a preferred orientation in space, [*the lens population is not randomly oriented*]{}, a fact which can have observable consequences. In particular, given an observable halo property $f({\mathbf{P}},{{\mathbf{\hat n}}})$ that depends on the line of sight projection (e.g. the projected axis ratio or projected substructure mass fraction), the mean value of $f$ over all ${\mathbf{P}}$ halos is simply $${\left\langle f|{\mathbf{P}} \right\rangle}_{halos} = \int \frac{d^2{{\mathbf{\hat n}}}}{2\pi} f({\mathbf{P}},{{\mathbf{\hat n}}}),$$ whereas the mean value of $f$ over all lenses is given by $${\left\langle f|{\mathbf{P}} \right\rangle}_{lenses} = \frac{1}{{\left\langle \sigma_B|{\mathbf{P}} \right\rangle}}
    \int \frac{d^2{{\mathbf{\hat n}}}}{2\pi} \sigma_B({\mathbf{p}}({\mathbf{P}},{{\mathbf{\hat n}}})) f({\mathbf{P}},{{\mathbf{\hat n}}})
\label{eq:losdist}$$ where ${\left\langle \sigma_B \right\rangle}$ is the average value of $\sigma_B$ over all lines of sight, $${\left\langle \sigma_B|{\mathbf{P}} \right\rangle} = \int \frac{d^2{{\mathbf{\hat n}}}}{2\pi} \sigma_B({\mathbf{p}}({\mathbf{P}},{{\mathbf{\hat n}}})).$$ Thus, in general, one expects that the mean value of $f$ over all lenses and over all halos will be different. In the next few sections, we identify a few halo properties that depend on line of sight projection, and determine whether lensing biases induced by triaxiality are likely to be significant.

The Model {#sec:model}
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We estimate the impact of halo triaxiality on the properties of lenses by considering a triaxial isothermal profile. The merit of this approach is its simplicity: because 