If A is better than B and B is better than C, must A be better than C?

If A, B and C are evaluated using a single numeric value, like size or speed then this would be the case.

Suppose that A, B and C are evaluated in 3 different categories. The three different categories are equally important and a score in one can not be compared to a score in another. We say that one of A, B or C is the best if they beat each of the others in at least 2 out of the 3 categories. But suppose this is not the case.

Here are the scores that A, B and C get in the 3 categories:
A: 4,5,6
B: 3,7,3
C: 1,6,7

A is better than B in two categories. B is better than C is two categories and C is better than A in two categories. What can we conclude?