For what it's worth -- I had one exchange with the person in question pretty early on, decided based on their response that the conversation wasn't going to go anywhere useful, and dropped it.

But I mostly refrained from downvoting them initially because there were people I respected who were continuing the discussion with every indication that it was being productive, and I value productive discussion even if I'm not getting anything out of it personally. (There are a lot of exchanges on this site that kinda sound like gibberish to me, and in at least some cases I'm fairly confident that this is because I don't understand the issue well enough to participate usefully in the discussion even as an observer, not because the participants are in fact spouting gibberish.)

After a very short while I stopped reading any of the comments on that thread except to sample them every once in a while to see if they were going anywhere, and it seemed pretty clear that they weren't. At that point I started downvoting everyone involved on the grounds that I want less high-volume discussion that makes no progress.

No general lesson here, just another data point.