Decades ago, my brother posited to me a the following scenario: When 2 children are cutting up a slice of cake to share, you should have one cut the cake in two and the other pick which slice they want. This way, the cutter is incentivized to try to cut the pieces as equally as possible. If they aren't equal, the picker will pick the bigger slice and the cutter will miss out.
My brother's question was this: Could a system for dividing a state into districts be similarly worked out?