Principles are ways of successfully dealing with reality to get what you want out of life.
Ray Dalio, one of the world’s most successful investors and entrepreneurs, cites principles as his key to success.
When they're at odds, you should work hard to resolve the disagreement.
If you are about to make a decision that the believability-weighted consensus thinks is wrong, think very carefully before you proceed. It's likely that you're wrong, but even if you're right, there's a good chance that you'll lose respect by overruling the process. You should try hard to get in sync, and if you still can't do that, you should be able to put your finger on exactly what it is you disagree with, understand the risks of being wrong, and clearly explain your reasons and logic to others. If you can't do those things, you probably should suspend your own judgment and go with the believability-weighted vote.