A Theory of Diversity

How can diversity be measured? What does it mean to value biodiversity? Can we assist Noah in constructing his preferences? To address these questions, we propose a multi‐attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set. We develop the basic intuitions and requirements for a theory of diversity and show that the multi‐attribute approach satisfies them in a flexible yet tractable manner. A natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements. The multi‐attribute framework allows one to make this program formally precise. It is shown that the program can be realized if and only if the family of relevant attributes is well‐ordered (“acyclic”). Moreover, there is a unique functional form aggregating dissimilarity into diversity, the length of a minimum spanning tree. Examples are taxonomic hierarchies and lines representing uni‐dimensional qualities. In multi‐dimensional settings, pairwise dissimilarity information among elements is insufficient to determine their diversity. By consequence, the qualitative and quantitative behavior of diversity differs fundamentally.     

薪酬—级别倒挂与公司慈善捐赠

公司的慈善捐赠是直接增进社会福利的有效手段，探究公司捐赠决策的行为逻辑具有重要意义。基于2015—2019年国有企业集团下属A股上市公司数据，考察了公司高管获得高于其所属集团负责人薪酬的薪酬—级别倒挂现象对慈善捐赠的影响。研究发现：薪酬—级别倒挂会促使公司高管出于迎合集团的动机增加慈善捐赠，即薪酬—级别倒挂程度越高，公司的慈善捐赠水平越高。区分慈善捐赠性质的检验表明，薪酬—级别倒挂影响下的捐赠主要是非连续、策略性捐赠，支持了迎合假说。进一步分析发现，迎合动机强烈、迎合难度更高以及迎合效果更好时，薪酬—级别倒挂对公司慈善捐赠的影响更明显。因此，国有企业集团在激励下属公司积极承担社会责任时，可以将其相应的考核机制与薪酬体系结合，从而实现更好的激励效果。