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Inferring cosmological parameters from time-delay strong lenses requires asignificant investment of telescope time; it is therefore tempting to focus onthe systems with the brightest sources, the highest image multiplicities andthe widest image separations. We investigate if this selection bias caninfluence the properties of the lenses studied and the cosmological parametersthat are inferred. Using a population of lenses with ellipsoidal powerlawdensity profiles, we build a sample of double and quadruple image systems.Assuming reasonable thresholds on image separation and flux, based on currentlens monitoring campaigns, we find that the typical density profile slopes ofmonitorable lenses are significantly shallower than the input ensemble. From asample of quadruple image lenses we find that this selection function canintroduce a 3.5% bias on the inferred time-delay distances if the ensemble ofdeflector properties is used as a prior for a cosmographical analysis. Thisbias remains at the 2.4% level when high resolution imaging of the quasar hostis used to precisely infer the density profiles of individual lenses. We alsoinvestigate if the lines-of-sight for monitorable strong lenses are biased.After adding external convergence, $\kappa$, and shear to our lens populationwe find that the expectation value for $\kappa$ is increased by 0.004 and 0.009for doubles and quads respectively. $\kappa$ is degenerate with the value of$H_0$ inferred from time delays; fortunately the shift in $\kappa$ only inducesa 0.9 (0.4) percent bias on $H_0$ for quads (doubles). We therefore concludethat whilst the properties of typical quasar lenses and their lines-of-sight dodeviate from the global population, the total magnitude of this effect islikely a subdominant effect for current analyses, but has the potential to be amajor systematic for samples of $\sim$25 or more lenses.

Observational selection biases in time-delay strong lensing and their impact on cosmography