  In theories in which the parameters of the low energy theory are not unique,
perhaps having different values in different domains of the universe as is
possible in some inflationary models, the fermion masses would be distributed
with respect to some weight. In such a situation the specifics of the fermion
masses do not have a unique explanation, yet the weight provides the visible
remnant of the structure of the underlying theory. This paper introduces this
concept of a weight for the distribution of masses and provides a quantitative
estimate of it from the observed quarks and leptons. The weight favors light
quark masses and appears roughly scale invariant (rho ~ 1/m). Some relevant
issues, such as the running of the weight with scale and the possible effects
of anthropic constraints, are also discussed.
