People have a difficult time comprehending the meaning of small probabilities.

Many individuals exhibit behavior that implies they are either unconcerned or extremely risk averse when deciding whether to purchase insurance against events that have a small probability of occurring. Unconcerned individuals are not willing to pay a penny, even if premiums are subsidized, whereas those who appear to be highly risk averse opt for premiums that are more than 10 times the expected losses.

This study provides answers to the following three questions:

(1) Are there any differences with respect to the willingness to pay (WTP) for insurance when the probabilities are ambiguous or exact in case the probability of a disaster is very small?

(2) What is the relative importance of worry (as an emotion) and subjective probability (as a cognitive aspect) for WTP for insurance when the probability of a disaster is very small?

(3) How sensitive are individualsâ€™ WTP to large increases in the ambiguous probability of disaster?

“Our findings show that a substantial percentage of individuals are not willing to pay anything for insurance when the probabilities of losses are either exact or ambiguous whereas others tend to be willing to pay surprisingly large amounts. In line with other research (e.g., Curley, Yates, & Abrams, 1986; Hogarth & Kunreuther, 1985), WTP is higher when probabilities are ambiguous than when they are known. **Strikingly, worry appears to be a major driver of WTP for insurance, whereas subjective probability judgments have hardly any impact.**”

Abstract:

We carry out a large monetary stakes insurance experiment with very small probabilities of losses and ambiguous as well as exact probabilities. Many individuals do not want to pay anything for insurance whether the probabilities are given exactly or are ambiguous. Many others, however, are willing to pay surprisingly large amounts. With ambiguity, the percentage of those paying nothing is smaller and the willingness to pay (WTP) of the other individuals larger than with exact probabilities. Comparing elasticities with ambiguity, **we find that worry is much more important than subjective probability in determining WTP for insurance**. Furthermore, when the ambiguous loss probability is increased by a factor of 1000, it has almost no effect on WTP.

Source: Schade, C., Kunreuther, H. and Koellinger, P. (2011), Protecting Against Low-Probability Disasters: The Role of Worry. Journal of Behavioral Decision Making. doi: 10.1002/bdm.754 (The full study can be found here)