This article discusses how upvotes and downvotes influence the quality of posts on online communities. The article claims that downvotes lead to more posts of lower quality from the downvoted commenter.
From the abstract:
Social media systems rely on user feedback and rating mechanisms for personalization, ranking, and content filtering. [...] This paper investigates how ratings on a piece of content affect its author’s future behavior. [...] [W]e find that negative feedback leads to significant behavioral changes that are detrimental to the community. Not only do authors of negatively-evaluated content contribute more, but also their future posts are of lower quality, and are perceived by the community as such. In contrast, positive feedback does not carry similar effects, and neither encourages rewarded authors to write more, nor improves the quality of their posts.
The authors of the article are Justin Cheng, Cristian Danescu-Niculescu-Mizil, and Jure Leskovec.
Edited to add:
I suspect in most communities votes are a measure of attention and this makes even downvotes rewarding. Downvotes are easier to get which could explain the disparity in the amount of contributions. This doesn't apply to LW due to the comment hiding system, I think.
Yes. Clearly bad karma in itself is not enough for trolls and others who frequently get downvoted - there need to be some more tangible effects like comment hiding. This should have been discussed by the authors but I can't see that they did that (only skim-read the paper, though).
This interesting sentence from the abstract confirms what you say about downvotes being rewarding:
Hence negative feeback is better than being ignored.