A reasonable strategy is probably to store a "fingerprint" of data that you have about the user, and allow anyone to rate videos but:
- Weigh the votes of anonymous users less heavily than the votes of members when aggregating the mean score.
- Exclude votes that look "gamed", like large numbers of anonymous votes from the same subnet, anonymous votes that went direct to the voting page, etc.
- Don't update statistics in realtime to let the users see the impact of their votes.
The "fingerprint" can include a cookie, IP address, browser user-agent string, time of vote, number of page views on the site with the same cookie before the vote (and after, if you're more ambitious). Users who come only to vote and aren't really involved in the rest of the site may have a higher probability of being there to game the vote. An anonymous cookie might be deleted by an user trying to game the site, but the IP address and user agent and a time span may be enough to get a feel for how "real" the user is. When an anonymous user signs in, you can convert the anonymous vote to a "real" vote. All of these mechanisms can be foiled, but if you weigh the votes from relatively uninvolved members of your community lower, this won't hurt so much.
All of your efforts will have to be probabilistic; there's no reliable way to perfectly eliminate gaming. You won't get the results perfectly accurate, but this is fine as long as the client understands the risks of gaming and potential inaccuracies. Fortunately, online polling is almost never scientific, and most customers will intuitively understand this once you explain this. In some cases, the gaming is useful anyway, because it'll generate traffic and interest; some customers may have very little concern about the quality of the poll.
What you're after here is mitigation, not perfection. Every online poll has the problem you are describing, especially if they allow anonymous votes.
There's a sort of polling equivalent to the "hellban", which is that you can appear to accept the vote from the user's perspective, but silently throw it away.