On further reflection: I'd thought of raising the question of which situations cut/choose does work. Generally it seems to be where an allocation-division decision is being made, and the allocation is largely simultaneous with the division, with both parties having equal information as to value. Or so it seems to me, though I think the question's worth thinking about more thoroughly.

That's a subset of multi-party decisionmaking situations, though it's a useful one to keep in mind.

I vaguely remember someone winning a noble prize for economics for coming up with ways to apply cut/choose in financial transactions but I couldn't find it in a quick Google. It may have been nearly 20 years ago though.