Help supervisors become peace makers by helping them constructively manage conflict.
The Five Disfunctions of a Team by Patrick Lencioni:
If we don't trust one another, then we aren't going to engage in open, constructive, ideological conflict. And we'll just continue to preserve a sense of artificial harmony (pg. 81). But why is a harmony a problem? It's the lack of conflict that's a problem. Harmony itself is good, I suppose, if it comes as a result of working through issues constantly and cycling through conflict. But if it comes only as a result of people holding back their opinions and honest concerns, then it's a bad thing. (pg. 92)
One of the most difficult challenges that a leader faces in promoting healthy conflict is the desire to protect members from harm. This leads to premature interruption of disagreements, and prevents team members from developing coping skills for dealing with conflict themselves. Finally, as trite as it may sound, a leader's ability to personally model appropriate conflict behavior is essential. By avoiding conflict when it is necessary and productive - something many executives do - a team leader will encourage this dysfunction to thrive. (pg. 206)