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Pascal's mugging
In philosophy, Pascal's mugging is a thought-experiment demonstrating a problem in expected utility maximization. A rational agent should choose actions whose outcomes, when weighed by their probability, have higher utility. But some very unlikely outcomes may have very great utilities, and these utilities can grow faster than the probability diminishes. Hence the agent should focus more on vastly improbable cases with implausibly high rewards.
The name refers to Pascal's Wager, but unlike the wager does not require infinite rewards. This removes any objections to the dilemma that are based on the nature of infinity.〔
==Problem statement==
In one description,〔 Blaise Pascal is accosted by a mugger who has forgotten his weapon. However, the mugger proposes a deal: the philosopher gives him his wallet, and in exchange the mugger will return twice the amount of money tomorrow. Pascal declines, pointing out that it is unlikely the deal will be honoured. The mugger then continues naming higher rewards, pointing out that even if it is just one chance in 1000 that he will be honourable, it would make sense for Pascal to make a deal for a 2000 times return. Pascal responds that the probability for that high return is even lower than one in 1000. The mugger argues back that for any low probability of being able to pay back a large amount of money (or pure utility) there exists a finite amount that makes it rational to take the bet – and given human fallibility and philosophical scepticism a rational person must admit there is at least ''some'' non-zero chance that such a deal would be possible. In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life. Convinced by the argument, Pascal gives the mugger the wallet.
The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the Less Wrong forum.〔Eliezer Yudkowsky, Pascal's Mugging: Tiny Probabilities of Vast Utilities. Less Wrong, 19 October 2007. http://lesswrong.com/lw/kd/pascals_mugging_tiny_probabilities_of_vast/〕 In one of Yudkowsky's examples, the mugger succeeds by saying "give me five dollars, or I'll use my magic powers from outside the Matrix to run a Turing machine that simulates and kills people". Here, the number uses Knuth's up-arrow notation; writing the number out in base 10 would require enormously more writing material than there are atoms in the known universe.〔
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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