Dear authors,

Thank you very much for your submission. I have read your paper with great interest and received feedback from two reviewers. Given this feedback and my own reading of the paper, I recommend a revision to address the minor concerns that the two referees raised and that I also noted while reading your manuscript.

Please note that both Olivier and I commented on the Big Ten Conference item which is, in my view, the major element of the revision. Olivier’s suggestion regarding the Bayesian statistics with the initial paper’s results used as priors can be seen as a general comment about your overall replication project and for exploratory discussions. However, I understand that you want to stick as close as possible to the tests used in the original paper. Last, both Olivier and I commented on payments. While these comments do not challenge your design, they might call for a dedicated subsection in the paper or, at least, a bit more emphasis.

I put my comments below. (As always, consider them with caution and feel free to contradict them: I might be mistaken.)

I am looking forward to receiving the revised version of your work.

Best regards,

Romain

——Recommender’s comments——

- In the original study, for Study 1, the authors have underlined some parts of the text. I checked in Qualtrics and, indeed, you have underlined these sentences. You might be willing to underline them in your paper as well (Table 5).

- You write that F&R did not mention that the Big Ten Conference had 11 teams and that they « assumed their participants would know that information ». In their paper, Note #3 discusses this point. The authors write that « most people believe the Big Ten has 10 teams, but, in fact, it has 11. ». It seems to me that the authors were aware of this uncertainty. They assumed that, overall, people would have ignorance beliefs 1/10 vs. 9/10 in the class formulation. They further add in the note: « Thus, for some participants, the class ignorance prior may have been 1/11 - 10/11. ».

Given this, you could just leave it as they did, couldn’t you? Another possibility would be, at the end of the survey, to ask a question about it. Something like: in your opinion, how many teams participate in the Big Ten Conference? (You could tailor the ignorance prior at the participant’s level.)

- I do not see any issue with the replacement of GM by IBM.

- I might be too much of an economist here but, in my view, the lack of real incentives in Study 4 is an important deviation from the original study. (People are likely to exert more cognitive efforts if they are paid, especially for significant amounts of money. 10$ here is a large amount given the time spent.) You mention this in Table 7 but not in Table 8. (By the way: you refer to Table 8 in Table 8. Is that a typo?)

- « while others were rounded to one decimal place —> 0.3 ». If I am not mistaken, they use 0.03 not 0.3.

- I think that there are some rationales for the choices of the authors of the original paper for the classification. For item 1 of S1: the chances are 1/7, which is 14.29%. So, assuming participants had to report percent integers, they could choose 14 or 15. So the authors considered both answers as correct. For the sports items: the probability is 1/10 (=10%) if they believe that there are 10 teams and 1/11 (=9.09%) if they think that there are eleven teams. So, they considered both answers as correct. For item 3, I agree that they should have considered 3% and 4% if they used the same method as for item 1. For Study 3, they can have used the same rule as for item 2 from S1 (in the case people thought there were 10 teams).

—> In my opinion, the original approach is very strict in determining which answers fit the class partition beliefs. People are not very good when it comes to probabilities. I think that your approach is more appropriate in this regard. Personally, I would have preferred a more continuous measure of the closeness/distance to one theory relative to the other. But this would bring you too far from the replication. (Maybe as exploratory discussions?)