Where there is something to be won, some people might cheat and if people have to judge who wins them self, some might make several accounts etc. But I doubt its a huge problem if the prizes are moderate. Cheating for a book or some drawing supplies etc. must be a low number. Besides that you can lock a vote to an IP address, so people wouldn't be able to cast more than a single vote from the same IP or they would either need a VPN or several internet connections to do it. So they could either spend their vote to down vote someone or give themselves the highest score. And again how desperate are people when the prizes ain't more than they are and its meant to be for fun. Also if you have to send out the prizes you have the address so it would be easy to see if two accounts share the same one.

Also you have the risk of someone noticing that an entry is stolen, so its a lot of trouble to go through to win I would say, and as you say should someone cheat so be it, its not the end up the world compared to having an active site. So setting up the technical things correct, no one would really have to "play" cop. Most people have no clue how to or interest in cheating in something like that, unless its obviously easy how to do it. So I wouldn't be to worried about it, if you lock to the IP address or do a little research of how other sites with voting does it, I would imagine that it could be easily solved.