Suppose you’ve got 1000 students to assign to two schools, each with 500 slots available. Everyone prefers the Good School to the Bad School. Which of the following is a fair way to decide who goes where?
Method A: Give each student a coin to flip and count on the Law of Large Numbers to insure that just about exactly 500 will flip heads. Those students go to the Good School.
Method B: Randomly assign each student to one of two groups. Then flip a single coin to determine which group goes to the Good School.
Method C: After taking note of the fact that, coincidentally, exactly half the students are white and half are black, flip a single coin to determine which race goes to the Good School.
Method D: Assign all the white students to the Good School.
(There’s also of course Method D-prime, where you assign all the black students to the Good School, but I don’t think we need to consider this one separately.)
I ask this question because economists have been very involved with the design of school-allocation mechanisms, particularly in Boston, and one of the things they worry about is fairness. So it seems important to stop and think about what fairness means in this context.