  The population of strong lensing galaxies is a sub-set of
intermediate-redshift massive galaxies, whose population-level properties are
not yet well understood. In the near future, thousands of multiply imaged
systems are expected to be discovered by wide-field surveys like Rubin
Observatory's Legacy Survey of Space and Time (LSST) and Euclid. With the
soon-to-be robust population of quadruply lensed quasars, or quads, in mind, we
introduce a novel technique to elucidate the empirical distribution of the
galaxy population properties. Our re-imagining of the prevailing strong lensing
analysis does not fit mass models to individual lenses, but instead starts with
parametric models of many galaxy populations, which include generally ignored
mass distribution complexities and exclude external shear for now. We construct
many mock galaxy populations with different properties and obtain populations
of quads from each of them. The mock `observed' population of quads is then
compared to those from the mocks using a model-free analysis based on a 3D
sub-space of directly observable quad image properties. The distance between
two quad populations in the space of image properties is measured by a metric
$\eta$, and the distance between their parent galaxy populations in the space
of galaxy properties is measured by $\zeta$. We find a well defined relation
between $\eta$ and $\zeta$. The discovered relation between the space of image
properties and the space of galaxy properties allows for the observed galaxy
population properties to be estimated from the properties of their quads, which
will be conducted in a future paper.
