Quantifying Lottery Choice Complexity

We develop interpretable, quantitative indices of the objective and subjective complexity of lottery choice problems that can be computed for any standard dataset. These indices capture the predicted error rate in identifying the lottery with the highest expected value, where the predictions are computed as convex combinations of choice set features. The most important complexity feature in the indices is a measure of the excess dissimilarity of the cumulative distribution functions of the lotteries in the set. Using our complexity indices, we study behavioral responses to complexity out-of-sample across one million decisions in 11,000 unique experimental choice problems. Complexity makes choices substantially noisier, which can generate systematic biases in revealed preference measures such as spurious risk aversion. These effects are very large, to the degree that complexity explains a larger fraction of estimated choice errors than proximity to indifference. Accounting for complexity in structural estimations improves model fit substantially.