It seems even weirder in the Xtreme Sleeping Beauty, where she’s awakened a thousand times : “my subjective probability for heads is 1⁄2, but I’m only willing to bet up to 6 cents”.
I guess I don’t see why it’s weird. The number of times she will bet is dependent on the outcome. So, even though at each awakening she thinks probability of heads is 1⁄2, she knows if it’s tails she’ll have to bet many more times than if heads. We’re essentially just making her bet more money on a loss than on a win.
In that case, what does it even mean to say “my subjective probability for heads is 1/2”? Subjective probability is often described in terms of bettings—see here.
Seems to me this is mostly a quarrel of definitions, and that when you say “people who believe the answer is 1⁄3 pictured counts in a 3 by 1 contingency table, and applied the wrong theory to it.”, you’re being unfair. They’re just using a different definition of “subjective probability”
“Subjective probability” is a basic term in decision theory and economics, though. If you want to roll your own metric, surely you should call it something else—to avoid much confusion.
I guess I don’t see why it’s weird. The number of times she will bet is dependent on the outcome. So, even though at each awakening she thinks probability of heads is 1⁄2, she knows if it’s tails she’ll have to bet many more times than if heads. We’re essentially just making her bet more money on a loss than on a win.
In that case, what does it even mean to say “my subjective probability for heads is 1/2”? Subjective probability is often described in terms of bettings—see here.
Seems to me this is mostly a quarrel of definitions, and that when you say “people who believe the answer is 1⁄3 pictured counts in a 3 by 1 contingency table, and applied the wrong theory to it.”, you’re being unfair. They’re just using a different definition of “subjective probability”
Don’t you think so?
Based on my interaction with people here, I think we all are talking about the same thing when it comes to subjective probability.
I agree that you can use betting to describe subjective probability, but there are a lot of possible ways to bet.
“Subjective probability” is a basic term in decision theory and economics, though. If you want to roll your own metric, surely you should call it something else—to avoid much confusion.
That is why I’d rather talk in terms of bets than subjective probability—they don’t require precise technical definitions.