Is it possible to have a preference relation that is complete but not transitive? I've been doing my own reading on non-rational preference relations.
I'm currently under the impression that transitivity follows as a direct result of completeness of preferences. However my (much more advanced colleagues) have told me this is not necessarily the case.
I'm still to understand how this can be. What would such preferences look like?
I'm quite surprised nobody has picked the obvious one:


I prefer rock over scissors.
I prefer scissors over paper.
I prefer paper over rock.


Complete, definitely not transitive.