Why does a post-doc fellowship application ask where else do I apply? I'm applying for a post-doc fellowship, and one thing that confused me is that they ask for:


  Names of other fellowships for which you are now applying


I have no problem with including them, but I wonder how is this information relevant to this particular application and whether it increases or decreases my chances if I mention I apply for other places or not. (I'm not going to lie of course though!)

Any ideas are appreciated.
It's hard to say about any specific fellowship (especially without knowing which one), but I've served on graduate admissions committees where we've asked applicants a similar question.  I don't recall any case in which I thought someone's answer changed whether they would be accepted, so I don't think you should worry much about this.  I see three ways in which the information is relevant.  I'll phrase everything in terms of my experience with graduate admissions, but the same reasoning probably applies for fellowships.


Sometimes we learn a little more about the applicant from where they decided to apply, since we learn which sorts of departments interest them the most.  The main case in which this could signal weakness is "reach schools": if you apply to a top department and tell them the only other schools you are applying to are much lower-ranked, then it amounts to saying you don't expect to be admitted.  I'd be wary of answering in that case, but I wouldn't worry about it otherwise.
Knowing where else a student has applied can help in recruiting, since it means we can take into account other offers or deadlines they may face and can make a pitch based on what we expect their other options might be.  (One way this plays out in practice is it helps us guess who might benefit from extra encouragement since they may have received an offer from Department X this week.)
Departments are interested in this sort of information for statistical reasons, so they can keep track of which other departments applicants consider similar to or competitive with them.  This reason has nothing to do with evaluating applications or recruiting students, and it could be satisfied with an anonymous questionnaire, but that's more work to administer than simply adding a question to the application (and it might get a lower response rate).