  It is shown that, in certain circumstances, systems of cultural rules may be
represented by doubly stochastic matrices denoted called possibility
transforms, and by certain real valued possibility densities with inner
product. Using such objects we may characterize a certain problem of
ethnographic and ethological description as a problem of prediction, in which
observations are predicted by properties of fixed points of transforms of pure
systems, or by properties of convex combinations of such pure systems. That is,
ethnographic description is an application of the Birkhoff theorem regarding
doubly stochastic matrices on a space whose vertices are permutations.
