Dutch book theorems

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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 or money pump is a set of bets that ensures a guaranteed loss, i.e. the gambler will lose money no matter what happens.^[1] A set of beliefs and preferences 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 agents must be Bayesian;^[2] in other words, rationality requires assigning probabilities to events that behave according to the axioms of probability, and having 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 these assumptions are called rational choice models. These assumptions are weakened in behavioral models of decision-making.

The thought experiment was first proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability,^{[citation needed]} and was more thoroughly explored by Leonard Savage, who developed them into a full model of rational choice.