Chapter 3: Measuring Directional Mobility: The Bartholomew and Prais-Bibby Indices Reconsidered

This paper attempts to interpret the Bartholomew (1973) index of mobility in terms of a directional mobility index based on the one-step expected states of movement corresponding to a specific state of transition matrix. A partial ordering of directional mobility of a general state of transition matrices, referred to as “upward mobility favoring sequential averaging (UMFSA),” is proposed using the algebraic equivalent of the generalized Lorenz ordering of expected states. When the underlying mobility depends on the initial distribution of the states, using a Bayesian approach, the indices are reexamined for a general class of matrices. This enables us to interpret the Prais (1955) and Bibby (1975) mobility index in this framework.