I didn't say anything about Dungeon World's procedure. In fact in post 813 I indicated my lack of certainty about DW.
In Apocalypse World, here is the resolution procedure for jumping a crevasse. It beging with the framing.
The core framing and resolution principle is set out on p 116 of the rulebook:
Whenever someone turns and looks to you to say something, always say what the principles demand. . . .
Whenever there’s a pause in the conversation and everyone looks to you to say something, choose one of these things [ie a GM move from the list] and say it.
The core principle that governs the making of GM moves is set out on p 117:
Always choose a move that can follow logically from what’s going on in the game’s fiction. It doesn’t have to be the only one, or the most likely, but it does have to make at least some kind of sense.
Generally, limit yourself to a move that’ll (a) set you up for a future harder move, and (b) give the players’ characters some
opportunity to act and react. A start to the action, not its conclusion.
However, when a player’s character hands you the perfect opportunity on a golden plate, make as hard and direct a move as you like. It’s not the meaner the better, although mean is often good. Best is: make it irrevocable.
These principles operate against the background rule (p 109) that "Your job as MC [= GM] is to say everything else: everything about the world, and what everyone in the whole damned world says and does
except the players’ characters."
So a player says that their PC goes somewhere, and then looks to the GM to tell them what they see or find there. The GM makes a move: "There's a crevasse in front of you. It's pretty wide, and is blocking you from going any further." That's the GM
putting the PC in a spot. At this point, it's pretty soft.
Suppose the player asks, "Can I jump it?" and the GM answers, "No, it's too wide". Then if the player declares nevertheless that their PC jumps it, they've handed the GM an opportunity on a plate. The GM can make as hard and direct a move as they like (consistent with the principles) - maybe "You take your running leap, and it's obvious that you've got no hope of making it across. You fall and land on a ledge somewhere down below. Take 3 harm, armour piercing." That's the GM
inflicting harm - in particular, the harm for a 2-story fall onto jagged ground (p 162).
Maybe when the player asks, "Can I jump it?" the GM answers, "It's pretty wide - you're not sure about your chances!" Suppose the player then declares that their PC jumps it nevertheless. Well, the core principle for player-side moves is, "if you do it, you do it" (p 12): "whenever the character does something that counts as a move, it’s the move and the player rolls dice." And this character is "doing it" - as per the rule for the basic move Act Under Fire (p 190),
When you do something under fire, or dig in to endure fire, roll+cool. On a 10+, you do it. On a 7–9, you flinch, hesitate, or stall: the MC can offer you a worse outcome, a hard bargain, or an ugly choice.
You can read “under fire” to mean any kind of serious pressure at all. Call for this move whenever someone does something requiring unusual discipline, resolve, endurance or care.
Jumping a crevasse that is so wide the character is not sure about their chances seems like it requires unusual discipline and resolve - so the player rolls the dice. If they get 10+, they make it. On a 7 to 9, the GM makes a soft move - maybe a hard bargain: "You take your run-up, but just as you get to the edge you have doubts, but you're committed and so you make your leap. You think you're not going to make it, but then you grab hold of the ledge on the other side - but your <whatever> is falling out of your pocket. You don't think you can save it from falling
and pull yourself up". The GM is
taking away their stuff.
On a 6 or less, the GM can make as hard and direct a move as they like - see above.
There's no point at which it's unclear
whose job it is to say what happens next, or
what the parameters are within which they are to say that.