Ungemach, C., Chater, N., & Stewart, N. (2009). Are probabilities overweighted or underweighted, when rare outcomes are experienced (rarely)? Psychological Science, 20, 473-479.

People often make decisions with risky outcomes. When presented with verbal descriptions of outcomes and their associated probabilities, people behave as if they overweight small probabilities. When the same outcomes are instead experienced in a series of samples, people behave as if they underweight small probabilities. We present two experiments showing that the reversal from overweighting to underweighting occurs even if the existing explanations are controlled for: (a) by using representative samples of events, underweighting cannot be attributed to undersampling of the small probabilities; (b) because earlier samples predicted decisions just as well as later samples, underweighting cannot be attributed to recency weighting; (c) and because frequency judgments were accurate, underweighting cannot be attributed to judgment error. Furthermore, we show that this reversal is also reflected in the best-fitting parameter values when applying prospect theory, the dominant model of risky choice.