You could build the system so that giving information would be useless. This could be achieved (depending on the system) by having users host their data on thei

You could build the system so that giving information would be useless. This could be achieved (depending on the system) by having users host their data on their own computers, or by using crypto that would render you unable to provide the data (i.e. they have the private key and you cannot provide anything but the ciphertext). That said it would only be as effective as your implementation, so hire (or be) a good crypto guy!