Here's what I'm picturing:
We'll have a flag button to report inappropriate content. Ideally, if enough respected posters (based on a reputation score) flag something then the system can remove it without a mod having to do anything. That way bad and unwelcome content is removed quickly without having to wait.
That's separate to the like / dislike buttons. They will work by recording a vote for or against a post and based on the votes it will give a good indication of whether a topic is contentious, popular, unliked (different to violating the rules) and so on.
I think the votes will decay over time otherwise the most popular topics ever would stay at the top of the list forever and it wouldn't be helpful for a working day-to-day view. I am picturing the highest rated content for the last week or two probably being most useful or promoted more and then things will gradually drop down. Of course it will be possible to have an absolute all-time view as well.
The likes and dislikes will feed into reputation somewhat and the amount of kudos given will depend on who's giving it. Ideally, the system should reinforce good behaviour and content and help diminish the effects of poor behavior but I'm aware that there will always need to be human overrides to protect against people gaming a system and collaborating to manipulate the results. If people flag or downvote a post against the flow or contrary to high-reputation posters for instance then the system should be able to learn from that or at least report an anomaly for investigation.
It may also be worth considering making heavily disliked posts automatically hidden or diminished (e.g. click to view) so they are not removed as such (like posting violations) but are not given the attention that they don't deserve.
So, you won't rate people or topics directly but how posts are rated and the reputations of the people doing those ratings will ripple through to both.