> if Alice prefers Central to Devonshire, and Bob prefers Devonshire to Central, then we could allow Alice and Bob to switch... There would be no incentive to l

> if Alice prefers Central to Devonshire, and Bob prefers Devonshire to Central, then we could allow Alice and Bob to switch... There would be no incentive to lie. To be fair, there is an incentive to lie when you add neighborhood and other preferences to the system. Say Sally, who wants Central, lives near Devonshire and thus is given better odds of getting a spot there. If Dick wants Devonshire but doesn't really care about Central, it gives him incentive to lie and rank Central higher to increase his chances of swapping with Alice. Far from an exotic scenario, this is exactly what happens in the SFUSD system.