A point of terminology: “utility function” usually refers to a function that maps things (in our case, outcomes) to utilities. (Some dimension, or else some set, of things on the x-axis; utility on the y-axis.) Here, we instead are mapping utility to frequency, or more precisely, outcomes (arranged — ranked and grouped — along the x-axis by their utility) to the frequency (or, equivalently, probability) of the outcomes’ occurrence. (Utility on the x-axis, frequency on the y-axis.) The term for this sort of graph is “distribution” (or more fully, “frequency [or probability] distribution over utility of outcomes”).
To the rest of your comment, I’m afraid I will have to postpone my full reply; but off the top of my head, I suspect the conceptual mismatch here stems from saying that the curves are meant to “quantify betterness”. It seems to me (again, from only brief consideration) that this is a confused notion. I think your best bet would be to try taking the curves as literally as possible, attempting no reformulation on any basis of what you think they are “supposed” to say, and proceed from there.
A point of terminology: “utility function” usually refers to a function that maps things (in our case, outcomes) to utilities. (Some dimension, or else some set, of things on the x-axis; utility on the y-axis.) Here, we instead are mapping utility to frequency, or more precisely, outcomes (arranged — ranked and grouped — along the x-axis by their utility) to the frequency (or, equivalently, probability) of the outcomes’ occurrence. (Utility on the x-axis, frequency on the y-axis.) The term for this sort of graph is “distribution” (or more fully, “frequency [or probability] distribution over utility of outcomes”).
To the rest of your comment, I’m afraid I will have to postpone my full reply; but off the top of my head, I suspect the conceptual mismatch here stems from saying that the curves are meant to “quantify betterness”. It seems to me (again, from only brief consideration) that this is a confused notion. I think your best bet would be to try taking the curves as literally as possible, attempting no reformulation on any basis of what you think they are “supposed” to say, and proceed from there.
I will reply more fully when I have time.