Ordinal efficiency and the polyhedral separating hyperplane theorem

• 成果类型: Article
• 署名作者: McLennan, A
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2001.2864
• 发表日期: 2002
• 页码: 435-449
• 关键词: Random assignment; EFFICIENCY; priority; separating hyperplane theorem

摘要

We study problems in which each of finitely many agents must be allocated a single object, based on the agents' rankings of pure outcomes. A random allocation is ordinally efficient if it is not ordinally dominated in the sense of there being another random assignment that gives each agent a first order stochastically dominant distribution of objects. We show that any ordinally efficient random assignment maximizes the sum of expected utilities for some vector of vNM utility functions that are consistent with the given ordinal preferences. One method of proof uses a new version of the separating hyperplane theorem for polyhedra. (C) 2002 Elsevier Science (USA).