100 tosses, presumed result of 50 heads and 50 tails, 150 interviews.
If the Beauties all guess tails all the time, they will get 100 right out of their 150 answers.
That looks like a 2/3 success rate, right? But is it?
Out of the 100 tosses, they got 50 of them wrong. Looked at this way, that's a 50% success rate. — Srap Tasmaner
Here's the spontaneous version of guessing-SB:
Suppose I'm going to teach Andy & Michael a little about probability. I'm going to flip a coin a bunch of times, but before each flip, they each guess. When they're right they get an M&M, and when we're done we'll count the M&M's and stuff. Now suppose before one toss, Michael guesses "Heads! Heads heads heads heads heads!!!!" If the coin lands heads, do I give him 1 M&M or 6? — Srap Tasmaner
Yes, it is. The bolded text tells the lab techs what to do - or more accurately, what not to do - on both days. It defines two protocols for TAILS: interview Monday, interview Tuesday. It defines two protocols for HEADS: interview Monday, sleep Tuesday. Even if they send her home that day, that would still be SOTAI.What happens on Tuesday&HEADS is a part of the HEADS protocol, so you excluded part of it. — JeffJo
(a) No it isn't. From the OP:
A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, Beauty will be awakened and interviewed on Monday only. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday. In either case, she will be awakened on Wednesday without interview and the experiment ends. — Srap Tasmaner
What matters is that there is a protocol on both days for both HEADS and TAILS. And that one of these four protocols is inconsistent with Beauty being interviewed. You keep treating the fact that she sleeps through a day as if that makes the day nonexistent,or that it is not something the lab techs have to have included in their protocol.The only thing that matters is one for heads and two for tails
?????(b) If it were part of the heads protocol, by eliminating it, you would be eliminating heads as an outcome. Simply being interviewed would tell you the coin landed tails.
Yep. Get two thousand volunteers. Order them randomly from #1 to #2,000. House #1 thru #1,0000 in the HEADS wing of your lab, and #1,001 thru #2,000 in the TAILS wing. Then flip your fair a coin.If that seems like a tendentious interpretation, consider what happens as you increase the number of tails interviews: whatever the ratio, that's your odds it was tails. Do a thousand tails interviews, and it's a near certainty -- according to thirders -- that a fair coin lands tails.
I toss fair coin twice. I ask for your credence that the first toss landed heads only on {HH, TH, TT}.
My question is this: do you think this is equivalent to SB? And why or why not? — Srap Tasmaner
Sorry, I'm not getting your experiment, or its equivalence to SB. — Srap Tasmaner
Here's a variation of the experiment. Suppose that for Tuesday and Heads Beauty is also awakened and interviewed. At every interview she is informed whether or not it is a Tuesday and Heads interview. She knows these rules prior to the experiment. Naturally if she is informed that it is Tuesday and Heads at the interview, she can conclude with certainty that she is in a state associated with heads.
However if Beauty is told that it is not Tuesday and Heads at her interview, should she condition on that information or not? — Andrew M
Mon Tue H 1/3 1/3 T 1/6 1/6
Mon Tue H 1/2 T 1/4 1/4
H T H 2 -1 T -2 1
In terms of your M&M example, if two people guess tails and they are correct, they both get an M&M. To reflect Sleeping Beauty, the experiment is set up such that only one person gets to guess when the outcome is heads. If the person conditions on the fact that they are getting to guess at all, then they will know that they are more likely to be in the tails track. — Andrew M
No, it isn't.Probability is about expectations.
That is not what the condition is. It is {AWAKE}, which is can also be written as ~{HEADS&Tuesday} or {HEADS&Monday,TAILS&Monday,TAILS&Tuesday}.it sure does look like the design of the experiment involves conditioning heads on ~Tuesday,
"Random" is not a property of what you are looking at in an experiment. It is a property of what you know about it, but can't see. Either because the experiment hasn't happened yet, or it has but you can't see what happened.One thing I'm generally uncertain about is how strongly to lean on "what day today is" being random.
Still some things to puzzle through, but I'm convinced. My sojourn in the land of halferism is at its end. — Srap Tasmaner
I do still disagree about how to interpret this thing though. The failure rate of my tails-guessing Beauties is still 1/2, no matter how much they pat themselves on the back. The argument you give here totally justifies conditioning on being interviewed, so the epistemic issue isn't there; it's in this conflict between the two ways of measuring success. — Srap Tasmaner
If you take a step back, SB looks a bit like a fucked up way of doing two trials of a single experiment. (No worries about the single coin flip -- the trial is asking different subjects for their credence.) But whichever way you split, by toss outcome or by day, it's not two trials: it's one trial each for two different experiments and which experiment is being run is determined by the coin toss, and is thus the source of Beauty's uncertainty. — Srap Tasmaner
Welcome back! — Andrew M
But she isn't asked for her confidence in that situation, so this argument is a red herring. A very appealing red herring, as you go on to describe, but irrelevant nonetheless.In standard SB, on (H & Tue) our Beauty receives no information at all. — Srap Tasmaner
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