New­comb’s Problem

TagLast edit: 2 Feb 2022 16:03 UTC by Heighn

Newcomb’s Problem is a thought experiment in decision theory exploring problems posed by having other agents in the environment who can predict your actions.

The Problem

From Newcomb’s Problem and Regret of Rationality:

A superintelligence from another galaxy, whom we shall call Omega, comes to Earth and sets about playing a strange little game. In this game, Omega selects a human being, sets down two boxes in front of them, and flies away.

Box A is transparent and contains a thousand dollars.
Box B is opaque, and contains either a million dollars, or nothing.

You can take both boxes, or take only box B.

And the twist is that Omega has put a million dollars in box B iff Omega has predicted that you will take only box B.

Omega has been correct on each of 100 observed occasions so far—everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars. (We assume that box A vanishes in a puff of smoke if you take only box B; no one else can take box A afterward.)

Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full.

Omega drops two boxes on the ground in front of you and flies off.

Do you take both boxes, or only box B?

One line of reasoning about the problem says that because Omega has already left, the boxes are set and you can’t change them. And if you look at the payoff matrix, you’ll see that whatever decision Omega has already made, you get $1000 more for taking both boxes. This makes taking two boxes (“two-boxing”) a dominant strategy and therefore the correct choice. Agents who reason this way do not make very much money playing this game. This is because this line of reasoning ignores the connection between the agent and Omega’s prediction: two-boxing only makes $1000 more than one-boxing if Omega’s prediction is the same in both cases, while the problem states Omega is extremely accurate in its predictions. Switching from one-boxing to two-boxing doesn’t give the agent a $1000 more, it results in a loss of $999,000.

Because the agent’s decision in this problem can’t causally affect Omega’s prediction (which happened in the past), Causal Decision Theory two-boxes. One-boxing is correlated with getting a million dollars, whereas two-boxing is correlated with getting only $1000; therefore, Evidential Decision Theory one-boxes. Functional Decision Theory (FDT) also one-boxes, but for a completely different reason: FDT reasons that Omega must have had a model of the agent’s decision procedure in order to make the prediction. Therefore, your decision procedure is run not only by you, but also (in the past) by Omega; whatever you decide, Omega’s model must have decided the same. Either both you and Omega’s model two-box, or both you and Omega’s model one-box; of these two options, the latter is preferable, so FDT one-boxes.

The general class of decision problems that involve other agents predicting your actions are called Newcomblike Problems.

Irrelevance of Omega’s Physical Impossibility

Sometimes people dismiss Newcomb’s problem because of the physical impossibility of a being like Omega. However, Newcomb’s problem does not actually depend on the possibility of Omega in order to be relevant. Similar issues arise if we imagine a skilled human psychologist who can predict other people’s actions with 65% accuracy.

Notable Posts

See Also

New­comb’s Prob­lem and Re­gret of Rationality

Eliezer Yudkowsky31 Jan 2008 19:36 UTC
144 points
616 comments10 min readLW link

New­comblike prob­lems are the norm

So8res24 Sep 2014 18:41 UTC
83 points
111 comments8 min readLW link

The Ul­ti­mate New­comb’s Problem

Eliezer Yudkowsky10 Sep 2013 2:03 UTC
46 points
116 comments1 min readLW link

New­comb’s prob­lem hap­pened to me

Academian26 Mar 2010 18:31 UTC
51 points
99 comments3 min readLW link

New­comb’s Prob­lem vs. One-Shot Pri­soner’s Dilemma

Wei Dai7 Apr 2009 5:32 UTC
14 points
16 comments1 min readLW link

Two-box­ing, smok­ing and chew­ing gum in Med­i­cal New­comb problems

Caspar Oesterheld29 Jun 2015 10:35 UTC
29 points
93 comments1 min readLW link

New­comb’s Prob­lem as an Iter­ated Pri­soner’s Dilemma

Jerdle5 Jan 2022 22:48 UTC
13 points
11 comments1 min readLW link

New­comb Variant

lsusr29 Aug 2023 7:02 UTC
25 points
22 comments1 min readLW link

You May Already Be A Sinner

Scott Alexander9 Mar 2009 23:18 UTC
50 points
37 comments3 min readLW link

Con­fu­sion about New­comb is con­fu­sion about counterfactuals

AnnaSalamon25 Aug 2009 20:01 UTC
54 points
42 comments2 min readLW link

Coun­ter­fac­tual Mugging

Vladimir_Nesov19 Mar 2009 6:08 UTC
80 points
296 comments2 min readLW link

AXRP Epi­sode 5 - In­fra-Bayesi­anism with Vanessa Kosoy

DanielFilan10 Mar 2021 4:30 UTC
35 points
12 comments36 min readLW link

Why 1-box­ing doesn’t im­ply back­wards causation

Chris_Leong25 Mar 2021 2:32 UTC
7 points
14 comments4 min readLW link

Meta De­ci­sion The­ory and New­comb’s Problem

wdmacaskill5 Mar 2013 1:29 UTC
10 points
12 comments2 min readLW link

FDT defects in a re­al­is­tic Twin Pri­son­ers’ Dilemma

Sylvester Kollin15 Sep 2022 8:55 UTC
37 points
1 comment26 min readLW link

“Ra­tional Agents Win”

Isaac King23 Sep 2021 7:59 UTC
8 points
33 comments2 min readLW link

Null-box­ing New­comb’s Problem

Yitz13 Jul 2020 16:32 UTC
33 points
9 comments4 min readLW link

Re­jected Early Drafts of New­comb’s Problem

zahmahkibo6 Sep 2022 19:04 UTC
112 points
5 comments3 min readLW link

A full ex­pla­na­tion to New­comb’s para­dox.

solomon alon12 Oct 2020 16:48 UTC
−6 points
12 comments3 min readLW link

Thoughts from a Two Boxer

jaek23 Aug 2019 0:24 UTC
18 points
11 comments5 min readLW link

New­comb’s Prob­lem stan­dard positions

Eliezer Yudkowsky6 Apr 2009 17:05 UTC
7 points
22 comments1 min readLW link

[Question] Is Agent Si­mu­lates Pre­dic­tor a “fair” prob­lem?

Chris_Leong24 Jan 2019 13:18 UTC
22 points
19 comments1 min readLW link

The Dick Kick’em Paradox

Augs SMSHacks23 Sep 2023 22:22 UTC
−5 points
21 comments1 min readLW link

Ra­tion­al­ists lose when oth­ers choose

PhilGoetz16 Jun 2009 17:50 UTC
−8 points
58 comments5 min readLW link

The dumb­est kid in the world (joke)

CronoDAS6 Jun 2021 2:57 UTC
23 points
9 comments1 min readLW link

Con­di­tional offers and low pri­ors: the prob­lem with 1-box­ing New­comb’s dilemma

Andrew Vlahos18 Jun 2021 21:50 UTC
2 points
4 comments1 min readLW link

Should VS Would and New­comb’s Paradox

dadadarren3 Jul 2021 23:45 UTC
5 points
36 comments2 min readLW link

Why do the­ists, un­der­grads, and Less Wrongers fa­vor one-box­ing on New­comb?

CarlShulman19 Jun 2013 1:55 UTC
27 points
300 comments2 min readLW link

Omega can be re­placed by amnesia

Bongo26 Jan 2011 12:31 UTC
23 points
44 comments1 min readLW link

Real-world New­comb-like Prob­lems

SilasBarta25 Mar 2011 20:44 UTC
25 points
35 comments2 min readLW link

Nate Soares on the Ul­ti­mate New­comb’s Problem

Rob Bensinger31 Oct 2021 19:42 UTC
57 points
20 comments1 min readLW link

Anti-Parfit’s Hitchhiker

k644 Feb 2022 23:37 UTC
2 points
3 comments1 min readLW link

Cri­tiquing Scasper’s Defi­ni­tion of Sub­junc­tive Dependence

Heighn10 Jan 2022 16:22 UTC
6 points
8 comments2 min readLW link

New­comb’s Lot­tery Problem

Heighn27 Jan 2022 16:28 UTC
1 point
9 comments1 min readLW link

[Question] New­comb’s Grandfather

Yair Halberstadt28 Jan 2022 8:56 UTC
5 points
29 comments1 min readLW link

The Calcu­lus of New­comb’s Problem

Heighn1 Apr 2022 14:41 UTC
3 points
5 comments2 min readLW link

[Question] What does Func­tional De­ci­sion The­ory say to do in im­perfect New­comb situ­a­tions?

Daniel_Eth7 May 2022 22:26 UTC
4 points
4 comments1 min readLW link

[Question] Are ya win­ning, son?

Nathan11239 Aug 2022 0:06 UTC
14 points
13 comments2 min readLW link

Break­ing New­comb’s Prob­lem with Non-Halt­ing states

Slimepriestess4 Sep 2022 4:01 UTC
18 points
9 comments5 min readLW link

Two New New­comb Variants

eva_14 Nov 2022 14:01 UTC
26 points
22 comments3 min readLW link

Why one-box?

PhilosophyStudent30 Jun 2013 2:38 UTC
11 points
98 comments3 min readLW link

Some Var­i­ants of Sleep­ing Beauty

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

New­comb’s para­dox com­plete solu­tion.

Augs SMSHacks15 Mar 2023 17:56 UTC
−12 points
13 comments3 min readLW link

Ex­tract­ing Money from Causal De­ci­sion Theorists

Caspar Oesterheld28 Jan 2021 17:58 UTC
26 points
31 comments1 min readLW link

The law of effect, ran­dom­iza­tion and New­comb’s problem

Caspar Oesterheld15 Feb 2018 15:31 UTC
7 points
1 comment1 min readLW link

A sur­vey of polls on New­comb’s problem

Caspar Oesterheld20 Sep 2017 16:50 UTC
3 points
8 comments1 min readLW link

A New Re­sponse To New­comb’s Paradox

Daniel Birnbaum15 Apr 2024 20:38 UTC
0 points
5 comments1 min readLW link

The Bind­ing of Isaac & Trans­par­ent New­comb’s Prob­lem

suvjectibity22 Feb 2024 18:56 UTC
−11 points
0 comments10 min readLW link

Re­peated Play of Im­perfect New­comb’s Para­dox in In­fra-Bayesian Physicalism

Sven Nilsen3 Apr 2023 10:06 UTC
2 points
0 comments2 min readLW link

A few mis­con­cep­tions sur­round­ing Roko’s basilisk

Rob Bensinger5 Oct 2015 21:23 UTC
90 points
135 comments5 min readLW link

Self-con­firm­ing pre­dic­tions can be ar­bi­trar­ily bad

Stuart_Armstrong3 May 2019 11:34 UTC
49 points
11 comments5 min readLW link

You’re in New­comb’s Box

HonoreDB5 Feb 2011 20:46 UTC
59 points
176 comments4 min readLW link

A model of UDT with a halt­ing oracle

cousin_it18 Dec 2011 14:18 UTC
68 points
102 comments2 min readLW link

Parfit’s Es­cape (Filk)

Gordon Seidoh Worley29 Mar 2019 2:31 UTC
39 points
0 comments1 min readLW link

Oper­a­tional­iz­ing New­comb’s Problem

ErickBall11 Nov 2019 22:52 UTC
34 points
23 comments1 min readLW link

Ex­ploit­ing New­comb’s Game Show

carterallen25 May 2023 4:01 UTC
8 points
2 comments2 min readLW link

The Pre­dic­tion Prob­lem: A Var­i­ant on New­comb’s

Chris_Leong4 Jul 2018 7:40 UTC
25 points
11 comments9 min readLW link

Coun­ter­fac­tu­als: Smok­ing Le­sion vs. New­comb’s

Chris_Leong8 Dec 2019 21:02 UTC
9 points
24 comments3 min readLW link

Ex­tremely Coun­ter­fac­tual Mug­ging or: the gist of Trans­par­ent Newcomb

Bongo9 Feb 2011 15:20 UTC
10 points
79 comments1 min readLW link

Ex­am­ple de­ci­sion the­ory prob­lem: “Agent simu­lates pre­dic­tor”

cousin_it19 May 2011 15:16 UTC
45 points
76 comments2 min readLW link

Open-minded updatelessness

10 Jul 2023 11:08 UTC
65 points
21 comments12 min readLW link