  We examine the luminosity function of white dwarfs (WDs) in the local
``complete'' WD sample ($d<20$ pc) of Holberg et. al. 2008. We find that the
fraction of bright and young WDs is anomalously high among the WDs detected in
multiple systems with main sequence (MS) companions compared to that of the
single WDs and theoretical expectations. This indicates a significant
observation bias against finding relatively faint WDs in multiple systems. At
the bright end ($M_V<11.5$), the amount of WDs with MS companions is
approximately equal to that of single white dwarfs, indicating that $\gtrsim
50\%$ of WDs have MS companions, consistent with the high multiplicity fraction
of early-type MS stars. If true, a significant fraction of WDs in multiple
systems within 20 pc may have not been detected yet, and the number density of
WDs in the solar neighborhood and elsewhere may be up to twice as much as
presently believed.
