Oh, you just have to make your model more interesting. If the involved parties have different value functions for the pizza, cutting can be more advantageous.
Suppose you really like tomatoes and I like everything equally. Than I will make a cut that has slightly more than half of the tomatoes in one set, and everything else in the other. This way I will gain almost all of the pizza (minus half the tomatoes plus epsilon).
Even more extreme, if your utility functions are `context-sensitive'. I.e. suppose there's a grid pattern on the pizza: horizontal mozzarella stripes and vertical ham stripes. I care about getting long mozzarella stripes, but don't want short stripes. Same applies to you and the ham stripes. Of course, the cutter has an advantage there.
Unless they can use tricky psychology to make the small piece look bigger, possibly.
Fair to me is I thought obvious, you cut it then flip a x sided coin.