I downvoted this post (with the implied "despite prominently opposing Alicorn's behaviors when they occured" intended to lend at least some degree of emphasis). We didn't need it. Meta crap is tiresome, doesn't need a new post ever time and that particular subject had already played itself out in the immediate context of the conflict in question. (I downvote most other meta threads too, so this isn't specific.)
I also don't think making this post was the politically optimal move for Silas to make. I tend to downvote people who don't seem to be acting effectively toward their perceived objectives.
Oh, and what the hell, I may as well give an actual answer while I'm here:
When to prohibit Alice from replying to Bob's arguments?
Never. Impement a jolly ignore feature already. It'll make everyone better off. Until that time use the "ignore feature" that everybody already has built in and just don't pay any attention or make any response to people you don't want to listen to.
The above said, I still would mostly avoid replying to Alicorn---or Bob or Alice or whatever the euphemism is supposed to be---if she happened to personally ask me to. Not out of obligation but because I do care to some degree about the preferences of others and also am aware of the cost associated with engaging in public conflict without good reason. (Sometimes I choose to pay that cost, but not always.) I would still reply when there was a position I particularly desired to oppose and when I did so my reply would clearly be addressing the audience and not personally with Ali-Bob-Corn. But if there wasn't a strong need to comment directly on a particular statement I would make my contributions to the conversation via particularly carefully constructed sibling comments and to whatever extent possible draw the attention of the conversation away from the Ali-Bob-Corn social rival and in a direction more useful for whatever my goals happened to be at the time.
There's not (last I checked) a community consensus on the issue, and I'd rather isolate the meta-discussion to its own thread, rather than splattered all over anywhere Alicorn posts a comment.
An ignore feature would indeed be a significant improvement. I'm not convinced that it's strictly necessary or sufficient, but I do think that it would be better to do than not.
In light of recent (and potential) events, I wanted to start a discussion here about a certain method of handling conflicts on this site's discussion threads, and hopefully form a consensus on when to use the measure described in the title. Even if the discussion has no impact on site policy ("executive veto"), I hope administrators will at least clarify when such a measure will be used, and for what reason.
I also don't want to taint or "anchor" the discussion by offering hypothetical situations or arguments for one position or another. Rather, I simply want to ask: Under what conditions should a specific poster, "Alice" be prohibited from replying directly to the arguments in a post/comment made by another poster, "Bob"? (Note: this is referring specifically to replies to ideas and arguments Bob has advanced, not general comments about Bob the person, which should probably go under much closer scrutiny because of the risk of incivility.)
Please offer your ideas and thoughts here on when this measure should be used.