You can limit the number of votes per user only if the users are logged (in their WordPress accounts). This also means that Vote Permissions has to be set to Registered Users Only.
We tested several times and it works properly on all browsers (IE, Firefox, Safari, Chrome).
Instead of limiting how many times they can vote, another option would be to block the voters by Cookie & Ip. You can set a time interval (30 days, for example). This means that once an user votes, for the next 30 days he will not be able to vote again on the same poll since he's blocked (by cookie and IP).
If you choose the second method, both logged and unregistered users will be able to vote.