Wire Disagreement Dilemma

You are locked in a room with two other people and a time bomb. To disarm the bomb, you must choose correctly between cutting the red wire or the blue wire on the bomb; cutting the wrong wire, or failing to cut either of the wires in time, will trigger the bomb. Any one of the three of you can choose to lunge forward and cut one of the wires at any time.

Each of you puzzles over the circuit-wiring schematic. You find an airtight, 100% certain proof that the red wire is the wire that needs to be cut. But simultaneously, your two allies report that they have come up with airtight, 100% certain proofs the blue wire needs to be cut! You cannot come to a consensus, either because you do not have time, or because you simply cannot understand each others' proofs.

Your choices are:

1. Lunge forward and cut the red wire.

2. Allow your allies to cut the blue wire.

How do you make your decision? Call this the Wire Disagreement Dilemma.

Notes:

1. According to the most straightforward application of classical logic, you should lunge forward and cut the red wire.

2. Philosophical Majoritarianism doesn't tell you exactly what to do. PM seems to be a heuristic that you use alongside other, sometimes conflicting, heuristics. As I've seen it outlined, it doesn't seem to tell you much about when the heuristic should be used and when it shouldn't.

3. There's a sense in which you never have an actual proof when you make a decision, you only have a memory that you had a proof.

4. Consider two people, Alice and Bob. Alice should not automatically give her own beliefs "magical precedence" over Bob's beliefs. However, there are many circumstances where Alice should give her own beliefs precedence over Bob's; there are also circumstances where Alice should defer to Bob.

5. This type of thinking is so rare, that (to my knowledge) we don't even have a short word to describe the difference between "I believe X because I reasoned it out myself" and "I believe X because someone smarter or more experienced than me told me X, even though, on my own, I would have believed Y."

In normal conversation, you have to use cumbersome phrases and idioms: for example, "it seems to me like X" in the former case and "my understanding is that X" in the latter case.

Experience vs. Hearing: As technical terms, I'd propose that in the former case we say "I Experience X" or "my Experience is X." In the latter case we can say "I Hear that X" or "my Hearing is X."

6. One asymmetry, when Alice is evaluating reality, is that she generally knows her own beliefs but doesn't necessarily know Bob's beliefs. Bob may be unavailable; Bob may be unable to correctly articulate his beliefs; Alice may misunderstand Bob's beliefs; there may not be time to ask Bob his beliefs; or Bob may deliberately deceive Alice about his beliefs.