Category: economics
Type: puzzle
Associated thinker(s): Nick Bostrom
Original publication or approximate period: Bostrom, “Pascal’s Mugging” (Analysis, 2009)
Difficulty: Advanced
Themes: expected utility, tiny probabilities, decision theory
Related experiments: Pascal’s Wager; The St. Petersburg Paradox
A stranger approaches Pascal in a dark alley and demands his wallet. Pascal refuses. The stranger then claims to have magical powers and offers an enormous but finite number of happy days in exchange.
In Bostrom’s dialogue, Pascal gives the claim a small, nonzero probability. He also assumes that his utility is unbounded, counts happy days linearly, and is neither risk-averse nor temporally discounting. Under those assumptions, the stranger can name a sufficiently large finite reward to make handing over the wallet maximize expected utility. The result depends on that setup; it is not a general theorem that any improbable claim can force acceptance.
Given the assumptions in Bostrom’s story, should Pascal hand over his wallet—and what, if anything, should a decision-maker change to resist the result?
The puzzle dramatizes how expected-utility calculations can be dominated by a very large payoff assigned a small but nonzero probability when utility is unbounded. It does not show that expected-utility theory is generally exploitable or that a real stranger’s promise deserves credence. The result depends on how probability and utility are represented, as well as on the story’s assumptions.
Bostrom’s short dialogue does not settle the puzzle or present a taxonomy of solutions; it ends with Pascal handing over his wallet. One later proposal, by Avram Hiller and Ali Hasan, asks Pascal to consider other, symmetric rewards that might be available if he declines. Their “many muggers” response says that a salient offer may lose its one-sided advantage when such non-salient alternatives are included. This is a specific proposal, not a general license to ignore small probabilities.
The story is not a robbery tip, and it does not show that taking small risks is irrational. Bostrom’s utility is unbounded, not an infinite payoff: the mugger offers a finite reward. In the dialogue, the result also relies on the assumed credibility of increasingly large promises, linear utility, and the absence of risk aversion or temporal discounting.
Bostrom’s footnote credits Eliezer Yudkowsky with naming the problem. Yudkowsky’s 2007 post uses a related but different example and ends by saying he did not yet have a satisfactory resolution.
The puzzle resembles Pascal’s Wager and the St. Petersburg paradox, but the cases are not identical. Hiller and Hasan argue that Pascal’s Mugging is deeper than the St. Petersburg case because the mugger asks Pascal to assign a probability to an extraordinary promise without first showing that he can deliver such an enormous reward. Their comparison is one later analysis, not part of Bostrom’s original argument.
Bostrom’s complete author-hosted PDF was retrieved and read. The dialogue specifies Pascal’s assumptions about unbounded utility, linear happy days, risk aversion, temporal discounting, and the mugger’s finite offers; its footnote credits Yudkowsky with the name. Yudkowsky’s 2007 post is a related but distinct original formulation. Hiller and Hasan’s peer-reviewed article was checked at the abstract, relevant response sections, and comparison with the St. Petersburg paradox; it proposes one later response and does not establish a consensus solution.
Research check: 2026-11-01. This is an original educational explanation, not a substitute for the primary texts or expert review. Additional comparisons are teaching prompts, not established historical variations.