Upvoted because this is a really clean and well-argued presentation of the position and it is a position I agree with. But weren’t basically all of these points made in that original discussion? I recall making a couple of them myself. I think this is the relevant sub-thread if people are interesting in seeing the arguments that were made on both sides.
One other consideration in favor of focusing on the payoff scheme is that in the literature I’ve seen hypothetical wagers are the only way of defining subjective probabilities to begin with. No one knows exactly what ‘I believe P(X)=.1’ means except that a gambler with such a belief would only take a bet on X if the payout greater than 10:1 and would only offer the bet if the payout was less than 10:1. I don’t know of another way to make sense of probabilities for one-off events. If someone has one please share.
Anyway, this was the payoff scheme I liked. It seems less awkward than some of yours that result in a 1⁄2 answer and I think it ensures we don’t violate conservation of information nicely.
Upvoted because this is a really clean and well-argued presentation of the position and it is a position I agree with. But weren’t basically all of these points made in that original discussion? I recall making a couple of them myself. I think this is the relevant sub-thread if people are interesting in seeing the arguments that were made on both sides.
One other consideration in favor of focusing on the payoff scheme is that in the literature I’ve seen hypothetical wagers are the only way of defining subjective probabilities to begin with. No one knows exactly what ‘I believe P(X)=.1’ means except that a gambler with such a belief would only take a bet on X if the payout greater than 10:1 and would only offer the bet if the payout was less than 10:1. I don’t know of another way to make sense of probabilities for one-off events. If someone has one please share.
Anyway, this was the payoff scheme I liked. It seems less awkward than some of yours that result in a 1⁄2 answer and I think it ensures we don’t violate conservation of information nicely.