  Using recent empirical constraints on the dark matter
halo--galaxy--supermassive black hole (SMBH) connection from $z=0-7$, we infer
how undermassive, typical, and overmassive SMBHs contribute to the quasar
luminosity function (QLF) at $z=6$. We find that beyond $L_\mathrm{bol} = 5
\times 10^{46}$ erg/s, the $z=6$ QLF is dominated by SMBHs that are at least
0.3 dex above the $z=6$ median $M_\bullet-M_*$ relation. The QLF is dominated
by typical SMBHs (i.e., within $\pm 0.3$ dex around the $M_\bullet-M_*$
relation) at $L_\mathrm{bol} \lesssim 10^{45}$ erg/s. At $z\sim 6$, the
intrinsic $M_\bullet-M_*$ relation for all SMBHs is slightly steeper than the
$z=0$ scaling, with a similar normalization at $M_* \sim 10^{11} M_\odot$. We
also predict the $M_\bullet-M_*$ relation for $z=6$ bright quasars selected by
different bolometric luminosity thresholds, finding very good agreement with
observations. For quasars with $L_\mathrm{bol} > 3 \times 10^{46}$ ($10^{48}$)
erg/s, the scaling relation is shifted upwards by $\sim0.35$ (1.0) dex for
$10^{11} M_\odot$ galaxies. To accurately measure the intrinsic $M_\bullet-M_*$
relation, it is essential to include fainter quasars with $L_\mathrm{bol}
\lesssim 10^{45}$ erg/s. At high redshifts, low-luminosity quasars are thus the
best targets for understanding typical formation paths for SMBHs in galaxies.
