A Dutch Book is a set of bets that you consider individually fair, but which collectively guarantee a loss

This usually happens when people commit probabilistic fallacies (e.g. the conjunction fallacy, believing when this can never be the case). Another common mistake is double counting probabilities

For example, if J believes that , we can propose two bets

  1. Pay 3 if heads, $0 if tails
  2. Pay 3 if tails, $0 if heads

Both bets make sense for J. However, if J takes both bets, then he faces a guaranteed loss of $1

Have the agent bet for propositions with credences (or FBQs) that are too high, and against propositions with credences (or FBQs) that are too low

For any given bet (set to be for the against case):

Player wins betPlayer loses bet

Dutch Book Theorem

Based on the Kolmogorov probability axioms,

  1. If any axiom is violated, a Dutch Book can be made.
  2. If no axiom is violated, then no Dutch Book can be made.