  Goods and services -- public housing, medical appointments, schools -- are
often allocated to individuals who rank them similarly but differ in their
preference intensities. We characterize optimal allocation rules when
individual preferences are known and when they are not. Several insights
emerge. First-best allocations may involve assigning some agents "lotteries"
between high- and low-ranked goods. When preference intensities are private
information, second-best allocations always involve such lotteries and,
crucially, may coincide with first-best allocations. Furthermore, second-best
allocations may entail disposal of services. We discuss a market-based
alternative and show how it differs.
