Ask HN: How would you anonymize the voting system for Reddit?

I am creating an app much like Reddit in that there will be upvoting & downvoting but there will not be comments nor user submissions. I don't want to track users. I don't want cookies nor anything like that. Users will not log in. I'd like an anonymous way to keep track of which users voted for what to keep integrity in the voting system...(eg allow up to n numbers of votes per user so we ignore bots, etc.).

Since I want to keep the data anonymous I thought about anonymizing the IP address? The system doesn't have to be perfect and I realize an apartment building, company, etc may have multiple users at the same IP address. For instance, take the IP address of "215.54.387.9"...if I simply use "215.54.387" and leave out the last "9" is that enough so that votes cannot be traced back to who voted for it? My understanding is that a government entity, etc needs to match the HTTP referer in combination w/ the IP address to track down the user's information, or am I wrong? Also, how would I deal with IPV6 addresses?

Is there a better way than w/ trying to anonymize the IP Addresses?