“It doesn’t make sense to assert that probability of Tuesday is 1⁄4 (in the sense that it’d take a really bad model to give this answer).”
Suppose if heads we wake Beauty up on Monday, and if tails we wake her up either on Monday or Tuesday (each with probability 1⁄2). In that case, when Beauty is awakened, she should it’s Monday with probability .75 and tails with probability .25.
“In the classical possible worlds model, you’ve got two worlds for each outcome of the coin flip, with probabilities 1⁄2 apiece, and so (Tuesday, tails) is the same event as (Monday, tails), weighing probability of 1⁄2.”
I agree with this. I just thought it would be more intuitive if people thought of “(Tuesday, tails) is the same event as (Monday, tails), weighing probability of 1/2” from the perspective of the experiment that I describe above (where we imagine Beauty is awakened on a random day within the space of possible days for each coin result).
I have no problem imagining a probability distribution for Tuesday, just like I can imagine a probability distribution for the mean of some random variable.
“It doesn’t make sense to assert that probability of Tuesday is 1⁄4 (in the sense that it’d take a really bad model to give this answer).”
Suppose if heads we wake Beauty up on Monday, and if tails we wake her up either on Monday or Tuesday (each with probability 1⁄2). In that case, when Beauty is awakened, she should it’s Monday with probability .75 and tails with probability .25.
“In the classical possible worlds model, you’ve got two worlds for each outcome of the coin flip, with probabilities 1⁄2 apiece, and so (Tuesday, tails) is the same event as (Monday, tails), weighing probability of 1⁄2.”
I agree with this. I just thought it would be more intuitive if people thought of “(Tuesday, tails) is the same event as (Monday, tails), weighing probability of 1/2” from the perspective of the experiment that I describe above (where we imagine Beauty is awakened on a random day within the space of possible days for each coin result).
I have no problem imagining a probability distribution for Tuesday, just like I can imagine a probability distribution for the mean of some random variable.