Expected accuracy as a measure of subjective complexity

We introduce uniform expected accuracy as a proxy for subjective complexity which is robust with respect to the underlying reward for solving the task correctly. The idea is that task A is classified as subjectively more complex than task B if the probability of correctly solving A is smaller than the probability of correctly solving B for any reward. We provide a full characterization of the incomplete order over the set of tasks that this criterion induces. This characterization implies that task A will be classified as subjectively more complex than task B if and only if A is both more difficult and much less known than B. This insight is consistent with the general idea within economics that complexity has both an objective and a subjective part. It is also aligned with the literature in psychology and information science which ---unlike economics--- have identified prior uncertainty as a key dimension of complexity. Then, using a lab experiment, where we can exogenously control both difficulty and uncertainty, we corroborate our theoretical predictions. Thus, the recently surging use of expected accuracy in economics as a proxy for subjective complexity is well warranted, as long as expected accuracy is elicited for multiple different rewards using the strategy method.