Rarity Anomalies Remain

Our choices apparently under-weigh rare events when we experience track records, even though we accurately estimate the frequencies of those events.  We over-weigh rare events, however, when we are told their probabilities.  Simple explanations of these anomalies are shot down in a recent Psychological Science:

When making decisions involving risky outcomes on the basis of verbal descriptions of the outcomes and their associated probabilities, people behave as if they overweight small probabilities. In contrast, 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 existing explanations of the underweighting observed in decisions from experience are not sufficient to account for the effect. Underweighting was observed when participants experienced representative samples of events, so it cannot be attributed to undersampling of the small probabilities. In addition, earlier samples predicted decisions just as well as later samples did, so underweighting cannot be attributed to recency weighting. Finally, frequency judgments were accurate, so underweighting cannot be attributed to judgment error. Furthermore, we show that the underweighting of small probabilities is also reflected in the best-fitting parameter values obtained when prospect theory, the dominant model of risky choice, is applied to the data.