I think a lot of collisions are unavoidable, for at least one of the skiers/boarders. And boarders have a bigger "blind spot," since they are less pointed towards where they are going, and unpredictable turning is just part of the deal/fun for them - like a surfer taking a sharp cut on a wave.
Responsibility for a collision is different than skiing a bit defensively, safely. I like the code simplicity of the uphill skier - and skier coming up from behind - being responsible to watch for those below or ahead (who don't have eyes in the back of their heads, don't you know).
Skiing defensively, safely, is another, related matter. To me, that is one of the things that makes a better skier safer, often (not counting the high angle yahoo who takes up most of the slope without looking anywhere but waaay downhill.)
To me, that is where lanes come in - not over ultimate responsibility, but just in terms of safety. I always try to ski predictably on a crowded slope, so that anyone fast behind me can predict and avoid me (and so I can avoid folks ahead of me pretty much myself). And I appreciate skiers who stake out a lane in front of me, to let me know how to avoid them, and let me have other lanes to choose from to stay safe, whether I'm faster or slower.
What goes along with that is I always aim to leave options for other skiers from behind and ahead: I leave ample space to the left and to the right, and I try to usually leave a good "lane" open between me and the edge of the run, and between me and other skiers on the other side, so that a faster skier has options around me in both directions - and I've not inadvertently "trapped" or "pinched off" him or her.
I don't make full high angle turns to hog too much of the run, but instead tailor my turns to fit the hill and other skiers, to have me taking up only a modest, appropriate width of hill, not preventing others from skiing. The dude taking up two-thirds of what looks like a green slope is just oblivious, to me. And dangerous, unless the slope is really empty.
Surprise turns are not a good idea on a crowded hill either: just stay rhythmic and predictable, for the most part, when it's crowded. To me, this is why other racers and former racers are so safe for me: I can tell where they are going to be, and they can tell where I will be, whatever their speed. No unpleasant surprises.
For the same reason, I have to be extra careful to make allowances with boarders: that sudden cut many of them love to make, quite naturally, might sweep them right in my path, if I don't allow for it.
On a crowded slope, slalom-like (or short turn carver) skis are a good idea also: they take up a more narrow lane, control speed more easily in less space, and can maneuver more precisely, more readily. You will end up the hero in a lot of otherwise near collisions, seems like.
I'm sure there are other such ways of defensive, safe skiing when that is called for.