Hopelessly optimistic despite the known evidence... "the remarkable durability of that error paints a more pessimistic picture of human reasoning than we were initially inclined to accept"

We knew this already, although we didn't pay attention, and Tversky & Kahneman certified this before 1974 (Nobel for Kahneman in 2000+ for that work)... The formation and revision of intuitions https://www.sciencedirect.com/science/article/pii/S0010027723000148

Conclusion by these intelligent scholars... "the remarkable durability of that error paints a more pessimistic picture of human reasoning than we were initially inclined to accept"

Abstract: This paper presents 59 new studies (N = 72,310) which focus primarily on the “bat and ball problem.” It documents our attempts to understand the determinants of the erroneous intuition, our exploration of ways to stimulate reflection, and our discovery that the erroneous intuition often survives whatever further reflection can be induced. Our investigation helps inform conceptions of dual process models, as “system 1” processes often appear to override or corrupt “system 2” processes. Many choose to uphold their intuition, even when directly confronted with simple arithmetic that contradicts it – especially if the intuition is approximately correct.

5 Concluding remarks

When we began studying the bat and ball problem, we assumed respondents missed it because they didn't bother to check. Accordingly, we assumed that they'd be able to solve it if we directed their attention to the features of the problem that differentiate it from the problem we thought they were unwittingly solving instead (bat and ball “lite”) or to the constraint the typical answer violates (that the prices differ by 100).

We discovered instead that many respondents maintain the erroneous response in the face of facts that plainly falsify it, even after their attention has been directed to those facts. Although subjects' apparent sensitivity to the size of the heuristic error merits further research, the remarkable durability of that error paints a more pessimistic picture of human reasoning than we were initially inclined to accept; those whose thoughts most require additional deliberation benefit little from whatever additional deliberation can be induced.