Why? Being predicted to not pay on tails is perfectly consistent with seeing a flip of tails (and not paying).
As I see it, the game proceeds as follows: You flip a coin. If it comes up tails, you are asked whether or not you want to pay $1. If it comes up heads, the predictor estimates whether you would have paid up on a result of tails: you get $2 if they predict that you would, otherwise you get nothing.
You know these rules, and that the predictor is essentially perfect for all practical purposes.
Hmm, I guess I misunderstood the setup, oops. I assumed that only those who are predicted to pay $1 on tails would be offered the game. Apparently… something else is going on? The game is offered first, and then the predictor makes the prediction?
Yes, that’s why I bracketed my interpretation as I did: in my reading, the only clause to which the prediction result applies is “you’ll win $2 on Heads”.
Why? Being predicted to not pay on tails is perfectly consistent with seeing a flip of tails (and not paying).
As I see it, the game proceeds as follows: You flip a coin. If it comes up tails, you are asked whether or not you want to pay $1. If it comes up heads, the predictor estimates whether you would have paid up on a result of tails: you get $2 if they predict that you would, otherwise you get nothing.
You know these rules, and that the predictor is essentially perfect for all practical purposes.
Hmm, I guess I misunderstood the setup, oops. I assumed that only those who are predicted to pay $1 on tails would be offered the game. Apparently… something else is going on? The game is offered first, and then the predictor makes the prediction?
Yes, that’s why I bracketed my interpretation as I did: in my reading, the only clause to which the prediction result applies is “you’ll win $2 on Heads”.