Multidimensional scaling of measures of distance between partitions

The techniques of multidimensional scaling were used to study the numerical behavior of twelve measures of distance between partitions, as applied to partition lattices of four different sizes. The results offer additional support for a system of classifying partition metrics, as proposed by Boorman (1970), and Boorman and Arabie (1972). While the scaling solutions illuminated differences between the measures, at the same time the particular data with which the measures were concerned offered a basis both for counterexamples to some common assumptions about multidimensional scaling and for some conjectures as to the nature of scaling solutions. The implications of the latter findings for selected examples from the literature are considered. In addition, the methods of partition data analysis discussed here are applied to an example using sociobiological data. Finally, an argument is made against undue emphasis upon interpreting dimensions in nonmetric scaling solutions.