Srap Tasmaner

@"Jeremiah" It's as we were discussing: each marble represents an interview event. To count coin toss outcomes you only need one red marble, but two b...

@"Michael" I think I'm a halfer now. (Still some things I'd like to be clearer on.) @"Andrew M", @"andrewk", @"JeffJo": do you find this argument as c...

Something I don't remember us talking about: should Beauty, knowing the rules of the experiment, subject her expectation of a tails interview to a dis...

This is still slightly puzzling to me. P(H | M1) = 1, right? And this is the thing about the double interview track: both them happen if and only if t...

So what? It's not a situation that arises. Neither she not the experimenters are ever in the position of knowing that the coin landed tails but wonder...

I misunderstood. But you are going to say exactly this about M2 and Tu (or T1 and T2), so the question stands.

When does anyone ever make a random selection from among only the tails interviews?

Continuing: How many times does Beauty expect to be asked for her credence? (1) If I knew it was heads, I'd know I'll be asked once. (2) If I knew it ...

Thanks. I think I finally understand the halfer position. (The one thing I'm not completely clear on is how the Monday interview is retroactively dete...

UNIMPORTANT ASIDE: I think this problem arose out of earlier problems and chitchat about decision-making given imperfect memory. I keep thinking that ...

The double interview is not a single event, for the simple reason that Beauty makes two decisions.

I know what you meant by "{H,T}". I was asking what your point is. You know the math better than I do, so if you have something to say, I'm going to l...

Meaning?

Here's the picture halfers actually use: http://i.imgur.com/0fqxqKd.jpg And I think they use the same sort of weighted expectation I keep posting, onl...

And when I see the word "just" used as it is here, I assume someone is trying to manipulate my intuitions. If ever a coin flip wasn't "just" a coin a ...

The post I referenced had a mistake! ($2 bets below for simplicity, since the coin is fair.) Before I gave the SB payoffs at even money as Bet H T Tos...

Mainly so we'd get to use that word. This is all stuff we've said before -- this comment summarizes the mechanism by which standard thirder wagering p...

Yet another take 1. (More to come.) Ignore the coin toss completely. The intention of the problem is that Beauty cannot know whether this is her first...

I remember reading at least some of Pears's The False Prison years ago and was impressed (v.1 is early LW, v.2 late). He argues for lots of continuity...

The problem with SB is that the outcomes are like a 2:1 biased coin, but the payouts (as @"andrewk" pointed out) are like a 3:1. If we ignore wagering...

Sleeping Beauty is a pretty unusual situation though. Some of us think it merits switching to counting occasions instead of counting classes of occasi...

There's a 50% chance you'll tell me "at all" that it's heads, and same for tails. But there's more than a 50% chance that a random selection from the ...

If that means the "subjective" interpretation of probability, it's just what the question is about. Maybe it ends up showing that "degree of belief" o...

Is it? I think the halfer intuition is that a coin toss is a coin toss -- doesn't matter if you're asked once on heads and twice on tails. But conside...

Done a little more sniffing around, and thirders frequently argue there's information here. Elga doesn't. <shrug> As SB, you are asked for your degree...

Hey look at that. He saw the Wednesday argument and slipped in a defeater!

Huh. Didn't realize my first argument might be a contradiction. I'll slog through the Lewis some more. He also notes that you can't jump straight to i...

I understand Elga's argument. I understand the wagering argument. Do you understand Lewis's argument? I don't. He tries to get you to accept P+(HEADS)...

This no good though. If you know you're wrong 1/3 of the time, your credence is really the 33%.

Oh right. Give the 50% answer you'd give on Monday, because there are more Monday interviews. I remember thinking about that a while ago -- you get to...

Geez, I've been staring at this far too long. The magic 1/6 is right there. We already have \small \cfrac{2}{3} credence that it's Monday, when our cr...

The simplest way to block the Wednesday argument is to change the experiment: they send you on your way immediately after your last interview. It's cl...

When you are first awakened, you are here: \small P(HEADS) = \cfrac{1}{3}(50\%)+\cfrac{1}{3}(0\%)+\cfrac{1}{3}(50\%)\approx 33\% The \small \cfrac{1}{...

That is P(HEADS | you told me it's Monday) = P(HEADS | you asked me) + 1/6 For Elga, that's 1/2 = 1/3 + 1/6 Here's how I got the idea to include Wedne...

No worries. The only reason to throw in awake-but-unasked is to show there's yet another way to carve up Beauty's credence. (And we cannot leave her a...

No that's wrong. We can imagine that on HEADS, we wake up Beauty Tuesday and send her on her way. That's no different from putting her back to sleep a...

It is a possible outcome; she just won't be asked about it. What's more, Wednesday & Heads and Wednesday & Tails are both part of the sample space. In...

Me too.

You scaled by 1/1. That's not the idea. Seriously, read a tutorial and then we can talk about the philosophy. I don't know what else to say.

You really just need to look up conditional probability again.

Dude, if she's not sleeping we wouldn't call the condition "awake". What matters is when she's asked.

What do you think this changes? Or, better still, can we just stick to the problem at hand?

If whether each happens is determined by the toss of a fair coin, they're all equal and 3/6 is right. (If the subspaces had unequal probabilities, you...

3/4. It is possible to have a heads on Tuesday, same as always. It's within the total space, just not the conditional space.

That is not how conditionals work. If it were, there would never be a point to conditional probability. You'd just always use 1, and P(A|B) would just...

I think there are two issues. First, getting conditionalizing on being awake right. It's clearest perhaps to imagine the coin being tossed after the f...

I didn't follow this part of the thread, so sorry for the late reply. Beauty isn't assigning 1/3 from a principle of indifference. (I made the same mi...

There is a 50% chance that Beauty will be interviewed once, and a 50% chance that she will be interviewed twice, determined by the toss of a fair coin...

I think I see why this is happening, even though the odds are 2-1 against heads. The $1 payoff matrix for a fair coin , betting at even money, is just...

Here's a slightly different argument. If, when awakened, Beauty knew it was Monday, she would answer 50%; if she knew it was Tuesday, she would answer...