ABSTRACT
Summary mobility measures induce a complete order on the set of mobility matrices and have the advantage of providing intuitive measurements and frrm rankings. However, it is clear that there are substantial probiPrw; in trying to reduce a matrix of transition probabilities into a single number. This is very much the problem of multidimensional inequality measurement addressed by Maasoumi (l 986), Ebert (l995a), and Shorrocks (1995). Dardanoni ( 199:3) offers the following example of three mobility matrices
[6 .35 o:] [" .3 '] [ ,, .4 ~] P1 = .35 .4 .2;:> ; p2 = .3 .5 ·: ; P:l = .:3 .4 .05 .25 '7 .l .2 .l .2 .I .I ./ The rows denote current state and columns denote future state. Suppose we
use some common summary immobility measures as proposed and discussed by, for instance, Bartholomew (1982) and Conlisk (I 990). Consider the second largest eigenvalue modulus, the trace, the determinant, the mean first passage time, and Bartholomew's measure. These indices are defined below. Any of the three matrices
ON MOBILITY 133
may be considered the most mobile depending on which immobility index is chosen. This is illustrated in the following table, which shows the most mobile mobility matrix according to the different indices.
