Earlier today, this answer to this question was converted to a comment by a moderator. The same moderator subsequently reconverted the comment back into an answer an hour or so later. One of the effects this had was that all comments (including my own) on the answer were also converted to comments on the question, which made it seem like I was commenting on the original question. I was not notified of my comment being moved in this manner. I don't really mind it having happened, but it did make me wonder:

What is the reasoning for the conversion in the first place (rather than, say, only deletion), and why was the decision reversed? Is there a general policy for when answers should be converted to comments, or indeed when the comments on those answers are themselves transferred to comments?

My main reason for asking is purely in the interest of transparency and understanding when such conversions might take place.

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    $\begingroup$ That was a case of doubt. -- Following your flag, I converted the answer to a comment and moved the comments on it (since the comments contained information I felt shouldn't be deleted). -- Then, the OP of the answer explained in a flag why he thought it is an answer, and since the explanation sounded (vaguely) reasonable, I undeleted the answer and deleted the duplicated comments. -- Just that. $\endgroup$
    – Stefan Kohl Mod
    Aug 28, 2021 at 16:35
  • $\begingroup$ @StefanKohl I see. I don’t think the answer answers the question at all, even after its edits to include the word “intuition”. It reveals nothing about amenable group actions, and only a loose idea for why amenable groups are called as such. It’s a good comment, and a good background (as in the very good other answer to the question), but does not answer the question. OP to the question seems to agree. I’m curious what explanation convinced you otherwise. $\endgroup$ Aug 28, 2021 at 17:16
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    $\begingroup$ I said it was a case of doubt. -- That is, I am not convinced it is an answer. Rather -- in dubio pro reo -- the OP convinced me to give it the chance to be judged by the community, by votes. -- Not more. $\endgroup$
    – Stefan Kohl Mod
    Aug 28, 2021 at 18:28
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    $\begingroup$ FWIW I think it is an answer, but just not a very good one. With no disrespect meant to Carlo as a mathematician in general. (I also don't think it's a very good question, as people seem to ask for "intuition" about technical concepts as a kind of catch-all phrase for "tell me a story I will like, but you have to guess what kinds of stories I like".) $\endgroup$
    – Yemon Choi
    Aug 28, 2021 at 20:16

1 Answer 1


For full transparency, this was my request to the moderators after the answer was converted to a comment:

I hope it's OK if I ask why this answer was deleted. The OP asks for intuition on the notion of an amenable action, the answer I propose refers to the measurability or existence of a mean (and I refer to where in the book cited by the OP the mean of the action is constructed). Now this may not be the most complete answer, but it does make a valid attempt at answering the question of the OP (and it does not solely address the etymology). Can't we let votes decide on the merit of the answer?

First of all, a "thank you" to the moderators for considering this request favorably.

The votes (three down, one up) clearly show the lack of merit of the answer, which I think is how the system should work.
Perhaps more relevant: a comment by RW on the answer provided a piece of information on two distinct types of amenability which may well be of interest to the OP and other MO users. This discussion would probably not have happened if the answer would have remained a comment, or at least the discussion would have been more cumbersome (requiring a comment on a comment rather than a comment on an answer).


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