Double-Crux is a technique for addressing complex disagreements by systematically uncovering the cruxes upon which the disagreement hinges. A crux for an individual is any fact that if they believed differently about it, they would change their conclusion in the overall disagreement. A double-crux is a crux for both parties. Perhaps we disagree on whether swimming in a lake is safe. A crux for each of us is the presence of crocodiles in water: I believe there aren't, you believe there are. Either of us would change our mind about the safety if we were persuaded about this crux.
Double-Crux differs from typical debates which are usually adversarial (your opinion vs mine), and instead attempt to be a collaborative attempt to uncover the true structure of the disagreement and want would change the disputants minds.