The primary difficulty of applying the information in the book, though, is that you are trying to manage a conflict between two other people and the book focuses on conflicts between yourself and others. However, there is some important conflict for you here (having to choose sides), so maybe the book can still help.

For ordinary intellectual disagreement (which is REALLY common even when everyone is behaving like a grown up!) the best thing to do is to call a committee meeting so everyone can hear everyone else’s opinions and get things thrashed out.

For the childish behavior that is unfortunately common in some climates, there is really no solution except separating the combatants. This is one of the things to find out about early in the process, and either avoid bad departments or have a plan early for dealing with the craziness.

I agree, work with your chair first but be prepared to insist on committee changes if someone is being too difficult.

Interestingly, in Australia, the PhD is examined by three external referees (one of whom has to be out of the country). This really cuts down on the master-servant aspects of a local committee system.

Also, I wouldn’t underestimate fait accomplait. That is, if you produce a high quality & complete document that makes a good faith effort to satisfy the recommendations of the entire committee, then it’s hard for them to really complain and it’s easy for a chair to “wrap it up.”