“That means that for our posterior from above, if you choose blue, the probability of the majority choosing red is about 0.1817. If you choose red, it’s the opposite: the probability that the majority will choose red is 1-0.1817 = 0.8183, over 4 times higher.”
It may well be that I don’t understand Beta priors, or maybe I just see myself as unique or non-representative. But intuitively, I would not think that my own choice can justify anywhere close to that large of a swing in my estimate of the probabilities of the majority outcome. Maybe I am subconsciously conflating this in my mind with the objective probability that I actually cast the tiebreaking vote, which is very small.
I mean definitely most people will not use a decision procedure like this one, so a smaller update seems very reasonable. But I suspect this reasoning still has something in common with the source of the intuition a lot of people have for blue, that they don’t want to contribute to anybody else dying.
“That means that for our posterior from above, if you choose blue, the probability of the majority choosing red is about 0.1817. If you choose red, it’s the opposite: the probability that the majority will choose red is 1-0.1817 = 0.8183, over 4 times higher.”
It may well be that I don’t understand Beta priors, or maybe I just see myself as unique or non-representative. But intuitively, I would not think that my own choice can justify anywhere close to that large of a swing in my estimate of the probabilities of the majority outcome. Maybe I am subconsciously conflating this in my mind with the objective probability that I actually cast the tiebreaking vote, which is very small.
I mean definitely most people will not use a decision procedure like this one, so a smaller update seems very reasonable. But I suspect this reasoning still has something in common with the source of the intuition a lot of people have for blue, that they don’t want to contribute to anybody else dying.