So when i was a kid we used to do this thing when we shared a snack. one kid would cut the snack in half and the other would pick which of the two halfs he wants. this way, even though the picker will always have a slight edge, the cut would be pretty fair.
I thought about generalizing this for cakes and for a lot of people. My intuition is:
- let the first two kids do the "cut and pick" routine.
- each kid will get a half of the cake.
- the two kids will repeat this routine with two new kids for their respective pieces.
- repeat this process until all kids have their own peice
I see two big problems with this method. One, is that this will only work for $2^n$ kids. The other is that because "pickers" have a slight edge, and one kid is guaranteed to "descend" from a line of pickers, this edge will become significant with a lot of kids and he will have a big advantage.
What would be a better way of doing this?