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Given the fact that you have to be logged in to upvote, and after you upvote you can't re-upvote - yes you can tell what someone upvoted.

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After you've downvoted you cant upvote either, so there could just be a flag that says you've done one or the other.

Not just could, but as the parent comment implied, given the nature of the system the answer is unequivocally yes.

The system serves to record the arrows you've clicked, therefore this information must be stored somewhere. Someone with access to this this information should be able to determine "what stuff an account upvoted," unless the system has been designed to obfuscate the connections(i.e. accounts & clicked items) at the database level.

You only need to be able to calculate what a user has done when the user views the comment. You can imagine storing each vote as a hash of (voter, comment, direction). Then when rendering the page, you calculate all possible hashes on the page and look for hits. If the comment count per page isn't too large, it won't take that long. It's fairly intensive and probably not worth it for a site like this, but possible. It would also screw up any offline voting-rings detection.

Edit: should have clarified that by user I meant a hash of name and password, so it's infeasible to calculate offline.

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