Submission declined on 6 November 2023 by WikiOriginal-9 (talk).
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Comment: Close but not quite enough independent, significant coverage. WikiOriginal-9 (talk) 07:42, 6 November 2023 (UTC)
The shooting room paradox is a hypothetical game in which the majority of players lose even though each player apparently should expect to win. The game was first described by philosopher John Leslie,[1] who also credits fellow philosopher David Lewis for inventing the game.[2]
The paradox edit
Leslie's original description of the problem is as follows:
Thrust into a room, you are assured that 90% of those who enter it will be shot. Panic! But you then learn that you will leave the room alive unless double-six is thrown, first time, with two dice. How is this compatible with the assurance that 90% will be shot? Successive batches of people thrust into the room are successively larger, exponentially, so that the forecast “90% will be shot” will be confirmed when double-six is eventually thrown. If knowing this, and knowing also that the dice falls would be utterly unpredictable even to a Laplacean demon who knew everything about the situation when the dice were thrown, then shouldn’t one’s panic vanish?
In other words, initially one person enters the room, and then nine, and then ninety, and so on until the game ends. Alternative descriptions may change the chance of losing or the expected proportion of losers, or add an incentive for playing, without changing the essential character of the paradox.
Attempted resolutions edit
Finite player pool edit
The paradox requires an unlimited pool of players, which is impossible. With a finite pool, it is possible to run out of players, and there is no paradox.[3]
Draft number prior edit
If someone is drafted for the shooting room, a question arises: In which round of the game will they play, if they play at all? Suppose each potential player is assigned a number that determines when they enter the room (if ever). Then there is no proper prior that gives equal probability to all draft numbers.[4]
See also edit
References edit
- ^ Leslie, John (1992). "Time and the Anthropic Principle". Mind. 101 (403): 521–540. doi:10.1093/mind/101.403.521. ISSN 0026-4423. JSTOR 2253901.
- ^ Leslie, John (December 1997). "Observer-relative chances and the doomsday argument". Inquiry. 40 (4): 427–436. doi:10.1080/00201749708602461. ISSN 0020-174X.
- ^ Eckhardt, William (1997). "A Shooting-Room View of Doomsday". The Journal of Philosophy. 94 (5): 244–259. doi:10.2307/2564582. ISSN 0022-362X. JSTOR 2564582.
- ^ Bartha, Paul; Hitchcock, Christopher (1999-03-01). "The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets". Synthese. 118 (3): 403–437. doi:10.1023/A:1005100407551. ISSN 1573-0964. S2CID 34035742.
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