Like darn near anything you are going to hear along the lines of project management, one of the keys to successful conflict resolution within a team is establishing a plan before the conflict occurs and gaining bipartisan support. When things are still rosy, agree that when you do (and you will) disagree, that there will be a time limit and a process for resolving the issue. There are several reasons for this:
You have to know when to say when on an issue – You aren’t going to change anyone’s mind after several attempts and you just need someone else to make the call. The project has to move forward and a festering conflict can stagnate and contaminate the entire team. Move the resolution on and get back to business.
Perhaps even you could use a fresh perspective – Luckily for you, like myself, you are never wrong. Perhaps the conflict could use a new set of eyes with, let’s say, a broader perspective. Focus on what matters and move on.
Allows you to isolate and contain the conflict – When it gets bad, it will be everywhere. In everyone’s minds, in their whispers, in their body language, and in their emails. The negative spiral has begun and you can forget about partnership. Avoid this death spiral by cutting the toxicity out before it infects your team. Isolate and escalate the issue per your resolution plan and keep the business at hand, at hand.
When you agree to escalate the conflict from the project level, you are attempting to preserve the harmony within the team as described above, however you may likely also be losing some of the facts and context surrounding the issue in the translation. Remember that no one is better suited to deal with the conflict resolution than those closest to the actual issue. They know what happened and what the facts are better than anyone. If they are unable to see through their emotions or find a common ground, you should strive to resolve the issue at your level; or someone else at the next level will – you just might not love the answer.