As a moderator, you are inevitably faced with users who legitimately have problems with decisions you make. Often, you may be able to discuss the decision with them and reach a consensus, but sometimes this may not be possible. How can you reliably tell when further discussion is doing more harm than good? At what point should you simply cut off the discussion and enforce your decision?
I think this is going to come down to recognizing a change in the user's behavior.
- If a user is generally chatty and is now responding with terse comments, there's a good chance they don't care any more
- If a user is responding just to get in the last word (eg. "Ok.", "I get it.", "Ok thanks", "Thank you.", etc), there's a good chance they don't care any more
- If the user repeats the same arguments, there's a good chance they don't care any more
- If the user attempts to rally their troops, even after others have moved on, there's a good chance they don't care any more
- If the user rejects any argument that doesn't support their point of view (even from 3rd parties), there's a good chance they don't care any more
I'd cut off the discussion after it reached any of those points with a simple "Thanks for your concern. I appreciate your arguments, but we are going to have to disagree in this case. Our decision stands." Your options at this point include simply locking the conversation to prevent them getting in the last word, or to simply ignore it if they attempt to prod you further.
People react in different ways, but typically they employ epigrammatic behaviour in their language which are often generic replies, rather than a legitimate argument that they are putting forward to you. This may be essentially a sign of defeat. On the other hand, someone who continually repeats their argument without acknowledging your input may also be lacking in interest.
The long and short of it is when people stop directly replying to you, then you know you will get no further.
Just with any kind of consensus (reaching terms accepted by all of the parties), it is just not always possible, especially in large communities. I had experience in a community of LARP rules designers, with around 3-4 people active at the same time at most, and sometimes we still failed too agree on some point. In a community of 10 users reaching consensus is just impossible most of the time, there will always be someone who is not satisfied fully.
After some time of discussion that is either specified, or after big enough amount of members asking for it, if consensus was not found in a free discussion, a voting took place. In our small LARP designers community we typically had to choose one of the two options, so it was not hard. Sometimes we asked members that were not active at the moment, as they were more interested in other parts of the rules, but it was mostly enough to just appoint one arbiter. In a community of 10 people where everyone has equal rights, you can just have something like SE Meta voting.
Consensus is good if you reach it, but again, most of the time it's simply not possible. And if you had to resort to voting again, you just have to say to the unsatisfied users that it's said, but not everyone's preferences can actually be applied.