Incidentally, if given the choice, the agent would choose option 1 over option 3. When making choices, unlosing agents are indistinguishable from vNM expected utility maximisers.

Or another way of seeing it, the unlosing agent could have three utility functions remaining: A>B>C, B>C>A, and C>A>B, and all of these would prefer option 1 to option 3.

What's more interesting about your example is that it shows that certain ways of breaking transitivities are better than others.