This is what you should probably do:
1) As soon as user votes, you should make an ajax call to the server and update the flag in the database and disable the voting using javascript.
2) If the user refreshes the page and tries to vote up again, the server would be knowing that the vote has already been made(as it is saved in database) so the voting system will appear disabled on the page.
3) If the user tries to enable the voting using chrome tools or firebug by modifying the source of page, you can create a check at database end by setting the composite key on userID and "vote" flag which would prevent the duplicate votes.
Hope it helps..
