  The ratio of the average tangential shear signal of different weak lensing
source populations around the same lens galaxies, also known as a shear ratio,
provides an important test of lensing systematics and a potential source of
cosmological information. In this paper we measure shear ratios of three
current weak lensing surveys -- KiDS, DES, and HSC -- using overlapping data
from the Baryon Oscillation Spectroscopic Survey. We apply a Bayesian method to
reduce bias in shear ratio measurement, and assess the degree to which shear
ratio information improves the determination of important astrophysical
parameters describing the source redshift distributions and intrinsic galaxy
alignments, as well as cosmological parameters, in comparison with cosmic shear
and full 3x2-pt correlations (cosmic shear, galaxy-galaxy lensing, and galaxy
clustering). We consider both Fisher matrix forecasts, as well as full
likelihood analyses of the data. We find that the addition of shear ratio
information to cosmic shear allows the mean redshifts of the source samples and
intrinsic alignment parameters to be determined significantly more accurately.
Although the additional constraining power enabled by the shear ratio is less
than that obtained by introducing an accurate prior in the mean source redshift
using photometric redshift calibration, the shear ratio allows for a useful
cross-check. The inclusion of shear ratio data consistently benefits the
determination of cosmological parameters such as S_8, for which we obtain
improvements up to 34%. However these improvements are less significant when
shear ratio is combined with the full 3x2-pt correlations. We conclude that
shear ratio tests will remain a useful source of cosmological information and
cross-checks for lensing systematics, whose application will be further
enhanced by upcoming datasets such as the Dark Energy Spectroscopic Instrument.
