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
- Pay 3 if heads, $0 if tails
- 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
For any given bet (set to be for the against case):
|Player wins bet||Player loses bet|
Dutch Book Theorem
Based on the Kolmogorov probability axioms,
- If any axiom is violated, a Dutch Book can be made.
- If no axiom is violated, then no Dutch Book can be made.