Decision Theory studies the influence of an individual's values, uncertainties and knowledge on their choices. A distinction is made between decisions based on knowledge from description, and decisions based on experience. In their review of existing work, the authors of the 2004 paper Decisions From Experience and the Effect of Rare Events in Risky Choice note a discrepancy in the behaviour of test subjects when making a risky choice. Their definition of risky choice as follows: test subject choose between two options, each with different payoffs. The payoffs are probabilistic, and one of the options has a risky event associated with it; the effect of the event is either positive or negative. Here risky is defined as having a probability of 1 in 5 or less.

In the 1979 experiment by Kahneman and Tversky, the test subjects were told the probability distribution of the payoff for both options before making the decision. In the more recent 2003 experiment by Barron and Erev the test subjects could learn by experience the possible payoffs: they were allowed to test both options however many times they wanted and received feedback before making a decision.

The authors discuss existing definitions for rational choice. The formulate Bernoulli's concept of expected utility: the expected utility is the sum of the probability of all constituents times the utility obtained by their payoffs. Kahneman and Tversky expand on this model and assign additionally a decision weight to each choice.

Using this model, it was found that, when the decision-makers where described the probabilities, they overweighted the rare event. Vice versa, in the experiment where the subjects where allowed to learn the payoffs by experience, the subjects generally underweighted the rare events.

Could it be that this discrepancy was not merely due to random chance or the setup of the respective experiments? In order to verify this an experiment was set up where both methods of obtaining knowledge where tested on the same set of questions. It was quickly shown that the phenomenon was reproducible in this test. Additionally, two hypotheses are tested to explain this discrepancy which the authors later refer to as the description-experience gap.

The first is that the search effort made by the test subjects when learning by experience is very limited: on average the test subjects made 15 draws for both options combined. Due to the skewed distribution of Bernoulli trials, this could lead some subjects to not encounter the risky event in their trials or to encounter it too few to make a good estimate. This would then lead to the decision-maker to underweight the rare event. They find that, given the probabilities and average number of draws by the participants, this could explain their results. Indeed, in a 2008 paper by Hertwig et al. (The Description–Experience Gap in Risky Choice: The Role of Sample Size and Experienced Probabilities) it is found that the number of draws plays a significant role in the underweighting of rare events: when motivating the decision-makers to make more draws the underweighting effect decreases.

Secondly the researchers investigate whether the ordering of results in draws have an effect. They hypothesise that the frequencies seen last are weighted more than frequencies seen early on in the learning from experience test. They find a statistically significant effect: the second half of draws predict 75\% of choices versus 59\% for the first half.

In conclusion, the authors provide significant results supporting their hypothesis that the description-experience gap can be explained by at least two factors. A root cause analysis for the limited number of draws, or _search effort, is performed, nor are there concrete hints for further research.

Decisions From Experience and the Effect of Rare Events in Risky Choice --- Ralph Hertwig, Greg Barron, Elke U. Weber, and Ido Erev Psychological Science 15(8).
2004-08 pages 534-9.

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