Probabilistic insurance is an insurance policy involving a small proba
bility that the consumer will not be reimbursed. Survey data suggest t
hat people dislike probabilistic insurance and demand more than a 20%
reduction in the premium to compensate for a 1% default risk. While th
ese preferences are intuitively appealing they are difficult to reconc
ile with expected utility theory. Under highly plausible assumptions a
bout the utility function, willingness to pay for probabilistic insura
nce should be very close to willingness to pay for standard insurance
less the default risk. However, the reluctance to buy probabilistic in
surance is predicted by the weighting function of prospect theory. Thi
s finding highlights the potential role of the weighting function to e
xplain insurance.