Can you give an example of circular preferences that aren't contextual and therefore only superficially circular (like Benja's Alice and coin-flipping examples are contextual and only superficially irrational), and that you endorse, rather than regarding as bugs that should be resolved somehow? I'm pretty sure that any time I feel like I have intransitive preferences, it's because of things like framing effects or loss aversion that I would rather not be subject to.