A robust measure of complexity

We introduce a robust belief-based measure of complexity. The idea is that task A is deemed more complex than task B if the probability of solving A correctly is smaller than the probability of solving B correctly regardless of the reward. We fully characterize the corresponding order over the set of tasks. The main characteristic of this relation is that it depends, not only on difficulty (like most complexity definitions in the literature) but also on ex ante uncertainty. Finally, we show that for every task for which information is optimally acquired, there exists a more complex task which always induces less effort regardless of the reward.