I think the key contribution of Double Crux is “diagram what the argument even is, before making it.” If you try to make your argument at the same time as you clarify what the precise topic is, you risk getting confused more easily. “Get on the same page first, then debate” also is a practical way to motivate collaborative rather than competitive discussion, in a way that still retains a driving force towards clarity (whereas many other “be nice to each other” priming techniques point you away from being clear.)
I think the key contribution of Double Crux is “diagram what the argument even is, before making it.” If you try to make your argument at the same time as you clarify what the precise topic is, you risk getting confused more easily. “Get on the same page first, then debate” also is a practical way to motivate collaborative rather than competitive discussion, in a way that still retains a driving force towards clarity (whereas many other “be nice to each other” priming techniques point you away from being clear.)