how to check for duplicate passwords

Is it possible to check if like 100 people are using the same pasword? without risking anyones password getting out?

I heard google does this, not allowing the user to set a password 1000 people are using.

what if users have access to their own records?(eg distributed database)

EDIT:

The number of users for what I'm doing right now is 10-10K

What if we ask each client if their password matches a given text anonymously(I can do it with some RSA encryption and stuff)? would it work? or I should give this idea up for good?