Consider Eliezer's final remarks in The Allais Paradox (I link purely for the convenience of those coming in in the middle):

Suppose that at 12:00PM I roll a hundred-sided die. If the die shows a number greater than 34, the game terminates. Otherwise, at 12:05PM I consult a switch with two settings, A and B. If the setting is A, I pay you $24,000. If the setting is B, I roll a 34-sided die and pay you $27,000 unless the die shows "34", in which case I pay you nothing.

Let's say you prefer 1A over 1B, and 2B over 2A, and you would pay a single penny to indulge each preference. The switch starts in state A. Before 12:00PM, you pay me a penny to throw the switch to B. The die comes up 12. After 12:00PM and before 12:05PM, you pay me a penny to throw the switch to A.

I have taken your two cents on the subject.

You're right insofar as Eliezer invokes the Axiom of Independence when he resolves the Allais Paradox using expected value; I do not yet see any way in which Stuart_Armstrong's criteria rule out the preferences (1A > 1B)u(2A < 2B). However, in the scenario Eliezer describes, an agent with those preferences either loses one cent or two cents relative to the agent with (1A > 1B)u(2A > 2B).