Ordinal Distance, Dominance, and the Measurement of Diversity

The purpose of this chapter is to consider a class of rules for comparing sets of objects¹ in terms of the degrees of diversity that they offer. Such comparisons of sets are important for many purposes. For example, in discussing biodiversity of different ecosystems, one is interested in knowing whether or not one ecosystem is more diverse than another. Similarly, when discussing issues relating to cultural diversities of various communities, one may be interested in knowing how these communities compare with each other in terms of cultural diversity. In the economics literature, there have been several contributions to the measurement of diversity. Weitzman (1992, 1993, 1998) develops a measure of diversity based on cardinal distances between objects. Among other things, Nehring and Puppe (2002) provide a conceptual foundation for cardinal distances in Weitzman’s framework. Weikard (2002) discusses an alternative measure of diversity; Weikard’s measure is based on the sum of cardinal distances between all objects contained in a set.