John Broome's arguments establish that if two options are not incomparable, then small improvements to one must tip rational preference, a constraint incomparability violates and thus generates inconsistent choice behavior.

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Incomparable(comparative evaluation of choices): When two or more options are so different in kind that you can't really measure them against each other to say which is better—like comparing a beautiful sunset to a delicious meal.
Inconsistent choice behavior(the problematic outcome that results from the incomparability violation): Making decisions that contradict each other—saying you prefer one thing over another in one situation, but then making the opposite choice in a similar situation.
John Broome(The statement references his specific arguments about rational preference): A contemporary British philosopher who specializes in decision theory and ethics, particularly how we should make rational choices between different options.
Rational preference(the axioms being questioned): The idea that a logical person's choices follow consistent rules—like preferring A to B and B to C means preferring A to C.

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