Your example bet is a probabilistic mixture of two options: $0 and $2. The agent prefers one of the options individually (getting $2) over any probabilistic mixture of getting $0 and $2.
In other words, your example rebuts the claim that an EUM can’t prefer a probabilistic mixture of two options to the expectation of those two options. But that’s not the claim I made.
Your example bet is a probabilistic mixture of two options: $0 and $2. The agent prefers one of the options individually (getting $2) over any probabilistic mixture of getting $0 and $2.
In other words, your example rebuts the claim that an EUM can’t prefer a probabilistic mixture of two options to the expectation of those two options. But that’s not the claim I made.