How diverse can spatial measures of cultural diversity be? : results from Monte Carlo simulations on an agent-based model

Cultural diversity is a complex and multi-faceted concept. Commonly used quantitative measures of the spatial distribution of culturally-defined groups 'such as segregation, isolation or concentration indexes' are often only capable of identifying just one aspect of this distribution. The strengths or weaknesses of any measure can only be comprehensively assessed empirically. This paper provides evidence on the empirical properties of various spatial measures of cultural diversity by using Monte Carlo replications of agent-based modeling (MC-ABM) simulations with synthetic data assigned to a realistic and detailed geographical context of the city of Amsterdam. Schelling's classical segregation model is used as the theoretical engine to generate patterns of spatial clustering. The data inputs include the initial population, the number and shares of various cultural groups, and their preferences with respect to co-location. Our MC-ABM data generating process generates output maps that enable us to assess the performance of various spatial measures of cultural diversity under a range of demographic compositions and preferences. We find that, as our simulated city becomes more diverse, stable residential location equilibria are only possible when particularly minorities become more tolerant. We test whether observed measures can be interpreted as revealing unobserved preferences for co-location of individuals with their own group and find that the segregation and isolation measures of spatial diversity are shown to be non-decreasing in increasing preference for within-group co-location, but the Gini coefficient and concentration measures are not.