Three Friends, One Restaurant

The board ends on mechanism design: write the rules so honest play is each person’s best move, and the warning that no rule gets every good property at once. This lesson is the oldest version of that warning, from voting.

Before you start. From Auctions & Mechanism Design you have mechanism design: choose a game’s rules so that people acting in their own interest produce the outcome you want, plus the result that no rule can have every good property at once. Here the rule turns many people’s rankings into one group choice, and the same kind of limit appears.