Preference structures had by no possible agent

Say that a preference structure is a total, transitive and reflexive relation (i.e., a total preorder) on centered worlds--i.e., world-agent pairs <w,x>. Then there is a preference structure had by no possible agent. This is in fact just an easy adaptation of the proof of Cantor's Theorem.

Let c be my own centered world <@,Pruss>. We now define a preference structure Q as follows. If agent x at world w, where <w,x> is not the same as <@,Pruss>, prefers her own centered world <w,x> to c, then we say that c is Q-preferable to <w,x>; otherwise, we say that <w,x> is Q-preferable to c. Then we say that all the centered worlds that according to the preceding are Q-preferable to c are Q-equivalent and all the centered worlds we said to be less Q-preferable than c are also Q-equivalent. Thus, Q ranks centered worlds into three classes: those less good than c, those better than c and finally c itself.

But now note that no possible agent has Q as her preference structure. First of all, I at the the actual world do not have Q as my preference structure--that's empirically obvious, in that the worlds do not fall into three equipreferability classes for me. And if <w,x> is different from <@,Pruss>, then x's preference-order at w (if any) between c and <w,x> differs from what Q says about the order.

So what? Well, I think this provides a slight bit of evidence for the idea that agents choose under the guise of the good.