PHILOSOPHY - Epistemology: The Sleeping Beauty Problem [HD]

In this video, Michael Campbell introduces the Sleeping Beauty problem. This is a problem in formal epistemology about how to correctly assign probabilities to an odd scenario in which we flip a coin and, depending on the outcome, wake Sleeping Beauty up according to two different patterns. We’ll discover some very strange consequences for our beliefs as a result.

Help us caption & translate this video!

[julianhill-boxedpixels]

I wonder how many people have watched this after playing Zero Time Dilemma ?

[Cyberlisk]

How to explain conditional probability without mentioning the term once. xD

[SteveThePster]

People need to stop talking about theories and arguments, relating to this problem. The answer is 1/2.

[FailedNuance]

The problem with figuring out which probability is the right answer to the question is that the answer changes depending on what the question is concerned with.
Q1: "What is the probability that the coin came up heads?"
A1: 1/2
Q2: "What is the probability that you are awake now because of a heads result?"
A2: 1/3
Q3: "What is the probability that you are awake now because of a tails result?"
A3: 2/3
If the question is only concerned with the coin and the coin alone, then it doesn't matter how many times one is woken up as a result.

[robertbereza]

I think that some people have touched on this slightly, but I feel inclined to write it nonetheless:
Why one way of reasoning results in 1/2 and another in 1/3 is because they answer different questions. One question is "What is the probability that the coin landed heads during the experiment" which quite clearly is 1/2, while the other question is "What is the probability you have been woken up when the coin has landed heads?" which in turn is 1/3.

[marcello]

I'm here because of hear it from "Zero Escape : Zero Time Dilemma" game

[simonmay]

Here’s an observation I’ve made before. The intended focus of the problem is: if the coin lands Heads she’s woken once (Monday); if Tails she’s woken twice (Monday and Tuesday) with amnesia in between. Beauty is meant to consider three indistinguishable awakenings – Heads/Monday, Tails/Monday and Tails/Tuesday. Her last memory is Sunday in all of these.

It matters how many times she’s given the amnesia drug in each coin outcome. In most versions of the problem, Beauty is only given the amnesia drug if the coin landed Tails, administered after the Monday awakening, not after the Tuesday one. In that scenario, with her last memory being Sunday, there would indeed be three possible awakenings for Thirders and Halfers to dispute. Either it’s 1/3 heads and 2/3 Tails or it’s 1/2 for either – depending on which position you take.

However, in the problem stated here, Beauty is given the amnesia drug after every awakening regardless of Heads or Tails. Does this matter? Yes, because she wakes up on Wednesday with the same memory loss as the other awakenings. Therefore, before Wednesday is verbally ruled out, there are five possible awakenings: Heads/Monday, Heads/Wednesday, Tails/Monday, Tails/Tuesday and Tails/Wednesday. It’s therefore relevant to ask what her answers are before and after Beauty is told whether it’s Wednesday.



If she’s a traditional ‘Thirder’ she would first say its 2/5 the coin landed Heads and 3/5 Tails; following Bayes, she would update these to 1/3 and 2/3 if told it’s not Wednesday. As a a ‘Halfer’, her first answer would be 1/2 for Heads or Tails; following Bayes, she would update to 3/7 Heads and 4/7 Tails if told it’s not Wednesday.


If subsequently told it’s Monday (Tuesday and Wednesday eliminated), what is her new credence? If she previously updated from 2/5 to 1/3 for Heads, she must update again to 1/2. If she previously updated from 1/2 to 3/7 for Heads, she must update to 3/5 for Heads and 2/5 for Tails.

I’ve not declared a Halfer or Thirder position here but I hope my observation about the exact number of amnesia doses on each outcome makes sense.

[pk]

Many of these so called 'problems' suffer from not being defined precisely

[simonmay]

This video is at significant variance with the original problem - as debated by Lewis and Elga. Stated correctly, the original protocol is as follows: if the coin lands heads, beauty will be woken on Monday, interviewed and sent home; if the coin lands tails, beauty will be woken on Monday, interviewed, put back to sleep, have her memory erased of the last awakening, woken up on Tuesday, interviewed and sent home. This gives us the traditional 1/2 vs 1/3 arguments of Lewis and Elga - based on the protocol of Heads = one awakening with no memory loss, Tails = two awakenings with one memory loss. 

Some statements of the problem have her being put to sleep again and woken on Wednesday.However the problem is essentially unchanged so long as only one potential memory loss can occur - between Monday and Tuesday (if the coin landed tails).

The video above, for both heads and tails, adds a further memory loss before a Wednesday awakening. This potentially changes the answer. For this version, if beauty awakes and is informed it's not yet Wednesday, the Lewis and Elga probabilities for heads will update to 3/7 vs 1/3 respectively. Before Wednesday is ruled out, their estimates will be 1/2 vs 2/5.

[jsteiger]

Goddammit, the answer is 1/2.  Anything else is over thinking the problem.  Oh, and BTW, the dress is blue and black.

[Zrostar]

Sleeping Beauty is aware of inescapable truth of the coin having only 2 sides. The probability of the coin being heads is always 1/2. What happened and what is possible are joined in an unnatural way while you're describing this problem.
They aren't the same thing at all. One is prescriptive and one is descriptive. Despite what the outcome could have been (prescriptive), Sleeping Beauty is being asked to make a statement about the past (descriptive). The only possible pasts that could exist are one where the coin landed heads and one where the coin landed tails.

[SpionCTFT]

This is a conditional probability question. What is the chance the coin landed on heads, given that you have been woken.
P(A|B)=P(AandB)/P(B) In case you did not know. (That's Probability of A given B)
B=You are woken therefore P(B)=3/4
A=Coin lands heads and P(AandB)=1/4
QED

That's not odd, because she learns that it is not (Tuesday and the coin came up heads). More than enought information to change the conditional probability.

[Noonycurt]

The probability of heads is always 1/2. It does not matter how many times they wake her up, or if they tell her it's Monday.

You don't have to add up the probabilities to 1, since the cases don't exclude each other.

[Pining_for_the_fjords]

Imagine a lottery where the number of winners is decided by a coin toss. If it's heads, only one person will win, but if it's tails then there will be more than one winner. It doesn't matter how many. Assuming the probability of heads or tails is 50/50, there will be more overall winners from a tails draw than from a heads draw. If you ask a random winner if they think that heads or tails was drawn on the day they won, the most likely answer would be tails.

You can adapt this to the sleeping beauty problem by having two sleeping beauties. Tell them that if the coin flips heads, one of the girls will be chosen at random to be woken, but if it's tails, they will both be woken. The coin is still 50/50, but when one of them wakes up, the chance that she is one of the two to be woken on a tails flip is double the chance that she wakes up alone on the heads flip.

[Copeharder_]

Can you state the problem again without moving through these slides? So disturbing

[jonkeuviuhc]

Let's just say that we ask Sleeping beauty what does she think the result of the coin flip, and she gives the same answer always. And we do this for so many times that any anomalies are balaced out.

1. We ask her every time we wake her up, and she says heads: She's wrigth 1 out of 3 times.

2. We ask her every time and she says tails: She's wright 2 out of 3 times.

3. We ask her only on wednesdays: She's wright one half of the time.

[rtothec]

Bad idea watching this before going to sleep.

[SmileyEmoji]

Change to "guess whether the coin was heads or tails. If you guess H and are correct you win $1 at the end of the experiment and if you guess tails and are correct you win $0.99 at the end of the experiment (total NOT per awakening). Run a simulation 10000 times and it should be clear that guessing H will win you more so it cannot be correct that the probability of H is less than 1/3 as 1/3*1 < 2/3*0.99

[Make_Boxing_Great_Again]

*Consider another experiment:*

A coin is flipped and if it is Heads you are directed draw a marble from bag A that contains 5 White marbles and 5 Black marbles. If it is Tails you are to draw a marble from bag B that contains 9 Black marbles and 1 White marble.

The experiment is run: The coin is flipped and the result of the coin flip is concealed from you. You are presented with a bag and directed to draw a marble from it. You know that the bag presented to you is either Bag A or Bag B but since the result of the coin flip was concealed from you, you are unsure which bag you are drawing from.

After running the experiment you ended up with a Black marble. What is the probability that Heads was the result of the initial coin flip?

*Discuss.*

[-h-work-week]

Confusing... because the approach is flawed in so many ways. Its 1/2 in all scenarios.