Measuring Aspects of Mobility, Polarization and Convergence in the Absence of Cardinality: Indices Based Upon Transitional Typology

Abstract

Social Mobility, Equality of Opportunity, Polarization, Convergence and Segmentation can each be construed as describing a particular transitional process between departure and arrival state population distributions. Frequently indices of their extent are based upon variables that have cardinal measure, however often the terms apply to groupings that are ordinal or categorical, devoid of meaningful cardinal distance, relating to transitions between non-comparable states (as with generational transitions from parental socio-economic class to a child’s educational or health status). In such contexts measurement must rely upon the anatomy of the transition process without dependence on cardinal measure. Accordingly, here indices and tests, applicable in both cardinal and ordinal environments, based upon the structure of an underlying transition process are proposed and implemented. The tools have diverse application, in illustration 3 examples from Canadian Generational relationships, the world size distribution of Gross National Product per capita and Chinese Social to Educational Class Structures are employed revealing many interesting features of transitional behaviors.