If you let anonymous users vote for any post on a site just one time and you log that vote by the user's IP, what's the likelihood that you'd be banning other users from voting and that the original user would be able to vote again after a certain amount of time because their IP address has changed? I'm guessing almost certainly.
Client side cookies can be deleted and server side cookies again have no way to reliably map said cookie to the anonymous user.
Does this mean there is no reliable way of tracking anonymous users indefinitely?
Using only IP addresses for user authentication/identification is extremely unreliable. There might be many hundreds or even thousands of users behind one IP (e.g a corporate network) and for most of those on home connections their IPs are likely to be dynamic and regularly changing.
You have to use Cookies for more reliable tracking. You can specify just about any time-to-live for a cookie, so that when an anonymous user returns, you can identify him.
Of course cookies can be deleted by users, so they could delete their cookies and vote again. However, is this likely to be a big problem? If someone really wants to game your poll, they could write a script. However, you could add a few basic security features: only allow some maximum votes per IP per day, and allow only so many votes per IP per second.