along the short axis of the halo.

The remainder of the paper will explore whether these results have a significant impact on the statistical properties of the halo population. Specifically, we will first consider the ellipticity distribution of lensing galaxies compared to that of galaxies as a whole. We will then discuss how these results affect the predicted quad-to-double ratio, and finally, we will investigate whether lensing halos are expected to have a significantly biased projected substructure mass fraction.

The Projected Axis Ratios of Lensing Halos {#sec:axis}
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As mentioned in the introduction, if one assumes that the ellipticity of the light and that of the mass are monotonically related, then one would naively expect that lensing galaxies that produce quads ought to be more elliptical than the average galaxy because the lensing cross section for quads increases with increasing ellipticity. Similarly, galaxies that produce doubles should tend to be more spherical. In this section, we discuss the impact of halo triaxiality on the distribution of axis ratios for double and quad lenses.

Given a line of sight ${{\mathbf{\hat n}}}$, we can compute the axis ratio $q({{\mathbf{\hat n}}})$ of the projected mass distribution (see Eq. \[eq:qproj\]). Using the distribution of 