Ordinal aggregation results via Karlin's variation diminishing property\

• 成果类型: Article
• 署名作者: Choi, Michael; Smith, Lones
• 署名单位: University of Iowa; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2016.12.001
• 发表日期: 2017
• 页码: 1-11
• 关键词: Single-crossing property; quasi-concavity; Variation diminishing property; Logsupermodularity; Signed-ratio monotonicity

摘要

When is the weighted sum of quasi-concave functions quasi-concave? We answer this, extending an analogous preservation of the single-crossing property in QS: Quah and Strulovici (2012). Our approach develops a general preservation of n-crossing properties, applying the variation diminishing property in Karlin (1956). The QS premise is equivalent to Karlin's total positivity of order two, while our premise uses total positivity of order three: The weighted sum of quasi-concave functions is quasi-concave if each has an increasing portion more risk averse than any decreasing portion. (C) 2016 Elsevier Inc. All rights reserved.