A Fair Apportionment of Dividing a Leftover Piece of Cake

Short Answer

A fair apportionment of dividing a leftover piece of cake between two children is to let child #1 cut the cake into two pieces and then to let child #2 pick which piece he or she wants. Consider the following apportionment of dividing the leftover piece of cake among three children. Let the first child cut the cake into two pieces. Then the second child is permitted to cut one of those pieces into two parts. Child #3 can select any of the pieces, followed by child #1 selecting one of the remaining pieces, followed by child #2 who gets the remaining piece. Is this allocation process fair if each child's goal is to maximize the size of his or her own piece of cake?
​
__________ (Yes, No)