  Different formulas relying measurable fragment isotopic observables to the
symmetry energy of excited nuclei have been proposed and applied to the
analysis of heavy ion collision data in the recent literature. In this paper we
examine the quality of the different expressions in the framework of the McGill
Canonical Thermodynamic Model. We show that even in the idealized situation of
canonical equilibrium and in the absence of secondary decay, these formulas do
not give a precise reconstruction of the symmetry energy of the fragmenting
source. However, both isotopic widths and isoscaling appear very well
correlated to the physical symmetry energy.
