A thumbs down option would allow for more effective communication about the quality of posts. There have been a number of posts I disagree with where I see lots of thumbs up. There should also be a thumbs down. That way you could see how many people have thumbs uped and thumbs downed.
If a poster violates the rules, then the report button should be used. If a voting system is implemented it will lead to abuse, like it does on any other website with one. People will be given thumbs down just because someone disagrees with them. Considering this a debate site, that is not the kind of conduct we want to allow.
Since this is a debate forum, any dissenters should justify their position. Just as in a court decision. If a judge wants to join in on the opinion, they don't have to say anything (thumbs up in our case), or they can write their own concurring opinion (also writing a full argument or commenting on a one you partially agree with). If they want to dissent, then they have to write their own opinion ("supporting argument" in our case) or join in with a fellow dissenter (commenting on an argument in which they agree). This way we can always know the opinion of the person commenting. If someone agrees, then we will assume they agree with everything in the post. However, if they disagree, we are left wondering whether they disagree with the first, second, or third paragraphs or even the grammar.
What good is knowing when someone disagrees if you don't know what they disagree with? Let's add to the justifications and not turn this into a facebook or reddit board where people just mindlessly like and dislike.
A thumbs-down communicates nothing but the idea that 'you're wrong'. Ultimately, policies will be agreed or disagreed upon, but the focus should be the dialogue conveyed to reach either decision, not the decision itself. Such a simple disagreement is near useless for discussion, the same applies to the thumbs-up.