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Newcomb's paradox
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Newcomb's paradox
please note:
- the content below is remote from Wikipedia
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{{short description|Thought experiment}}{| class="wikitable infobox"! {{diagonal split header|Actualchoice| Predictedchoice}}! A + B(B has $0)! B(B has $1,000,000)- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
| $1,001,000 |
| $1,000,000 |
The problem
There is a reliable predictor, another player, and two boxes designated A and B. The player is given a choice between taking only box B or taking both boxes A and B. The player knows the following:JOURNAL, D. H., Wolpert, G., Benford, The lesson of Newcomb's paradox, Synthese, June 2013, 190, 9, 1637â1646, 10.1007/s11229-011-9899-3, 41931515, 113227,- Box A is transparent and always contains a visible $1,000.
- Box B is opaque, and its content has already been set by the predictor:
- If the predictor has predicted that the player will take both boxes A and B, then box B contains nothing.
- If the predictor has predicted that the player will take only box B, then box B contains $1,000,000.
Game-theory strategies
In his 1969 article, Nozick noted that "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly." The problem continues to divide philosophers today.NEWS, Bellos, Alex, Newcomb's problem divides philosophers. Which side are you on?,weblink 13 April 2018, The Guardian, 28 November 2016, en, Bourget, D., Chalmers, D. J. (2014). "What do philosophers believe?" Philosophical Studies, 170(3), 465â500. In a 2020 survey, a modest plurality of professional philosophers chose to take both boxes (39.0% versus 31.2%).WEB,weblink PhilPapers Survey 2020, Game theory offers two strategies for this game that rely on different principles: the expected utility principle and the strategic dominance principle. The problem is called a paradox because two analyses that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout.- Considering the expected utility when the probability of the predictor being right is certain or near-certain, the player should choose box B. This choice statistically maximizes the player's winnings, setting them at about $1,000,000 per game.
- Under the dominance principle, the player should choose the strategy that is always better; choosing both boxes A and B will always yield $1,000 more than only choosing B. However, the expected utility of "always $1,000 more than B" depends on the statistical payout of the game; when the predictor's prediction is almost certain or certain, choosing both A and B sets player's winnings at about $1,000 per game.
Causality and free will{| class"wikitable infobox"
! {{diagonal split header|Actualchoice| Predictedchoice}}! A + B! B| Impossible |
| $1,000,000 |
Consciousness and simulation
Newcomb's paradox can also be related to the question of machine consciousness, specifically if a perfect simulation of a person's brain will generate the consciousness of that person.ARXIV, R. M., Neal, Puzzles of Anthropic Reasoning Resolved Using Full Non-indexical Conditioning, math.ST/0608592, 2006, Suppose we take the predictor to be a machine that arrives at its prediction by simulating the brain of the chooser when confronted with the problem of which box to choose. If that simulation generates the consciousness of the chooser, then the chooser cannot tell whether they are standing in front of the boxes in the real world or in the virtual world generated by the simulation in the past. The "virtual" chooser would thus tell the predictor which choice the "real" chooser is going to make, and the chooser, not knowing whether they are the real chooser or the simulation, should take only the second box.Fatalism
Newcomb's paradox is related to logical fatalism in that they both suppose absolute certainty of the future. In logical fatalism, this assumption of certainty creates circular reasoning ("a future event is certain to happen, therefore it is certain to happen"), while Newcomb's paradox considers whether the participants of its game are able to affect a predestined outcome.{{citation |last1=Dummett |first1=Michael |title=The Seas of Language |publisher=Clarendon Press Oxford |year=1996 |pages=352â358}}.Extensions to Newcomb's problem
Many thought experiments similar to or based on Newcomb's problem have been discussed in the literature. For example, a quantum-theoretical version of Newcomb's problem in which box B is entangled with box A has been proposed.JOURNAL, International Journal of Quantum Information, 1, 3, 2003, 395â402, Piotrowski, Edward, Jan Sladowski, Quantum solution to the Newcomb's paradox, 10.1142/S0219749903000279, quant-ph/0202074, 20417502,The meta-Newcomb problem
Another related problem is the meta-Newcomb problem.JOURNAL, Analysis, 61, 4, Bostrom, Nick, 2001, The Meta-Newcomb Problem, 309â310, 10.1093/analys/61.4.309, The setup of this problem is similar to the original Newcomb problem. However, the twist here is that the predictor may elect to decide whether to fill box B after the player has made a choice, and the player does not know whether box B has already been filled. There is also another predictor: a "meta-predictor" who has reliably predicted both the players and the predictor in the past, and who predicts the following: "Either you will choose both boxes, and the predictor will make its decision after you, or you will choose only box B, and the predictor will already have made its decision."In this situation, a proponent of choosing both boxes is faced with the following dilemma: if the player chooses both boxes, the predictor will not yet have made its decision, and therefore a more rational choice would be for the player to choose box B only. But if the player so chooses, the predictor will already have made its decision, making it impossible for the player's decision to affect the predictor's decision.See also
Notes
{{reflist|30em}}References
- JOURNAL, Bar-Hillel, Maya, Margalit, Avishai, 1972, Newcomb's paradox revisited, British Journal for the Philosophy of Science, 23, 4, 295â304, 686730, 10.1093/bjps/23.4.295,
- Campbell, Richmond and Sowden, Lanning, ed. (1985), Paradoxes of Rationality and Cooperation: Prisoners' Dilemma and Newcomb's Problem, Vancouver: University of British Columbia Press. (an anthology discussing Newcomb's Problem, with an extensive bibliography).
- Collins, John. "Newcomb's Problem", International Encyclopedia of the Social and Behavioral Sciences, Neil Smelser and Paul Baltes (eds.), Elsevier Science (2001).
- BOOK
, Gardner
, Martin
, 1986
, Knotted Doughnuts and Other Mathematical Entertainments
,weblink
, registration
, W. H. Freeman and Company
, 0-7167-1794-8
, 155â175
, , Martin
, 1986
, Knotted Doughnuts and Other Mathematical Entertainments
,weblink
, registration
, W. H. Freeman and Company
, 0-7167-1794-8
, 155â175
- JOURNAL, Levi, Isaac, 1982, A Note on Newcombmania, Journal of Philosophy, 79, 6, 337â342, 2026081, 10.2307/2026081, (An article discussing the popularity of Newcomb's problem.)
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