Log votes against user?

Hi,

I have a multisite network. It has a custom post type called Ideas. I want to allow all logged in users on the network to be able to vote on these posts.

The problem is multiple users may be on using the same IP and browsers (think students in libraries). So even with "Use IP Check" disabled, if I log in with one user and vote, then log out and back in with a different user, the new user can't register a vote on the same post because a cookie is already set. The cookie seems to be persistent irrespective of which user is logged in.

So is there a way I can limit the votes by user, rather than by cookie or IP? ie if username A has voted on this post, don't allow them to vote again. But if username B has not voted on this post, allow them etc

I think this is the only way I can do it...

Thanks