This equivalence is a feature of the mathematics of infinite utility aggregation itself, not a product of how prospects are compared, so no comparison-method revision can dissolve it.

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Equivalence (in mathematics)(as used in mathematics and logic): When two different things have exactly the same value or outcome—they're interchangeable because they produce identical results.
Infinite utility aggregation(as used in philosophy of mathematics and ethics): A mathematical problem that arises when you try to combine the satisfaction levels of an endless number of people, which creates puzzles that are hard to solve consistently.
Prospects(as used in decision theory and philosophy): Possible future outcomes or scenarios that someone might choose between—like comparing what happens if you pick option A versus option B.
Utility aggregation(as the main framework being described): A method for combining and comparing the well-being or satisfaction of multiple people to make fair decisions.

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