Pascal's Mugging¶

In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization.

Version: v1 · 2026-09-28 · History
Domain-specific #: 11220
Domain group: Humanities
Origin domain: Philosophy
Subdomains: Decision Theory, Thought Experiments → Philosophy

Core Idea¶

Pascal's Mugging is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization.

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 weighted 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; this leads first to counter-intuitive choices, and then to incoherence as the utility of every choice becomes unbounded. The name refers to Pascal's Wager, but unlike the wager, it does not require infinite rewards. This sidesteps many objections to the Pascal's Wager dilemma that are based on the nature of infinity.

For Pascal's Mugging, the abstraction is narrower than the article's general subject matter: a positive case must preserve In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in mathematics, logic, and statistics, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the LessWrong forum.
Constitutive relation — In Bostrom's description, Blaise Pascal is accosted by a mugger who has forgotten their weapon.
Operating condition — In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life.
Recognition evidence — 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 3\uparrow\uparrow\uparrow\uparrow3 people".
Admissible variation — Moreover, in many reasonable-seeming decision systems, Pascal's mugging causes the expected utility of any action to fail to converge, as an unlimited chain of successively dire scenarios similar to Pascal's mugging would need to be factored in.
Characteristic consequence — Convinced by the argument, Pascal gives the mugger the wallet.
Failure boundary — On the one side, by multiplying an expected utility calculation, assuming loss of five dollars to be valued at , loss of a life to be valued at and probability that the mugger is telling the truth at the solution is to give the money if and only if Assuming that l is higher than so long as t is higher than which is assumed to be true, it is considered rational to pay the mugger.

What It Is Not¶

Not the whole field of mathematics, logic, and statistics. The node requires the specific identity stated by In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization.
Not an over-broad reading. The name refers to Pascal's Wager, but unlike the wager, it does not require infinite rewards.
Not an over-broad reading. However, the mugger proposes a deal: the philosopher gives them his wallet, and in exchange the mugger will return twice the amount of money tomorrow.
Not an over-broad reading. Pascal declines, pointing out that it is unlikely the deal will be honoured.
Not automatically St. Petersburg Paradox. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Pascal's Mugging applies literally inside mathematics, logic, and statistics wherever the source-defined carrier and relation can be established. Its documented habitats include:

Consequences and remedies. One advocated remedy might be to only use bounded utility functions: rewards cannot be arbitrarily large.
Problem statement. The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the LessWrong forum.
Problem statement. Philosopher Nick Bostrom later elaborated the thought experiment in the form of a fictional dialogue.
Problem statement. Subsequently, other authors published their own sequels to the events of this first dialogue, adopting the same literary style.
Problem statement. In Bostrom's description, Blaise Pascal is accosted by a mugger who has forgotten their weapon.
Problem statement. However, the mugger proposes a deal: the philosopher gives them his wallet, and in exchange the mugger will return twice the amount of money tomorrow.

Outside mathematics, logic, and statistics, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Pattern or should be marked as analogy.

Clarity¶

A clear use of Pascal's Mugging names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization. The strongest recognition evidence in the frozen account is: 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 3\uparrow\uparrow\uparrow\uparrow3 people". A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification The name refers to Pascal's Wager, but unlike the wager, it does not require infinite rewards. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Pascal's Mugging compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—in Bostrom's description, Blaise Pascal is accosted by a mugger who has forgotten their weapon.—and the practical consequence—convinced by the argument, Pascal gives the mugger the wallet. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
State the relation. Use the source-grounded identity: In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization.
Check operation and conditions. In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life.
Demand recognition evidence. 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 3\uparrow\uparrow\uparrow\uparrow3 people".
Test variation. Change an implementation or setting while preserving moreover, in many reasonable-seeming decision systems, Pascal's mugging causes the expected utility of any action to fail to converge, as an unlimited chain of successively dire scenarios similar to Pascal's mugging would need to be factored in.
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Pattern.

Knowledge Transfer¶

Within the home domain. Knowledge about Pascal's Mugging transfers literally when a new case preserves the same carrier type, relation, and recognition test. One advocated remedy might be to only use bounded utility functions: rewards cannot be arbitrarily large. The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the LessWrong forum.

Beyond the home domain. No canonical parent is asserted for Pascal's Mugging. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

Some of the arguments concerning this paradox affect not only the expected utility maximization theory, but may also apply to other theoretical systems, such as consequentialist ethics, for example. This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization; recognition evidence → 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 3\uparrow\uparrow\uparrow\uparrow3 people"

Applied / In Practice¶

In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → Problem statement; invariant → In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization; boundary → the case exits the class when the name refers to Pascal's Wager, but unlike the wager, it does not require infinite rewards

Structural Tensions¶

T1 — Stable identity versus admissible variation. The name refers to Pascal's Wager, but unlike the wager, it does not require infinite rewards. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. However, the mugger proposes a deal: the philosopher gives them his wallet, and in exchange the mugger will return twice the amount of money tomorrow. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. Pascal declines, pointing out that it is unlikely the deal will be honoured. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. Some of the arguments concerning this paradox affect not only the expected utility maximization theory, but may also apply to other theoretical systems, such as consequentialist ethics, for example. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the LessWrong forum. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Pascal's Mugging literally, co-instantiate Pattern, or only resemble it?

T6 — Autonomy versus reduction. In Bostrom's description, Blaise Pascal is accosted by a mugger who has forgotten their weapon. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Pascal's Mugging distinguish that the broader parent Pattern leaves together?

Structural–Framed Character¶

Pascal's Mugging is structural-leaning. Its structural side is the repeatable organization summarized by In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization. Its framed side is the mathematics, logic, and statistics vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Pattern. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the LessWrong forum. In Bostrom's description, Blaise Pascal is accosted by a mugger who has forgotten their weapon. It further constrains recognition and variation through: In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life. 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 3\uparrow\uparrow\uparrow\uparrow3 people".

What is domain-bound. mathematics, logic, and statistics supplies the operative entities, technical vocabulary, warrants, and exceptions that make Pascal's Mugging literal. Its documented scope includes the condition that One advocated remedy might be to only use bounded utility functions: rewards cannot be arbitrarily large. Another bounded application condition is that The term "Pascal's mugging" to refer to this problem was originally coined by Eliezer Yudkowsky in the LessWrong forum. These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—Moreover, in many reasonable-seeming decision systems, Pascal's mugging causes the expected utility of any action to fail to converge, as an unlimited chain of successively dire scenarios similar to Pascal's mugging would need to be factored in.—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Thought Experiment.

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Pascal's Mugging. The reviewed identity is: In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

Current abstraction Pascal's Mugging Domain-specific

Parents (1) — more general patterns this builds on

Pascal's Mugging is a kind of Thought Experiment Prime

Pascal's mugging is a thought experiment exposing a problem in expected-utility maximization.

Hierarchy paths (2) — routes to 2 parentless roots

Pascal's Mugging → Thought Experiment → Counterfactual Reasoning

Show alternative path (1)

Neighborhood in Abstraction Space¶

Pascal's Mugging sits in a sparse region of the domain-specific corpus (69^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Narrative Devices & Literary Forms (15 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Pattern. The parent omits the specialist differentia. Tell: Can the case establish In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization?
St. Petersburg Paradox. A gamble whose expected monetary value is infinite yet which real deciders will pay only a few coins to enter, exposing that a value function linear in money mishandles fat-tailed payoffs and must be replaced by a concave or bounded utility. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Certainty Effect. Capture the way people overweight an outcome made fully certain relative to one merely probable of equal expected value, so the move from 0.99 to 1.0 commands a disproportionate premium the arithmetic does not justify. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Newcomb's Problem. A decision-theory problem in which a highly reliable prior predictor conditions an opaque box's payoff on a forecast of whether an agent will take one box or two, setting evidential and causal recommendations against dominance reasoning. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Pascal's Mugging remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside mathematics, logic, and statistics lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Pattern?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Pascal%27s_mugging (revision 1326220106).
Preserved source candidate: http://www.nottingham.ac.uk/climateethicseconomics/documents/papers-workshop-5/marray.pdf
Preserved source candidate: http://hdl.handle.net/2027/spo.3521354.0019.018
Preserved source candidate: https://blog.givewell.org/2011/08/18/why-we-cant-take-expected-value-estimates-literally-even-when-theyre-unbiased/
Preserved source candidate: https://web.archive.org/web/20160219020522/http://lesswrong.com/lw/kd/pascals_mugging_tiny_probabilities_of_vast/#thingrow_t1_ui9
Preserved source candidate: https://longtermrisk.org/files/how-the-simulation-argument-dampens-future-fanaticism.pdf
Preserved source candidate: https://web.archive.org/web/20211123012535/https://longtermrisk.org/files/how-the-simulation-argument-dampens-future-fanaticism.pdf
Preserved source candidate: http://lesswrong.com/lw/h8k/pascals_muggle_infinitesimal_priors_and_strong/
Preserved source candidate: https://web.archive.org/web/20160627080608/http://lesswrong.com/lw/h8k/pascals_muggle_infinitesimal_priors_and_strong/

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.