To avoid multiple voting from the same person (computer) we log the voting IPs and count the votes from the same IP. When the voting feature was first available, we did the same check with cookies which proved somewhat (a lot!) problematic since anyone could wipe his cookies and vote again or even switch browser and again, vote again.
The IP logging method is used from almost all applications that somehow enable voting in the net. The drawback is that sometimes a whole household with say 3 computers, is seen as a single IP. So if someone from the house votes, the others cannot, or people cannot use all their votes as their ip was used from another person under the same router/IP.
These votes may have been cast by anyone under the same IP (which is always someone in your house/company sub-network)