Can Overestimation and Underweighting of Rare Events Coexist at the Same Time?

Actually, yes. Studies of human reaction to low probability (rare) events reveal an interesting difference between judgment and decision-making in repeated settings. Judgments (probability estimations) appear to reflect over-sensitivity to rare events. Immediately following an aversive rare-event people believe (or say they believe) the risk decreases yet at the same time they exhibit more cautious behavior (like buying insurance).

Previous research demonstrates overestimation of rare events in judgment tasks and underweighting of rare events in decisions from experience. The current paper presents three laboratory experiments and a field study that explore this pattern. The results suggest that the overestimation and underweighting pattern can emerge in parallel. Part of the difference between the two tendencies can be explained as a product of a contingent recency effect: although the estimations reflect negative recency, choice behavior reflects positive recency. A similar pattern is observed in the field study: immediately following an aversive rare-event (i.e., a suicide bombing), people believe the risk decreases (negative recency) but at the same time exhibit more cautious behavior (positive recency). The rest of the difference is consistent with two well established mechanisms: judgment error and the use of small samples in choice. Implications for the two-stage choice model are discussed.

Source: The Coexistence of Overestimation and Underweighting of Rare Events and the Contingent Recency Effect, Greg Barron and Eldad Yechiam, Judgment and Decision Making 4, no. 6 (October 2009) (PDF)