Suppose you had a piece of cake to divide up between two people. Each boy wants to get the biggest piece of course. Is there a fair way to make sure each gets half? Most of you probably know the classic answer. One boy cuts, the other chooses. That way the first boy is motivated to make a perfect cut. There are versions out there for multiple boys.
Have you ever tried this in real life? It quickly becomes clear that it is not particularly fair. Get a piece of cake and try to split it in half. It’s hard to do. It’s even harder if you are five years old without a lot of fine motor control. One piece will be significantly bigger than the other. The task of choosing which piece is bigger is much easier than making two equal halves. The second boy has a huge advantage. The unfairness moves to the level of choosing which boy gets assigned which role. Intelligent children will thus try to be the chooser rather than the divider. How do you decide who gets to be the chooser?
You could flip a coin. Flipping a coin is fair. But if you’re going to do that, why not have either of them slice the cake. Rather than flipping to decide roles, the winner of the coin flip gets to directly choose which slice they want. That’s a fair method, why complicate things with roles?
Applied math is hard.