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On the basis of a real high stakes insurance experiment with small probabilities of losses, we demonstrate that concern is a more important driver of WTP for insurance than subjective probability estimates when there is ambiguity surrounding the estimate. Concern is still important when probabilities are exactly given. It also helps explaining the low probability insurance puzzle well known from the literature, where a part of individuals pays too much and a part nothing for coverage, a result we are able to replicate. In our experiment, belonging to either the group of threshold persons or to those that pay far too much, is not related to probability judgments but to the degree an individual is concerned in our decision situation.
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