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Sleep­ing Beauty Paradox

TagLast edit: 16 Apr 2024 14:02 UTC by Radford Neal

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, some argue that she will do best by acting as if the probability is one half (while others argue that probability one third gives the correct result if decision theory is correctly applied). If instead the bets get paid out once per awakening, one can again argue about whether or not acting as if the probability is one third has the best expected value.

External Links

See Also

If a tree falls on Sleep­ing Beauty...

ata12 Nov 2010 1:14 UTC
147 points
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Agree­ment on anthropics

KatjaGrace10 Mar 2011 4:38 UTC
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The First-Per­son Per­spec­tive Is Not A Ran­dom Sample

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Full Non-In­dex­i­cal Con­di­tion­ing Also As­sumes A Self Sam­pling Pro­cess.

dadadarren12 Feb 2022 1:46 UTC
17 points
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A Sim­plified Ver­sion of Per­spec­tive Solu­tion to the Sleep­ing Beauty Problem

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

Are co­in­ci­dences clues about missed dis­asters? It de­pends on your an­swer to the Sleep­ing Beauty Prob­lem.

Harlan5 Jul 2021 19:12 UTC
32 points
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Sleep­ing Beauty, Clon­ing Beauty, and Fre­quen­tist Ar­gu­ments In An­thropic Paradoxes

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The Val­idity of Self-Lo­cat­ing Probabilities

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Ab­sent-Minded Driver and Self-Lo­cat­ing Probabilities

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12 points
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Dis­solv­ing Sleep­ing Beauty

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

An­thropic Para­doxes and Self Refer­ence

dadadarren6 Jun 2021 2:52 UTC
6 points
2 comments2 min readLW link

An­thropic Rea­son­ing and Per­spec­tive-Based Ar­gu­ments

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

An­throp­ics and Embed­ded Agency

dadadarren26 Jun 2021 1:45 UTC
7 points
2 comments2 min readLW link

Top YouTube chan­nel Ver­i­ta­sium re­leases video on Sleep­ing Beauty Problem

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25 points
22 comments1 min readLW link
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56 comments6 min readLW link

Some Var­i­ants of Sleep­ing Beauty

SMK and EOC
1 Mar 2023 16:51 UTC
34 points
10 comments8 min readLW link

The Benev­olent Billion­aire (a pla­gia­rized prob­lem)

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8 points
11 comments4 min readLW link

The Closed Eyes Ar­gu­ment For Third­ing

omnizoid31 Mar 2024 22:11 UTC
1 point
22 comments4 min readLW link

Why Two Valid An­swers Ap­proach is not Enough for Sleep­ing Beauty

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6 points
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[Question] Has any­one ac­tu­ally changed their mind re­gard­ing Sleep­ing Beauty prob­lem?

Ape in the coat30 Jan 2024 8:34 UTC
14 points
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Sub­jec­tive Ques­tions Re­quire Sub­jec­tive information

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[Question] Change My Mind: Thirders in “Sleep­ing Beauty” are Just Do­ing Episte­mol­ogy Wrong

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67 comments6 min readLW link

Beauty and the Bets

Ape in the coat27 Mar 2024 6:17 UTC
7 points
31 comments12 min readLW link

[Question] Is Adam Elga’s proof for thirdism in Sleep­ing Beauty still con­sid­ered to be sound?

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How Many LHC Failures Is Too Many?

Eliezer Yudkowsky20 Sep 2008 21:38 UTC
36 points
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Les­sons from Failed At­tempts to Model Sleep­ing Beauty Problem

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16 comments14 min readLW link

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

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

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

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

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Shmi12 Jul 2018 6:52 UTC
26 points
34 comments2 min readLW link

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

neq17 May 2010 14:34 UTC
17 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
8 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

Con­ser­va­tion of Ex­pected Ev­i­dence and Ran­dom Sam­pling in Anthropics

Ape in the coat3 Sep 2023 6:55 UTC
9 points
9 comments7 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
5 points
0 comments4 min readLW link

“Who I am” is an ax­iom.

dadadarren25 Apr 2021 21:59 UTC
7 points
8 comments1 min readLW link

An­throp­ics: differ­ent prob­a­bil­ities, differ­ent questions

Stuart_Armstrong6 May 2021 13:14 UTC
25 points
10 comments15 min readLW link

An­thropic de­ci­sion the­ory for self-lo­cat­ing beliefs

Stuart_Armstrong12 Jul 2021 14:11 UTC
17 points
2 comments1 min readLW link

The Val­idity of Self-Lo­cat­ing Prob­a­bil­ities (Pt. 2)

dadadarren25 Aug 2021 1:53 UTC
6 points
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46 points
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Bet­ter and Worse Ways of Stat­ing SIA

dadadarren28 Oct 2021 16:04 UTC
4 points
0 comments3 min readLW link

You Don’t Need An­throp­ics To Do Science

dadadarren7 Nov 2021 15:07 UTC
6 points
4 comments2 min readLW link
(www.sleepingbeautyproblem.com)

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0naut20 Feb 2022 8:03 UTC
8 points
9 comments3 min readLW link

Prim­i­tive Per­spec­tives and Sleep­ing Beauty

dadadarren26 Mar 2022 1:55 UTC
21 points
14 comments6 min readLW link

The fair­ness of the Sleep­ing Beauty

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

The Solu­tion to Sleep­ing Beauty

Ape in the coat4 Mar 2024 6:46 UTC
8 points
77 comments13 min readLW link

An­trop­i­cal Prob­a­bil­ities Are Fully Ex­plained by Differ­ence in Pos­si­ble Outcomes

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19 points
7 comments5 min readLW link

Sleep­ing Beauty – the Death Hypothesis

Guillaume Charrier5 May 2023 23:32 UTC
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8 comments5 min readLW link

“Solv­ing” self­ish­ness for UDT

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39 points
52 comments8 min readLW link

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Sleep­ing Beauty Not Resolved

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18 points
53 comments8 min readLW link

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

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3 comments2 min readLW link

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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
5 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

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dadadarren5 Aug 2018 13:45 UTC
5 points
24 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
6 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
22 points
34 comments2 min readLW link

Per­spec­tive Rea­son­ing and the Sleep­ing Beauty Problem

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