Lucy Keer

So we have the following setup (from that post): "a machine produces boxes with (ordererd) pairs of bits in them, each bit viewable through its own door"

Now we ask 3 questions: 1. Is the first box in state 0? 2. Is the second box in state 0? 3. Are the boxes both in the same state? Obviously these overlap: e.g. to be consistent, if you answered Y to 1. and N to 2., you'd also answer N to 3.

Given this, it all works. E.g. for question 1 P(first 0) = P(first 0, second 0) + P(first 0, second 1) = -½ + ½ = 0 So answer is N. Same for the others.

Now, where that -½ comes from was a bit opaque to me. I mean I could follow the algebra, just didn't have much intuition for how it got there. So I played around for a while and came up with the following.

Motivating idea: NNN is inconsistent, so all four possible assignments don't work. But {first box 0, second box 0} is *especially* bad. It's the wrong answer to all three questions. Other three boxes are only the wrong answer to one question.

So... we penalise bad answers, and, because {first box 0, second box} is particularly bad, it gets clobbered three times instead of just once, driving it negative. That's vague. But I'll outline a precise version.