Should I tell other interviewers where else I've interviewed?
Some professors and other interviewers have asked me where else I have interviewed. Should I tell interviewers where else I've interviewed?
Yes, it is very likely in your best interests. If you have other interviews at comparable schools, then you will benefit from saying so. If you don't, then it's not so clear. However, departments will assume your job search is not going well if you are reluctant to address the issue and they haven't heard impressive rumors about your interviews, so avoiding discussing interviews won't really help. Instead of saying something awkward like "I'd rather not talk about that", it's better to be up front and optimistic. "This is my first interview" is better than "This is my only interview so far".
Here are a few reasons why telling about other interviews can help your case:
As a general rule, people want something more if they know other people also want it. Valuing a second opinion is rational behavior.
Even when it doesn't change the outcome, competition can speed things up. If a search committee member is trying to make an offer and still needs some final committee or administrative approval, it's helpful to be able to say "Let's move fast, since she is also interviewing at X, Y, and Z, and we'd like to make a good impression by coming up with the first offer." If it's too late for that, they can say "She already has an offer from X, so we need to act before she decides."
In principle, you could hurt your chances if you list a lot of schools typically considered much more desirable (which could make the school you are currently interviewing at feel they would just be wasting their time trying to compete). However, in this case you are probably already in trouble, since the rumors of your busy interview schedule may already worry the search committee. Instead of trying to cover things up, it's better to acknowledge that you have these other interviews. If you are worried about this risk, you can address it by making your interest clear throughout the interview.
I cannot speak for faculty interviews personally and this may be redundant information but I interviewed at multiple "top ranked" schools for PhD admissions and in everyone of them I was asked where else I was interviewing and I told them the truth.
Having said this, nowadays, most job talk notifications are available on the website of the university or college or institution where you are interviewing and it is relatively easy to determine this from a google search of your name. For instance, this year our department is hiring for 2 different job lines and there are quite a few faculty candidates giving talks every week. We always Google their names to find out where else they are interviewing. In the case of one particular candidate it was very useful to find out that that that candidate had put up a list of other institutions where he/she was interviewing this particular season.
I do not think personally that giving them information about where else you are interviewing will add or subtract from your overall job application materials and probabilities.
Best of luck for getting a job !
If you don't want to disclose that, you can simply say: "I'd rather not discuss this", and you can look straight into your interviewer eyes with that. I've seen candidates do that; it may have looked harsh, but there's no obligation on the candidate's side to tell anything beyond the contents of the job talk.
You can also try to convert this into a joke like "Enough to earn me a free roundtrip this year". An American faculty should take that as a hint that you don't want to talk about it. An international faculty may need a more straight answer like the one I gave above. (I am talking about the US here as the largest academic market; in UK, as far as I understand, you won't have more than 30 minutes face time with the faculty of the hiring institution, and they probably have more important things to ask than the # of interviews you have.)
Having said that, you need to weight in the benefits of telling vs. not. For one thing, you may not have all the invitations out yet on your first fly-out, so you really don't know yet what other interviews you might have. On the other hand, by the time you reach your sixth destination (if you are lucky to get that many), the first place may already have told you, "Sorry, we made the offer to somebody else". So nominally you may have interviewed there, but really you won't get an offer from them.
As a bottom line, you need to do what others in your discipline do. You don't want to look like a fool in the environment where everybody keep their secrets by telling left and right about your choosing between Harvard and Stanford (and thus losing a chance to get a far more realistic offer from Alabama); and you don't want to look like a fool hinting at many undisclosed interviews when your adviser had told them that this is the only interview you have when they called him/her, or your other interviews were posted on a job market rumor website.