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All of Lotaria's Comments + Replies

Beauty and the Bets
Lotaria10

I'm glad that someone engages with non-Lewisian halfism but this is clearly wrong on a very basic level. To understand why, let's consider a simpler problem:

Two coins are tossed. Then you are told state of one of the coins, but you don't know whether it's the first coin or the second. Then you are told whether it was the first coin or the second. What should be your credence that the state of both coins are the same 1. before you were told the state of one of the coins? 2. after you were told the state of one of the coins? 3. after you were told which coin

... (read more)
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1Ape in the coat
What if no one is answering your questions? You are just shown one coin with no insight about the algorithm according to which the experimenter showed you it, other that this is the outcome of the coin toss. There is actually the least presumptious way to reason about such things. And this is the one I described. But nevermind that. Let's not go on an unnecessary tangent about this problem. For the sake of the argument I'm happy to concede that both 1/2 and 1/3 are reasonable answers to it. However Conitzer's reasoning would imply that only 1/2 is the correct answer. As a matter of fact he simply assumes that 1/2 has to be correct, refusing to entertain the idea that it's not the case. Not unlike Briggs in Technicolor. If she just flipped the coin then the answer is 1/2. If she observed the event "the coin is Tails" then the answer is 1/3. If she observed the event "the coin is Heads" the answer is 1/3. But doesn't she always observes one of these events in every iteration of the experiment? No, she doesn't. This is the same situation as with Technicolor Sleeping Beauty. She observes the event "Blue" instead of "Blue or Red" only when she's configured her event space in a specific way, by precommited to this outcome in particular. Likewise here. When the Beauty precommited to Tails, flips the coin and sees that the coin is indeed Tails she has observed the event "the coin is Tails", when she did no precommitments or the coin turned out to be the other side - she observed the event "the coin is Heads or Tails". Of course something has gone wrong. This is what you get when you add amnesia to probability theory problems - it messes the event space in a counterintuitive way. By default you are able only to observe the most general events which have probability one. Like "I'm awake at least once in the experiment" or "the room is either Blue or Red at least once in the experiment". To observe more specific events you need precommitments. To see that this actually wo
Beauty and the Bets
Lotaria10

In one of your previous posts you said that 'What Beauty actually learns is that "she is awoken at least once"' and in this post you say "Therefore, if the Beauty can potentially observe a rare event at every awakening, for instance, a specific combination , when she observes it, she can construct the Approximate Frequency Argument and update in favor of Tails."

I think this is a mistake, because when you experience Y during Sleeping Beauty, it is not the same thing as learning that "Y at least once." See this example: https://users.cs.duke.edu/~conit... (read more)

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1Ape in the coat
It's not that she observed "C today" but it doesn't allow her to update any probabilities because "reasons". The core point of the previous post is that she didn't observe "C today", because "today" is ill-defined for the probability experiment she is participating in. I talk about it in more details in a comment thread starting from here. Pay attention to Markvy's attempts to formally define event "Today is Monday" for the Sleeping Beauty setting and failing to do so, while its easy to do for some other problems like Single Awakening or No-Coin-Toss.  She didn't know the sequence in advance, like, for example, she knew that she is to be awakened on Monday. She made a guess and managed to guess right. The difference is that on a repetition of the probability experiment, she is awakened on Monday in every iteration of it, but the sequence of the tosses is the same as she precommited to only in a smal fraction of all iterations of the experiment. I'm glad that someone engages with non-Lewisian halfism but this is clearly wrong on a very basic level. To understand why, let's consider a simpler problem: Two coins are tossed. Then you are told state of one of the coins, but you don't know whether it's the first coin or the second. Then you are told whether it was the first coin or the second. What should be your credence that the state of both coins are the same 1. before you were told the state of one of the coins? 2. after you were told the state of one of the coins? 3. after you were told which coin was it? 1. You have four equiprobable outcomes: HT, TH, HH, TT So the answer is 1/2 2. Now there are two possibilities. Either you were told "Heads" or you were told "Tails". In first case outcome TT is eliminated, in the second outcome HH is. In any case you end up with only one possible outcome where the states of the coin are the same and two outcomes where they are not. Therefore the answer is 1/3 3. Here we initially had either HT TH TT or HT TH HH as possible
A Simplified Version of Perspective Solution to the Sleeping Beauty Problem
Lotaria10

There is new information in the first scenario, but how does it allow you to update the probability that the coins are different without thinking of today as randomly selected?

Imagine you are woken up every day, but the color of the room may be different. You are asked the probability that the coins are different.

HH: blue blue
HT: blue red
TH: red blue
TT: red red

Now you wake up and see "blue." That is new information. You now know that there is at least one "blue", and you can eliminate TT. 

However, I think everyone would agree that the probability is s... (read more)

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4dadadarren
Sorry for the late reply, didnt check lesswrong for a month. Hope you are still around. After your red/blue example I realized I was answering to rashly and made a mistake. Somehow I was under the impression the experiment just have multiple awakenings without memory wipes. That was silly of me cause then it wont even be an anthropic problem. Yes, you are right. With memory wipes there should be no update. The probability of different toss result should remain at 1/2.
A Simplified Version of Perspective Solution to the Sleeping Beauty Problem
Lotaria50

I find this idea very interesting, especially since it seems to me that it gives different probabilities than most other version of halfing. I wonder if you agree with me about how it would answer this scenario (due to Conitzer):

Two coins are tossed on Sunday. The possibilities are

HH: wake wake
HT: wake sleep
TH: sleep wake
TT: sleep sleep

When you wake up (which is not guaranteed now), what probability should you give that the coins come up differently?

According to most versions of halfing, it would be 2/3. You could say that when you wake up you learn that y... (read more)

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1dadadarren
For the first question, perspective-based reasoning would still give the probability of 2/3 simply because there is no guaranteed awakening in the experiment. So finding myself awake during the experiment is new information even from the first-person perspective, eliminating the possibility of TT. For the second question, the probability remains at 1/2. Due to no new information. For either question "the probability of today being the first day" is not meaningful and has no answer.
Sleeping Beauty Resolved (?) Pt. 2: Identity and Betting
Lotaria10

I'm talking about the method you're using. It looks like when you wake up and experience y you are treating that as equivalent to "I experience y at least once."

This method is generally incorrect, as shown in the example. Waking up and experiencing y is not necessarily equivalent to "I experience y at least once."

If you yourself believe the method is incorrect when y is "flip heads", why should we believe it is correct when y is something else?

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1Radford Neal
After my other response to this, I thought a bit more about the scenario described by Conitzer. A completely non-fantastic version of this would be as follows (somewhat analogous to my Sailor's Child problem, though the whole child bit is not really necessary here): You have two children. At age 10, you tell both of them that their Uncle has flipped two coins, one associated with each child, though the children are told nothing that would let them tell which is "their" coin. When they turn 20, they will each be told how "their" coin landed, in two separate rooms so they will not be able to communicate with each other.. They will then be asked what the probability is that the two coin flips were the same. (The two children correspond to two awakenings of Beauty.) If you are one of these children, and are told that "your" coin landed heads, what should you give for the probability that the two flips are the same? It's obvious that the correct answer is 1/2. But you might argue that their are four equally-likely possibilities for the two flips - HH, HT, TH, and TT - and that observing a head eliminates TT, giving a 1/3 probability that the two flips are the same. This is of course an elementary mistake in probabilistic reasoning, caused by not using the right space of outcomes. Suppose that one of the children is left-handed and one is right-handed. Then there are actually eight equally-likely possibilities - RHH, LHH, RHT, LHT, RTH, LTH, RTT, LTT - where the initial R or L indicates whether the first coin is for the right-handed child or the left-handed child. Suppose you are the right-handed child. Observing heads eliminates LHT, RTH, RTT, and LTT, with the remaining possibilities being RHH, LHH, RHT, and LTH, in half of which the flips are the same. So the answer is now seen to be 1/2. But why is this the right answer to this non-fantastical problem? (I take it that it is correct, and that this is not controversial.) The reason is that we know how probability wo
1Radford Neal
In any not-completely-fantastical scenario, Beauty's experiences on Monday are very unlikely to be repeated exactly on Tuesday, so "experiences y" and "experiences y at least once" are effectively equivalent. Any argument that relies on her sensory input being so restricted that there is a substantial probability of identical experiences on Monday and Tuesday applies only to a fantastical version of the problem. Maybe that's an interesting version of the problem (though maybe instead it's simply an impossible version), but it's not the same as the usual, only-mildly-fantastical version.
Sleeping Beauty Resolved (?) Pt. 2: Identity and Betting
Lotaria10

The question is about what information you actually have.

In the linked example, it may seem that you have precisely the information "there is at least one heads." But if you condition on that you get the wrong answer. The explanation is that, in this type of memory loss situation, waking up and experiencing y is not equivalent to "I experience y at least once." When you wake up and experience y you do know that you must experience y on either monday or tuesday, but your information is not equivalent to that statement.

If you asked on sun... (read more)

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1Radford Neal
Beauty's information isn't "there is at least one head", but rather, "there is a head seen by Beauty on a day when her nose itches, the fly on the wall is crawling upwards, her sock is scrunched up uncomfortably in her left shoe, the sharp end of a feather is sticking out of one of the pillows, a funny tune she played in high school band is running though her head, and so on, and so on.".
Sleeping Beauty Resolved (?) Pt. 2: Identity and Betting
Lotaria10

I'm referring to an example from here: https://users.cs.duke.edu/~conitzer/devastatingPHILSTUD.pdf where you do wake up both days.

Your argument seemed similar, but I may be misunderstanding:

"Treating these and other differences as random, the probability of Beauty having at some time the exact memories and experiences she has after being woken this time is twice as great if the coin lands Tails than if the coin lands Heads, since with Tails there are two chances for these experiences to occur rather than only one."

It sounds like you are ... (read more)

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1Radford Neal
The crucial point is that Beauty's experiences on wakening will not be confined to whatever coin flips may have been added to the experiment, but will also include many other things, such as whether or not her nose itches, and how much the fluorescent light in her room is buzzing. The probability of having a specific set of ALL her experiences is twice as great if she is woken twice (more precisely, approximately twice as great, if this probability is small, as it will be in any not-very-fantastical version of the problem). Arguing that whether or not her nose itches is irrelevant, and so should not be conditioned on, is contrary to the ordinary rules of probability, in which any dispute over whether some information is relevant or not is settled by simply including it, which makes no difference if it is actually irrelevant. Refusing to condition on such information is like someone who's solving a physics problem saying that air resistance can be ignored as negligible, and then continuing to insist that air resistance should be ignored after being shown a calculation demonstrating that including its effects has a substantial effect on the answer.
Sleeping Beauty Resolved (?) Pt. 2: Identity and Betting
Lotaria10

I don't understand the reasoning for using irrelevant information.

If you are saying that there is twice the probability of experiencing y "at least once" on tails, doesn't that fail for the same argument Conitzer gave against halfers? His example was that you wake up both days and flip a coin. If you flip heads, what is the probability that both flips are the same? You are twice as likely to experience heads at least once if the coin tosses are different. But it is irrelevant. The probability of "both the same" is still 1/2.

On the other hand, in reality there might be some relevant information (such as noticeable aging, hunger, etc) but the problem is meant to exclude that.

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1Radford Neal
I don't understand your question. Are you saying that Beauty flips a coin whenever she wakes up? And she then wonders whether the coin she just flipped is the same as another coin she has flipped or will flip? But she may not wake up on Tuesday, in which case there aren't two flips, so I don't understand....