The correct name is "waste of time"

I know what you're referencing, and I appreciate you keeping the question generic. To that end, I'll keep my reply generic as well.

No, it's not a debate; it's a trap. If the good-faith participant agrees to the debate, it will go down exactly like you said.

If the one acting in good faith refuses to debate the bad-faith one (because they know that's what they're going to do), then the bad-faith one will just gloat that the good-faith person is a coward who won't debate them.

Either way, the one acting in bad faith "wins".

If the person judging the debate is a republican then absolutely.

If two people agree to a debate, but one of them participates in bad faith

That part was enough for me. Under these circumstances, not even a conversation can take place let alone a debate. Try to protect yourself from toxic people by not wasting your time with them. I know it's easier said than done cause I'm trying to recover from a similar situation.

I think those are called "presidential debates" these days.

If I was the good faith party I'd prepare with a list of inflamatory but true claims on the bad faith party and any time they try to sidestep, throw the accusations at them and force them to go on the defensive instead of giving them a platform to try and legitimize their bullshit. If you're talking about what everyone thinks you are, theres no 'rising above' it, you gotta attack it.

No. That's a food fight with children.

I'm still rocking my "Will You Shut Up, Man? bumper sticker.

Sort of. What passes for "debate" often isn't as controlled as it ought to be and people don't necessarily know how it should be done - "what do you mean, 'yeah well, your mother' isn't a valid argument?!".

When it's clearly bad faith, there's no way to get any value out of that situation, so I'd be edging slowly towards the door.

Depends on the context. Academically? No, that would just be wrote off. In a more relaxed, social setting? I think most people see no differences between an argument or debate.

Ideally, an audience would pick up on the bad-faith side not addressing arguments, engaging in personal attacks, making unjustified claims, etc. and be unimpressed. The interrupting especially should prompt some intervention by a moderator, but usually they don't have a means of preventing it from happening other than chastising after the fact so it still relies on some degree of human decency.

I'd still call it a debate, just a poor quality one.

It's not a debate in the traditional sense. If you were on a High School debate team and did this you would get thrown off the team. But those debates have moderators and coaches whose goal is to get the kids to improve how they think and how they present their arguments. And perhaps most importantly, there is not an army of journalists looking to distill the debate into 10-second sound bites for the next week.

Modern political debates are really elongated ads. Each candidate is selling themselves to voters. If one candidate decides that the behavior you describe will get more voters to buy in, and they turn out to be correct, then they did well in the debate, no matter what the country's Model UN moderators might think.

Still, the debates are important because it will likely be the only chance we get to see the candidates respond to each other, in real time. Particularly in this election, where the fitness of both candidates is in question. This will be the only chance for voters to find out how each candidate really gets it, without a media filter in front of them.