of the problem. Do/Would you mind if conveys a request (for assent from the addressee), but the request is often perfunctory: the speaker intends to go ahead with the action, but is expressing polite consideration towards the addressee — not threatening the addressee's face — by conveying a request. So folded in with the yes-no question and the request is a component of everyday politeness.
Now back to the forensic linguistics breakfast. I forget how we got to the topic, but at one point we shifted to talking about how so many people in the U.S. consent to police searches (in the absence of a search warrant or probable cause) when it is clearly against their best interests. They know there are drugs in the trunk, yet they still let the cops search the trunk when asked Do you mind if we search the trunk?
Elizabeth Traugott and I noted that a surprising number of people in the U.S. seem not to know they have a right to refuse — this despite the prominence of the consent-asking routine in television shows like Law and Order. The police aren't asking the question out of considerateness; the law requires them to get consent.
But, I suggested, some people might not appreciate this point fully and take the question to be more like ordinary conversation (softening the cops' intention to search the trunk), rather than as a legal formula.
On to how to answer the cops' question, recalling the discussion of yes and no above. Peter Tiersma was pretty sure that judges would insist that the answer no on its own was an answer to the "literal" yes-no question — that is, to mean 'no, I don't mind', giving consent. But he wasn't sure if there was case law on the point. Nor was he sure what cops (and judges) do with answers like No, don't search the trunk, which appear to first give consent and then refuse the search.
Meanwhile, I'm hoping that someone has a line on some of this.