I have nothing to do with academy, so take my answer just as something that I'd expect based on my understanding of human interaction and behaviour.
The main resource you have is your own reputation, and that will be severely harmed if people are accusing you of being unfair, biased or "not objective enough". You might be able to get away with it once in a while, but overall, it's quite enough for the system to work. Worst case scenario, you slow down the propagation of the work in question, but in practice, the paper will find another way (another reviewer, journal...). Even if you succeed, you risk harming your reputation, which is extremely important in a field centered around collaboration with peers and promising understudies.
You only considered competition between individual scientists, which is mostly a thing of (1) competing for grants and (2) competing for reputation. I've already dealt with reputation. Competition for grants might be important for you if you're trying to adapt the process for something like performance reviews - it's the clearest cut case where hurting others can help you. However, it doesn't have much to do with the peer review process - that would indeed introduce a very strong motivation to be "as unfair as you can be without actually appearing unfair".
However, there's also another competition going on - that between individual reviewers and their journals. If your paper was rejected based on grounds that are seen as fair and objective, you'll likely also be rejected by other journals. If not, the other journals might jump on the opportunity to publish your paper, while also implying that another journal has treated the paper unfairly. You can't do this very often if you want your journal/reviewers to keep being relevant!
Points to take away
If you want to use a similar system for another domain, make sure that similar incentives are at play.
- Have multiple independent reviewers, and let people choose their reviewer (while the reviewer has a chance to decline).
- Make sure there's not a lot of "authority" in play - for example, superior-underling relation doesn't make for good peers. Peer review works best with consensus and with reasonably objective / shared values.
- Make everything public (in the team / company). No anonymity, no "hidden" reviews. This is necessary for the reputation-based controls to work. In a way, it's a redundancy in the peer review system - it allows people to "review" the reviews themselves.
It works best in mostly flat hierarchies. Thinking in terms of a performance review in a company, peer review will be a poor choice if managers order people around. On the other hand, if managers have to persuade others to follow with their plan, it might work great :)