You've made me realize a critical point, which I haven't really addressed.

Intuition is an experience, just like feelings and rational or irrational thought. Experience is whatever is happening, regardless if the source is from the world or from inside yourself or from the universe or cosmos. You experience an intuition as one of many features of your existence.

All experience is equal. Analysis is not better than intuition, and vice versa. All we can do is "process" our experience, and that processing "becomes" more experience. (After all, your thoughts are recorded in memor. You can "retrieve" them and "replay" them.)

Consensus from a truth units perspective is about putting our experiences on the table for one another -- what happened to us and how we reacted to it. "Fact" and intuition all start with equal value. If we listen to one another, we can acknowledge everyone's experiences and validate them as experiences.

Then we can between us explore, discuss, and decide what we agree on, and what from there we can further agree on. If we face a threat or problem we agree needs a collective or social solution, then for many of us, we will see consensus is a high priority based on our past collective problem-solving experiences.

If we are six people in a lifeboat, and one of us is drilling holes in the bottom of the boat, hopefully five of us will agree the hole-drilling must be stopped before we sink. (Although if all five of us were Buddhist monks, we might choose our own deaths over violence against the hole-driller. If four of us wanted to save our lives, I'd likely join with them.)