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Cyan comments on The Domain of Your Utility Function - Less Wrong
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In the standard definition, the domain of the utility function is the set of states of the world and the range is the set of real numbers; the preferences among states of the world are encoded as inequalities in the utility of those states. I read your comment as asserting that there exists real numbers a, b, c, such that a > b, b > c, and c > a. I conclude that you must have something other than the standard definition in mind.
If A is Alaska, B is Boston, and C is California, the preferences involve preferring being in Alaska if you are in Boston, preferring being in Boston if you are in California, and preferring being in California if you are in Alaska. The act of expressing those preferences using a utility function does not imply any false statements about the set of real numbers.
Preferring A to B means that, given the choice between A and B, you will pick A, regardless of where you currently are (you might be in California but have to leave). This is not the same thing as choosing A over B, contingent on being in B.
You can indeed express the latter set of preferences you describe using a standard utility function, but that's because you've redefined them so that they're no longer intransitive.