I'm one of those people who feels personally called out by xkcd's "Duty Calls" ("someone is wrong on the internet").
(Not as much as I used to. At some point I stopped reading most of the subreddits that I would argue on, partly for this reason, and Hacker News, for unrelated reasons, and now I don't do it as much.)
As pastimes go, there's nothing particularly wrong with internet arguments. But sometimes I get involved in one and I want to stop being involved in one and that's not easy.
I could just, like, stop posting. Or I could let them say something, and then respond with something like, "yeah, I'm still not convinced, but I don't really have time to get into this any more". But then the other person wins, and that's terrible. It potentially looks to onlookers like I stopped because I couldn't find something to say any more. And in at least some cases, it would feel kind of rude: if they've put a lot of thought into their most recent post, it's a bit dismissive to just leave. In the past, when people have done that to me, I've disliked it, at least some times. (Well, at least once. I remember one specific occasion when I disliked it, and there may have been others.)
Another thing I could do is respond to their most recent post, and then say "and now I'm done". But that feels rude, too, and I certainly haven't liked it when people have done it to me. (Why not? It puts me in the position where I don't know whether to respond. Responding feels petty, and kind of a waste of time; not responding feels like they win, and that's terrible.) If they do reply, then I'm shut off completely; I can't even make a minor clarification on the order of "no, you somehow interpreted me as saying exactly the opposite of what I actually said".
So I don't like those tactics. There are probably mental shifts I could make that would bring me more inclined towards them, but… about a year ago I came up with another tactic, which has seemed quite helpful.
What I do now is say something to the effect of: "after this, I'm limiting myself to two more replies in this thread."
This has various advantages. It feels less rude. It doesn't look like I'm quitting because I have no reply. It helps the conversation reach a more natural conclusion. And it also feels a lot easier to do, partly for the above reasons and partly for the normal reasons precommitment helps me to do things.
For some quantitative data, I went over my reddit history. It looks like I've used it ten times. (I don't think I've ever used it outside of reddit, though I initially thought of this after an argument on Facebook.)
In thread #5, I made 11 comments in total; but in others, my max comment count was 6. This feels like I mostly did a decent job of not getting sucked in too deeply. And since I generally got the last word in (threads #2 and #7 were the only exceptions), I think (though I don't specificly remember) I rarely had the feeling of "if I don't reply now then they win and that's terrible". Thread #7 is the only one I think I still feel lingering resentment about. From before I thought of this tactic, I can think of at least two arguments where I didn't get the last word and I still feel lingering resentment. (One is the argument that triggered me to think of this tactic.)
So generally this seems like a success. Ideally we'd compare to a world where I didn't think of this tactic, but I'm not really sure how to do that. (We could go over my reddit arguments where I didn't use it, but that's clearly going to have sampling bias. We could go over my reddit arguments from before I thought of it, but we can't know when I would have used it or how things would have progressed. Possible experiment: going forward, each time I want to limit my future replies, I toss a coin for whether I actually do it in that comment. Keep track of when I did this. I am unlikely to actually run this experiment.) For a way it plausibly might not have been a success: I suspect it's the case that having limited my total investment, I spent more effort on many of these comments than I would have otherwise. If these arguments would have ended just as quickly in any case, then this tactic caused me to spend more time and effort on them.
I'm a bit surprised that I only ran into the two-more-comments limit once. A part of me would like to interpret that along the lines of: once I started putting more effort into my comments, I demolished my opponents' arguments so thoroughly that they accepted defeat. But this seems unlikely at best.
I will say that none of these comment chains felt like collaborative discussions. Some of them started that way, but by the end, they all just felt like "I am right and you are wrong". (This is not very virtuous of me, I admit.) My thinking had been that this tactic would be most valuable in collaborative discussions. But it seems I don't have many of those on reddit, at least not ones that I spend much time on. So, no direct evidence on that yet.
I'm not sure how to handle replies to other people, or replies in subthreads other than the main one. A strict wording would suggest that I should count subthreads against the limit, but I haven't so far and it hasn't caused me problems. Even a weak wording would suggest that I should count replies to other users against the limit, but I've only had one of those and didn't reach the limit whether you count them or not.
I'd ideally like to have a get-out clause like "…unless I actually decide that replying after that is worth my time". But I'm not quite sure that's the "unless" that I want. (Plus it seems kind of rude, but it's not like I'm being super polite as-is.) Anyway, I haven't needed that clause yet.
As I've gotten older, I've become more and more fine with just leaving an internet argument. The *other guy is winning* feeling is 95% gone.
Now, that doesn't mean I won't make a comment or two, but if the other person wants to get into a back and forth that seems like it's going to be draining I'm completely fine with just not participating anymore.
All this to say is that maybe it'll get easier for some?
(FWIW, I'm ~40 and I've been arguing on the internet since I was 12-ish)
What I've usually done in such situations is to reply to the last message and say something like "I'm not planning to continue this discussion; please feel free to have the last word. If there's something further that you particularly want a response to, say so and I'll respond, but then that's it."
I think "at most two more replies" is probably better, not least because you can say it more briefly.
Me too: I've never tried pre-announcing my done-ness, or trying to ramp down that slowly. But I can imagine it's more effective than my normal mechanism of being clear in my last response that I'm unlikely to participate further.
I do think that the internal commitment to stop engaging and the external announcement that you're in exit mode are both very important, and the specific form of them probably less so.
I use this exact policy in some situations. I've found that once I announce "two remaining comments" it generally manages to wrap up in one.
It potentially looks to onlookers like I stopped because I couldn't find something to say any more.
This seems measurable, in principle.
For a way it plausibly might not have been a success: I suspect it's the case that having limited my total investment, I spent more effort on many of these comments than I would have otherwise. If these arguments would have ended just as quickly in any case, then this tactic caused me to spend more time and effort on them.
This seems unlikely given the number of times you didn't hit the limit.
Anyway, I haven't needed that clause yet.
Probably a result of the non-collaborative nature/feel.
If you'd like to break the habit of getting into internet arguments in the first place, this might be the right thing (for YouTube):