Entropy, desegregation, and proportional rationing

• 成果类型: Article
• 署名作者: Moulin, Herve
• 署名单位: University of Glasgow; HSE University (National Research University Higher School of Economics)
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2015.12.002
• 发表日期: 2016
• 页码: 1-20
• 关键词: assignment; Bipartite rationing; proportionality; segregation; Consistency; entropy

摘要

An assignment of students to schools displays zero-segregation if all schools have the same distribution of the different types of students (ethnic, geographical, gender). We axiomatize the choice of an optimally desegregated assignment under arbitrary capacity constraints. The celebrated Consistency axiom, together with standard rational choice requirements, identify the choice rule minimizing a canonical index of proportional fairness: the entropy of the assignment matrix. This is an alternative vindication of the Mutual Information index of segregation recently characterized in Frankel and Volij (2011). A similar result holds in the capacity-constrained extension of the bipartite rationing model: there we must minimize the entropy of the rationing matrix augmented by individual deficits. (C) 2015 Elsevier Inc. All rights reserved.