It looks like the spectrum (if you can call it that) is even more varied and complicated than I had anticipated. It seems that the overriding determinant for using initiative is when it's useful for ordering events, but there seems to be some variation on when that's necessary. Some are saying that's only when someone has declared, or has already made, a hostile action. Others use initiative to order actions between PCs when there is no encounter, at least not with another group, which I would probably say falls a bit outside the discussion since I'm specifically asking about the "combat encounter". Those types of "initiative rolls" I would consider more generally to be Dexterity contests between PCs that don't relate directly to the mechanics associated with the combat round. However, some are saying both at the same time, which is fine. Contested checks have varied applications.
I haven't kept up with the thread as it's grown, but I'd like to respond to some of the comments, so I'll just do that in the order they came up.
My answer is - it depends... In short - I don't have any hard rules, I call initiative when it feels right to call it.
First of all, I like, "it depends." It sounds like for you the "triggering event" is based on how you, as DM, feel the tension is building up to the point of initiative being rolled. That's a consideration that hadn't occurred to me in my opening post as my style tends to be more simulationist than narrativist.
I usually follow your method, but possibly not at long distance where not much is actually going to happen.
As for long distance, I don't have my DMG in front of me, but it gives some distances for range of vision under optimal conditions, or am I remembering the playtest? Anyway, the point is that
encounter distance, according to the figures given, could conceivably be something like two miles on a clear day, but I have never set up an encounter where that kind of distance was in use. Not that I never would, but there's usually some kind of intervening topography or trees or whatever, which cuts down visibility to within longbow range at most, so the problem of not much happening hasn't really come up for me.
What I think would be useful are some kind of parameters for distances that sound travels under various conditions. When I've looked into this to establish these things for myself I've been unable to find conclusive numbers for a normal range of hearing. There seems to be a lot of disagreement on the internet over how far away certain sounds can be credibly heard, and humidity, and wind direction and speed seem to play an important role. By my own calculations, the sound of normal conversation drops to the volume of a quiet whisper from about 100' away, which seems like a good benchmark for hearing creatures that aren't trying to be stealthy, but I'm no expert in acoustics and haven't verified my numbers yet.
Something else I forgot to mention in my opening post are the rules for chases in the DMG. This is an initiative-based system for resolving chases and, to me, falls squarely under the umbrella of the combat encounter. Since a chase is mostly movement taking place, it could happen before or after actual fighting, or even without any fighting occurring at all, so it's clear to me that hostile actions, meaning actual attacks, are not really a prerequisite for rolling initiative. In my opinion, it might have been better to have given rules for "encounters", rather than for "combat", but that really just boils down to semantics.
Often a fight starts mid conversation, or a fight is interrupted by a conversation, then starts again and initiative is rerolled.
You see, I wouldn't re-roll necessarily, unless there had been a shift of both parties attitudes away from hostility, because I see this as the continuation of the same encounter. Under normal rules you only roll initiative once and that order holds for the entire encounter, so I'd probably only re-roll if I was using the speed factor variant, which I'm not currently doing, but I am planning on trying it out.
