The claim “I think this coin is heads with probability 50%” is an expression of my own ignorance, and 50% probability means that I’d bet at 1 : 1 odds (or better) that the coin came up heads.
Just a minor quibble—using this interpretation to define one’s subjective probabilities is problematic because people are not necessarily indifferent about placing a bet that has an expected value of 0 (e.g. due to loss aversion).
Therefore, I think the following interpretation is more useful: Suppose I win [some reward] if the coin comes up heads. I’d prefer to replace the winning condition with “the ball in a roulette wheel ends up in a red slot” for any roulette wheel in which more than 50% of the slots are red.
(I think I first came across this type of definition in this post by Andrew Critch)
Just a minor quibble—using this interpretation to define one’s subjective probabilities is problematic because people are not necessarily indifferent about placing a bet that has an expected value of 0 (e.g. due to loss aversion).
Therefore, I think the following interpretation is more useful: Suppose I win [some reward] if the coin comes up heads. I’d prefer to replace the winning condition with “the ball in a roulette wheel ends up in a red slot” for any roulette wheel in which more than 50% of the slots are red.
(I think I first came across this type of definition in this post by Andrew Critch)