PhD application asking what other insitution I am applying to, how to answer? I understand that schools are trying to gauge the chances of an offer being accepted by a potential candidate. Similarly to what has been described for job applications and other questions that a lower ranked program might not offer admission to someone who applied to just top schools.

How much should a candidate divulge about the other schools he/she is applying to? If applying to a top school will it decrease your chances if you are stating you are applying to another top school?

I find this kind of questions a bit intrusive and that might even compromise to some degree my application. Perhaps some people that have been in admission commitees can shed some light on the dynamics related to applicants that applied to several schools.
Repeat after me:

“I'd rather not tell you.”