The problem we saw in tonight's presidential debate is familiar to any mediator: How do you keep angry people from interrupting each other? Chris Wallace demonstrated clearly tonight that good journalists are not necessary good facilitators!
There's actually a fairly simple solution. You have to establish a ground rule at the beginning - no interruptions. And you have to enforce it, not after four, five, or six interruptions, but the very first time it happens.
You need to stop the proceedings cold, right there, turn physically towards the interrupter and speak directly and firmly: "Mr. Trump, our ground rule is no interruptions, and we won't be able to proceed if people don't stick to it. I need your commitment to support the process. Can you give it?" And then you need to wait silently for the interrupter to give it. In 35 years of mediation and facilitation, I've never had a client refuse to do so.
I've trained thousands of mediators and seen that the tendency for most mediators, like Chris Wallace tonight, is the opposite. They ignore interruptions at first, hoping they will go away. But they don't. One interruption will always be followed by more.
Parties size up very quickly whether they can get away with ignoring rules or not. If you give them several experiences of squeezing in their interruptions unrebuked, they see that the rule isn't really serious, and the problem gets worse and worse.
Once the rule is clearly established - it rarely takes more than one or two interventions like the above - the parties tend to accept the guardrail and behave. You can in fact ease up on strictness later and allow some back and forth without losing control - IF you've established the norm early.