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.
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.