  The weak gravitational lensing of distant galaxies by large-scale structure
is expected to become a powerful probe of dark energy. By measuring the
ellipticities of large numbers of background galaxies, the subtle gravitational
distortion called "cosmic shear" can be measured and used to constrain dark
energy parameters. The observed galaxy ellipticities, however, are induced not
by shear but by reduced shear, which also accounts for slight magnifications of
the images. This distinction is negligible for present weak lensing surveys,
but it will become more important as we improve our ability to measure and
understand small-angle cosmic shear modes. I calculate the discrepancy between
shear and reduced shear in the context of power spectra and cross spectra,
finding the difference could be as high as 10% on the smallest accessible
angular scales. I estimate how this difference will bias dark energy parameters
obtained from two weak lensing methods: weak lensing tomography and the shear
ratio method known as offset-linear scaling. For weak lensing tomography,
ignoring the effects of reduced shear will cause future surveys considered by
the Dark Energy Task Force to measure dark energy parameters that are biased by
amounts comparable to their error bars. I advocate that reduced shear be
properly accounted for in such surveys, and I provide a semi-analytic formula
for doing so. Since reduced shear cross spectra do not follow an offset-linear
scaling relation, the shear ratio method is similarly biased but with smaller
significance.
