Dutch book arguments
set of odds and bets which guarantees a profit, regardless of the outcome of the gamble
In decision theory, economics, and probability theory, the Dutch book arguments are a set of results showing that agents must satisfy the axioms of rational choice to avoid a kind of self-contradiction called a Dutch book. A Dutch book, sometimes also called a money pump, is a set of bets that ensures a guaranteed loss, i.e., the gambler will lose money no matter what happens. A set of bets is called coherent if it cannot result in a Dutch book.
The Dutch book arguments are used to explore degrees of certainty in beliefs, and demonstrate that rational bet-setters must be Bayesian; in other words, a rational bet-setter must assign event probabilities that behave according to the axioms of probability, and must have preferences that can be modeled using the von Neumann–Morgenstern axioms.
In economics, they are used to model behavior by ruling out situations where agents "burn money" for no real reward. Models based on the assumption that actors are rational are called rational choice models. That assumption is weakened in behavioral models of decision-making.
The thought experiment was first proposed by the Italian probabilist Bruno de Finetti and the English polymath Frank P. Ramsey, apparently independently, in order to justify Bayesian probability. It was more thoroughly explored by Leonard Savage, who developed it into a full model of rational choice.
Operational subjective probabilities as wagering odds
Assume we have two players, A and B. Player A must set the price of a promise to pay $1 if John Smith wins tomorrow's election.
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This entry incorporates text from “Dutch book arguments” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.