The finding is surprising, but I think their methodology is a bit flawed.

Study 1 shows "Difference-in-Differences analysis of engagement with 154,122 posts by 1068 accounts before and after the policy change". All this tells us is that existing accounts did not have a noticeable change. It doesn't suggest anything about accounts created after where the culture of Twitter (appears) to have shifted quite a bit from before going private.

Basically "okay cool, existing accounts didn't change their behavior". What about new accounts? More anonymous accounts? Can we understand anything else about platform growth and interaction? What about classes of user w/ respect to verified users, anonymous accounts vs accounts tied to real identities?

Study 2 is also very limited to draw that conclusion because people are less likely to honestly report their engagement with content or beliefs that could be punishing in a given political environment. This was most astutely observed by the French polymarket user who crushed it betting on the 2024 election using neighbor-polling methodology [0]. Essentially, it appears to be more reliable to ask about the preferences of a respondent's social circle than ask the respondent directly.

[0] - https://www.cbsnews.com/news/french-whale-made-over-80-milli...