Designing Maximally, or Otherwise, Diverse Teams: Group-Diversity Indexes for Testing Computational Models of Cultural and Other Social-Group Dynamics

Given a set of known numbers, there are many measures of the degree of inhomogeneity within the set such as the standard deviation, the relative mean difference, and the Gini coefficient. This paper discusses conceptual issues (such as qualitative versus quantitative diversity, and the group as a population versus as a sample), desired properties (such as symmetry and invariance properties), and technical considerations (such as working with differences versus deviations, or absolute versus squared values) in choosing an index suitable for describing the degree of inhomogeneity or diversity in a group of people or computer agents. In particular, it is argued that the relative mean difference and the Gini coefficient are not well-suited as indexes of cultural diversity. This paper then addresses two apparently neglected inverse problems: Given a pre-specified degree of inhomogeneity, what set of unknown numbers has the desired degree of inhomogeneity? And, in particular, what set has the maximal possible degree of inhomogeneity? The solution requires that the set of permissible numbers be bounded with minimum and maximum values. A key benefit of such inverse procedures is that agent-based groups with pre-selected degrees of cultural diversity can be formed to test hypotheses using the full range of possible diversities and thereby avoid statistical problems due to restriction of range effects.