  We describe a model-independent integral constraint which defines an upper
limit to the allowed degree of evolution in the ratio of black hole (BH) mass
to host galaxy luminosity or mass, as a function of redshift. Essentially, if
the BH/host ratio is excessive at redshift z, then it would imply that the
total mass density in BHs above some M_BH(min) is larger at that redshift than
at z=0, which is impossible. This argument requires no knowledge of host or BH
properties, only a lower limit to the observed luminosity density in the
brightest galaxies at some z. We calculate this upper limit from a variety of
luminosity and mass functions in different bands from redshifts z=0-2. We show
that it is consistent with passive evolution of spheroid populations (with a
fixed M_BH/M_host relation) in all cases, and provides tighter constraints than
have generally been obtained previously, ruling out at >6 sigma observational
and theoretical estimates suggesting that M_BH/M_host was significantly larger
at high redshifts than locally, although relatively weak (factor ~2 by z=2)
evolution is still allowed. We discuss a variety of possible 'loopholes' or
changes in the BH/host populations and correlations, and show that they
typically lower the upper limits and strengthen our conclusions.
