  We present simulations of multi-year RV follow up campaigns of the {\it TESS}
small exoplanet yield on the Automated Planet Finder telescope, using four
different schemes to sample the transiting planets' RV phase curves. For
planets below roughly 10 M$_\oplus$ we see a systematic bias of measured masses
that are higher than the true planet mass, regardless of the observing scheme
used. This produces a statistically significant difference in the mass-radius
relation we recover, where planet masses are predicted to be too high and too
similar across the entire super-Earth to Neptune radius range. This bias is due
in part to only reporting masses that are measured with high statistical
significance. Incorporating all mass measurements, even those that are
essentially only upper limits, significantly mitigates this bias. We also find
statistically significant differences between the mean number of planets
measured at the 1-, 3-, and 5$\sigma_{\rm K}$ level by the different
prioritization schemes. Our results show that prioritization schemes that more
evenly sample the RV phase curves produce a larger number of significant mass
detections. The scheme that aims to most uniformly sample the phase curve
performs best, followed closely by the scheme which randomly samples, and then
an in quadrature sampling approach. The fourth scheme, out of quadrature,
performs noticeably worse. These results have important implications for
determining accurate planet compositions and for designing effective RV follow
up campaigns in the era of large planet detection surveys such as $K2$, $TESS$,
and $PLATO$.
