If there were three players, B and C would both call at half, cutting out player A.
You can't solve this by letting the cutter also call out, because you can't trust him to both cut and choose at the same time.
You can with certain types of pizza cutters. With this sort (http://www.amazon.com/RSVP-World-Class-Pizza-Cutter/dp/B0000...) for example you can propose a cut by aligning the cutter before actually performing the cut.
If you can't trust the cutter to cut the slice he said he was going to cut for himself, after demonstrating the proposed cut, then you can't trust the cutter to not simply devour the entire pizza right there in front of everybody.
The guy does have a knife after all ... what are the others going to do to stop him!
If there were three players, B and C would both call at half, cutting out player A.
You can't solve this by letting the cutter also call out, because you can't trust him to both cut and choose at the same time.