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

Who Cares More? Allocation with Diverse Preference Intensities