Pascal's mugging
In philosophy, Pascal's mugging denotes a thought-experiment due to Eliezer Yudkowsky[1] and Nick Bostrom[2], 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.
Original statement
In Bostrom's paper[2] 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. Convinced by the argument, Pascal gives the mugger the wallet.
Consequences and remedies
Pascal's mugging is relevant for considering low probability, high stakes events such as existential risk or charitable interventions with a low probability of success but extremely high rewards. Common sense seems to suggest that spending effort on too unlikely scenarios is irrational.
One remedy might be to only use bounded utility functions: rewards cannot be arbitrarily large. [3][4] Another approach is to use Bayesian reasoning to (qualitatively) judge the quality of evidence and probability estimates rather than naively calculate expectations.[5] Other approaches are to penalize the prior probability of hypotheses that argue that we are in a surprisingly unique position to affect large numbers of other people who cannot symmetrically affect us[6], or reject the providing the probability of a payout first[7]. Other tactics against the mugging are possible, each with their own drawbacks. [8][9]
See also
References
- ^ 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/
- ^ a b Nick Bostrom, Pascal's mugging. Analysis (2009) 69 (3): 443-445. doi:10.1093/analys/anp062 http://www.nickbostrom.com/papers/pascal.pdf
- ^ De Blanc, Peter. Convergence of Expected Utilities with Algorithmic Probability Distributions (2007), http://arxiv.org/abs/0712.4318
- ^ Cowen, Tyler, and Jack High. 1988. Time, Bounded Utility, and the St. Petersburg Paradox. Theory and Decision 25 (3): 219–223. doi:10.1007/BF00133163.
- ^ Holden Karnofsky, Why We Can’t Take Expected Value Estimates Literally (Even When They’re Unbiased). GiveWell Blog August 18, 2011 http://blog.givewell.org/2011/08/18/why-we-cant-take-expected-value-estimates-literally-even-when-theyre-unbiased/
- ^ Pascal's mugging. LessWrong Wiki, http://wiki.lesswrong.com/wiki/Pascal's_mugging
- ^ Peter Baumann. Counting on numbers. Analysis 69 (3):446-448 (2009)
- ^ ArisKatsaris, Tactics Against Pascal's Mugging. LessWrong, 25 April 2013 http://lesswrong.com/lw/h1i/tactics_against_pascals_mugging/
- ^ http://www.gwern.net/mugging