I don't see the value of neg rep. I don't think I've ever given any ; they just seem so passive aggressive to me. The couple times I received some it was definitely in that spirit: "I refuse to engage with you and I refuse to talk about my opinion but I just wanted to let you know that I think you SUCK!"
I'm on another board where posts can be graded and the grading curve is explicit in the rules.
Neg grades are meant for (from worst to lightest): severe transgressions of the rules, promoting illegal activities, severe personal attacks, offensive (racist, sexist, etc) messages, unreadable (poor grammar, text speak, animated gif abuse), disrupting a constructive discussion (snark, commenting without reading, off topic posts).
On the opposite, posi grades reward: well researched and well sourced posts, well constructed arguments, inspiring and unique ideas, remarkably informative, constructive and pertinent ideas.
Mods are very strict about enforcing the fact that grades can't reward or punish opinions, just behaviors. Also, grades are public. It's worked really well to encourage an atmosphere of calm, well built and useful discussion, even on inflammatory topics.