Dutch Book Arguments¶
A finite fair-bet portfolio test that exposes incoherent event prices through a guaranteed loss in every admissible outcome.
Core Idea¶
A classical Dutch book argument tests quoted fair prices for event bets. If the agent accepts either side of each ticket at its quoted price, another trader can sometimes combine finitely many tickets so the agent loses money in every possible outcome. Under this specified betting convention, immunity to finite sure-loss books corresponds to a finitely additive probability assessment on the finite generated event algebra.[^ref-343940b1de86]
Scope of Application¶
The test applies to finite event assessments with declared outcomes, prices and admissible stakes. It can reveal that prices for an exhaustive partition add to more than one or that a sure event is priced below one. It does not automatically apply to a person who may refuse the bets, or prove countable additivity and expected-utility axioms.[^ref-343940b1de86]
Clarity¶
The decisive issue is guaranteed, not merely possible, loss. Two tickets each priced at 0.60 on mutually exclusive, exhaustive events jointly cost 1.20 but pay exactly one. If the agent buys both, the loss is 0.20 whichever event occurs. If a sure-event ticket is priced at 0.90 and the agent sells it, the loss is 0.10 in every state.[^ref-343940b1de86]
Manages Complexity¶
A portfolio exposes a contradiction among prices that might not be obvious from the tickets one at a time. The finite probability-extension theorem summarizes the no-sure-loss condition, but only for the specified event algebra and trade convention.[^ref-343940b1de86]
Abstract Reasoning¶
To check a proposed book, state who buys and sells each ticket, sum the net payoff to the quoting agent, and test every admissible outcome. A risky bet with one winning state is not a strict Dutch book. Reversing a buy and sell direction can reverse the conclusion entirely.[^ref-343940b1de86]
Knowledge Transfer¶
The partition and sure-event cases share quoted prices, two-sided fair trades, finite aggregation and an all-state loss test. A preference money pump shares an exploitation analogy but uses a different set of primitives. Probability and Consistency are related live identities, yet neither is currently asserted as a strict parent of this diagnostic method. No canonical DAG edge was changed.[^ref-343940b1de86]
[^ref-343940b1de86]: Martina Fedel, Hykel Hosni and Franco Montagna, “A logical characterization of coherence for imprecise probabilities” (2010), §1.1, Definition 1.1 and Theorem 1.1, especially PDF pp. 8–9.
Neighborhood in Abstraction Space¶
Dutch Book Arguments sits in a sparse region of the domain-specific corpus (76th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Financial Markets & Pricing Anomalies (13 abstractions)
Nearest neighbors
- Black–Scholes Model — 0.85
- Greater Fool Theory — 0.83
- Vickrey Auction — 0.83
- Fair Division — 0.82
- Bertrand competition — 0.82
Computed from structural-signature embeddings · 2026-10-08