  We investigate the ability of three-integral, axisymmetric, orbit-based
modeling algorithms to recover the parameters defining the gravitational
potential (M/L ratio and black hole mass Mh) in spheroidal stellar systems
using stellar kinematical data. We show that the potential estimation problem
is generically under-determined when applied to long-slit kinematical data of
the kind used in most black hole mass determinations to date. A range of
parameters (M/L, Mh) can provide equally good fits to the data, making it
impossible to assign best-fit values. We illustrate the indeterminacy using a
variety of data sets derived from realistic models as well as published
observations of the galaxy M32. In the case of M32, our reanalysis demonstrates
that data published prior to 2000 are equally consistent with Mh in the range
1.5x10^6-5x10^6 solar masses, with no preferred value in that range. While the
HST/STIS data for this galaxy may overcome the degeneracy in Mh, HST data for
most galaxies do not resolve the black hole's sphere of influence and in these
galaxies the degree of degeneracy allowed by the data may be substantial. We
investigate the effect on the degeneracy of enforcing smoothness
(regularization) constraints. However we find no indication that the true
potential can be recovered simply by enforcing smoothness. For a given
smoothing level, all solutions in the minimum-chisquare valley exhibit similar
levels of noise. These experiments affirm that the indeterminacy is real and
not an artifact associated with non-smooth solutions. (Abridged)
