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Sleep­ing Beauty Paradox

TagLast edit: 15 Mar 2021 20:31 UTC by Yoav Ravid

The Sleeping Beauty Paradox is a question of how anthropics affects probabilities.

Sleeping Beauty volunteers to undergo the following experiment. On Sunday she is given a drug that sends her to sleep. A fair coin is then tossed just once in the course of the experiment to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday, given a second dose of the sleeping drug, and awakened and interviewed again on Tuesday. The experiment then ends on Tuesday, without flipping the coin again. The sleeping drug induces a mild amnesia, so that she cannot remember any previous awakenings during the course of the experiment (if any). During the experiment, she has no access to anything that would give a clue as to the day of the week. However, she knows all the details of the experiment.

Each interview consists of one question, “What is your credence now for the proposition that our coin landed heads?”

One argument says that since Beauty will see the same thing on waking whether the coin came up heads or not, what she sees on waking provides no evidence one way or the other about the coin, and therefore she should stick with the prior probability of one half.

Another argument replies that the two awakenings when the coin comes up tails imply that waking up itself should be considered evidence in favor of tails. Out of all possible situations where Beauty is asked the question, only one out of three has the coin showing heads. Therefore, one third.

A third argument tries to add rigor by considering monetary payoffs. If Beauty’s bets about the coin get paid out once per experiment, she will do best by acting as if the probability is one half. If the bets get paid out once per awakening, acting as if the probability is one third has the best expected value.

External Links

See Also

A Sim­plified Ver­sion of Per­spec­tive Solu­tion to the Sleep­ing Beauty Problem

dadadarren31 Dec 2020 18:27 UTC
5 points
10 comments5 min readLW link
(www.sleepingbeautyproblem.com)

If a tree falls on Sleep­ing Beauty...

ata12 Nov 2010 1:14 UTC
122 points
28 comments8 min readLW link

An­thropic Rea­son­ing and Per­spec­tive-Based Ar­gu­ments

dadadarren1 Sep 2020 12:36 UTC
15 points
59 comments2 min readLW link

Sleep­ing Beauty, Clon­ing Beauty, and Fre­quen­tist Ar­gu­ments In An­thropic Paradoxes

dadadarren9 Nov 2020 23:17 UTC
5 points
11 comments4 min readLW link

Dis­solv­ing Sleep­ing Beauty

Chris_Leong24 Jan 2021 8:10 UTC
9 points
21 comments4 min readLW link

How Many LHC Failures Is Too Many?

Eliezer Yudkowsky20 Sep 2008 21:38 UTC
26 points
139 comments1 min readLW link

“Solv­ing” self­ish­ness for UDT

Stuart_Armstrong27 Oct 2014 17:51 UTC
38 points
50 comments8 min readLW link

Sleep­ing Beauty Re­solved?

ksvanhorn22 May 2018 14:13 UTC
11 points
75 comments10 min readLW link

Sleep­ing Beauty Re­solved (?) Pt. 2: Iden­tity and Betting

ksvanhorn2 Jun 2018 2:43 UTC
7 points
50 comments6 min readLW link

Sleep­ing Beauty Not Resolved

Chris_Leong19 Jun 2018 4:46 UTC
17 points
52 comments8 min readLW link

Sleep­ing Beauty: Is Disagree­ment While Shar­ing All In­for­ma­tion Pos­si­ble in An­thropic Prob­lems?

dadadarren1 Aug 2019 20:10 UTC
6 points
11 comments10 min readLW link

Sleep­ing Beauty gets coun­ter­fac­tu­ally mugged

Stuart_Armstrong26 Mar 2009 11:44 UTC
4 points
34 comments2 min readLW link

Sleep­ing Beauty as a de­ci­sion prob­lem (solved)

Bongo10 Oct 2010 3:15 UTC
7 points
3 comments2 min readLW link

Sleep­ing Beauty Prob­lem Can Be Ex­plained by Per­spec­tive Disagree­ment (II)

Xianda_GAO_duplicate0.532150578239571919 Jul 2017 23:00 UTC
5 points
42 comments4 min readLW link

Sleep­ing Beauty should re­main pure

KatjaGrace9 Jan 2011 17:40 UTC
1 point
0 comments9 min readLW link

Sleep­ing Beauty Prob­lem, An­thropic Prin­ci­ple and Per­spec­tive Reasoning

dadadarren9 Mar 2019 15:21 UTC
2 points
22 comments8 min readLW link

Sleep­ing Beauty Prob­lem Can Be Ex­plained by Per­spec­tive Disagree­ment (I)

Xianda_GAO_duplicate0.532150578239571919 Jul 2017 22:11 UTC
1 point
0 comments6 min readLW link

Sleep­ing Beauty Prob­lem Can Be Ex­plained by Per­spec­tive Disagree­ment (IV)

Xianda_GAO_duplicate0.532150578239571926 Jul 2017 1:01 UTC
1 point
7 comments5 min readLW link

Sleep­ing Beauty Prob­lem Can Be Ex­plained by Per­spec­tive Disagree­ment (III)

Xianda_GAO_duplicate0.532150578239571922 Jul 2017 14:50 UTC
0 points
0 comments2 min readLW link

The Sleep­ing Beauty Prob­lem and The Dooms­day Ar­gu­ment Can Be Ex­plained by Per­spec­tive In­con­sis­tency

dadadarren5 Aug 2018 13:45 UTC
2 points
27 comments1 min readLW link
(www.sleepingbeautyproblem.com)

Iter­ated Sleep­ing Beauty and Copied Minds

lucidfox21 Dec 2010 7:21 UTC
3 points
34 comments4 min readLW link

The Sleep­ing Beauty prob­lem and trans­for­ma­tion invariances

aspera23 Aug 2015 20:57 UTC
2 points
7 comments1 min readLW link

The Ul­ti­mate Sleep­ing Beauty Problem

Scott Garrabrant30 Sep 2013 0:48 UTC
9 points
39 comments1 min readLW link

Meetup : MIRIx: Sleep­ing Beauty dis­cus­sion

agilecaveman23 Dec 2015 4:29 UTC
2 points
0 comments1 min readLW link

Monty Hall Sleep­ing Beauty

PhilGoetz18 Sep 2015 21:18 UTC
3 points
18 comments1 min readLW link

Re­peated (and im­proved) Sleep­ing Beauty problem

Linda Linsefors10 Jul 2018 22:32 UTC
12 points
5 comments2 min readLW link

More mar­bles and Sleep­ing Beauty

Manfred23 Nov 2014 2:00 UTC
7 points
4 comments3 min readLW link

Vari­a­tions on the Sleep­ing Beauty

casebash10 Jan 2016 13:00 UTC
0 points
6 comments2 min readLW link

An­thropic de­ci­sion the­ory I: Sleep­ing beauty and selflessness

Stuart_Armstrong1 Nov 2011 11:41 UTC
20 points
34 comments2 min readLW link

Per­spec­tive Rea­son­ing and the Sleep­ing Beauty Problem

dadadarren22 Nov 2018 11:55 UTC
4 points
10 comments2 min readLW link

The fair­ness of the Sleep­ing Beauty

MrMind7 Jul 2015 8:25 UTC
2 points
2 comments3 min readLW link

An­thropic De­ci­sion The­ory III: Solv­ing Selfless and To­tal Utili­tar­ian Sleep­ing Beauty

Stuart_Armstrong3 Nov 2011 10:04 UTC
6 points
3 comments3 min readLW link

An­thropic De­ci­sion The­ory IV: Solv­ing Selfish and Aver­age-Utili­tar­ian Sleep­ing Beauty

Stuart_Armstrong4 Nov 2011 10:55 UTC
2 points
24 comments4 min readLW link

Prob­a­bil­ity is a model, fre­quency is an ob­ser­va­tion: Why both halfers and thirders are cor­rect in the Sleep­ing Beauty prob­lem.

shminux12 Jul 2018 6:52 UTC
24 points
34 comments2 min readLW link

Beauty quips, “I’d shut up and mul­ti­ply!”

neq17 May 2010 14:34 UTC
14 points
358 comments6 min readLW link

Prob­a­bil­ity is fake, fre­quency is real

Linda Linsefors10 Jul 2018 22:32 UTC
12 points
7 comments1 min readLW link

The Beauty and the Prince

Chris_Leong26 Jun 2018 13:10 UTC
8 points
40 comments2 min readLW link

Sleep­ing anti-beauty and the pre­sump­tu­ous philosopher

Stuart_Armstrong17 Feb 2011 14:59 UTC
6 points
12 comments1 min readLW link

Sleep­ing Ju­lia: Em­piri­cal sup­port for thirder ar­gu­ment in the Sleep­ing Beauty Problem

Alex V3 Nov 2020 0:21 UTC
4 points
13 comments2 min readLW link

[Question] A short talk on SB and friends

Jon Zero29 Nov 2020 21:07 UTC
10 points
0 comments1 min readLW link

Out-of-body rea­son­ing (OOBR)

Jon Zero9 Jan 2021 16:10 UTC
4 points
0 comments4 min readLW link

Agree­ment on anthropics

KatjaGrace10 Mar 2011 4:38 UTC
4 points
1 comment2 min readLW link
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