It's self-locating information that she can update on. — Andrew M
One should update one's probabilities when given new information. — Andrew M
Variation 2
Suppose I toss a fair coin; if it comes up heads, I ask you if it was heads or tails; if it comes up tails, I don't. When asked, you should always guess "heads".
Now move the likelihood that I'll ask in each case.
Variation 3
If the coin comes up heads, I ask you once to guess; if it comes up tails, I ask you twice.
This is different from our case because for each round you know the first question is the first question. That one's 50-50, but once I ask again, you know to answer "tails". — Srap Tasmaner
Now suppose there were a way to fix it so you didn't know how many times you were being asked or whether a question was a first or a second. All you know is that on tails you'll be asked twice. What do you guess? — Srap Tasmaner
It needs two blue balls and one red ball. — Jeremiah
Let's just stick with the OP, then we all know we are debating the same problem and not something else. — Jeremiah
Monday and heads is still only one out of the three possible outcomes. — Jeremiah
Would you consider the 2/3 debacle an argument against the 1/3 argument and for the 1/2 argument? — Jeremiah
She knows it must be either Monday or (Tuesday and Tails) — Andrew M
Do you agree that P(Heads|Awake) = 1/3? — Andrew M
These cases are different because being asked (again) provides you with additional information, whereas it doesn't in the original case. You're going to be asked regardless, and you have no idea if you've been asked before. — Michael
One thing that occurred to me is that if there's betting, splitting the payoffs among multiple people is wrong. — Srap Tasmaner
Information about the toss can very much change that. If she is able to actually see the result of the toss, the odds become a certainty one way or another, not 50/50. So information does change the odds, and she has information beyond the simple fact that a coin was tossed.This one is begging a different answer. From Sleeper's perspective, this has not been established.
— noAxioms
She already knows that it was a fair coin toss and that a fair coin toss has a 50% chance of landing heads. Nothing can change that. — Michael
Don't know what you mean. — Srap Tasmaner
Elga rejects my premiss: his (E7) contradicts my (L1). I reject Elga’s
premiss: my (L6) contradicts his (E1).
So since there are three possible awakenings and only one is when the coin comes up heads, then won't that mean she has a 33% chance of it being heads? — Jeremiah
This would follow Bayesian philosophy on probability which suggest we should update our probability models when we get new information. — Jeremiah
Do you mean that if both people who are asked if it's tails correctly guess tails then that should only be counted as 1 success rather than 2? — Michael
When awakened Beauty does not know if it is Monday or Tuesday. — Jeremiah
She's more likely to be awakened on Monday than Tuesday — Srap Tasmaner
There are four equal probabiltiy states (each equally has 50% chance of being visited eventually, all depending on the coin toss. Monday and Tuesday are eventual certainties):
A Monday Heads
B Monday Tails
C Tuesday Heads
D Tuesday Tails
The sleeper wakes up and knows not which of the four it is, but she has the additional knowledge (new information) that it is not C, so 33% chance of each of the other choices, and only one of those is heads. Odds are 33% — noAxioms
The 33% comes from the sleeper knowing that there will not be a waking on Tuesday if the result is heads, but there will be a waking on the other three scenarios. In this case, new information is gained (it is not Tuesday/heads), and the odds are not 50/50 — noAxioms
Not exactly. If you're calculating wagers and payoffs, you'd need to add up all the gains and losses for the odds to make sense. — Srap Tasmaner
1 point for successfully guessing heads and 0.5 points for successfully guessing tails (because you get two opportunities — Michael
Suppose instead you're offering 2-1 against heads, and I still wager $1 on tails each time I'm asked.
On heads, it's the same: expected loss of $0.50.
On tails, I only make $0.50 each time, for an expected profit of $0.50.
My profit and loss cancel out, so 2-1 is a fair book, representing the true odds. — Srap Tasmaner
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