What prevents reviewers from providing biased and very negative reviews? One of the fundamental features of science, maybe even the most important, is that publication of scientific results is peer-reviewed. 

I want to understand why peer review is effective in the scientific community, because I want to apply principles of peer review to a different domain.

As I understand it, a researcher is reviewing work of a competitor who is producing scientific results in exchange for grant funds and reputation, usually same as the reviewing researcher does. Of course, this competition may not be very direct, but the reviewer is in an overlapping area of research. In addition, there is some natural bias of every human being to groom their own ego. Based on this, I expect most reviews to be very negative. However, it seems that biased and extremely negative reviews are rare for decent submissions. 

What stops reviewers from providing biased negative reviews?
I think the main factor that makes the peer-review system to not fall in the trap you described is that academics are finally interested in the advance of science. If I have to review a good paper, then I enjoy it and want to see it published. If I review an almost good paper, I suggest some improvements and enjoy if these are incorporated and the work is published. The very mild advantage I may have if I reject more papers does not really seem to be worth it, if I have to act unfair and unreasonable to get this advantage.

Another factor may be: The reviewer is not anonymous for the editor. Editors are often influential people and writing consistently bad and unfair reviews will make you look like a mean and unfair person. Also, the editor will not choose you again as a reviewer if you write such reviews and you will be effectively eliminating yourself from the review system for that journal (while you can still submit papers).

In view of the bounty I gave the question another thought and here is one more thing: Community. Science is well organized in communities (e.g. I consider myself as part of the mathematical community, the applied math community, the community on mathematical imaging, the optimization community and some more). As part of a community one has a sense that there are some rules one should follow to be a valuable member of the community and of these rules is fairness. Being unfair feels like a misconduct by the unwritten community rules. So even though one may get along with several cases of unfair behavior, it feels like one is cheating the system. But staying a respected member of the communities is very important both for the scientific standing and also for productivity. This reasoning also explains that bad behavior sometimes happens, when several competing communities form which are somehow "enemies of each other": One can stay a respected member of one of the communities while still treating members from the other community unfair.