By being empathetic, actively listening, reframing the conversation, keeping the focus on the issues, separating the people from the problem, and using caucusing when necessary, a good mediator can help parties reach a resolution A good mediator knows that parties in a mediation may be irrational or emotional and understands how to manage these situations. Here are some ways that a good mediator can deal with irrational parties in a mediation that is mutually beneficial.

Empathy: The mediator should be empathetic towards the parties and acknowledge their feelings and perspectives. This can help de-escalate emotions and build trust between the parties and the mediator.
Active Listening: A good mediator listens actively to what each party is saying and asks open-ended questions to clarify their positions. This can help identify underlying issues and concerns that may be causing irrational behavior.
Reframe: The mediator can help reframe the conversation in a positive and productive manner. By rephrasing negative comments or reframing issues, the mediator can help parties find common ground and work towards a resolution.
Keep the Focus: A good mediator keeps the focus on the issues at hand and avoids getting distracted by personal attacks or emotional outbursts. The mediator can gently guide the parties back to the issues being discussed and help them find a way forward.
Separate the People from the Problem: The mediator can help the parties separate their emotions and feelings from the problem they are trying to solve. By acknowledging their emotions but keeping the focus on the problem, the mediator can help parties find common ground and work towards a solution.
Caucusing: If necessary, the mediator can caucus with each party separately to help them manage their emotions and find a way to work collaboratively with the other party.

Overall, a good mediator uses a range of techniques to help parties manage their emotions and find a way forward.