  We present stacking polarized intensity as a means to study the polarization
of sources that are too faint to be detected individually in surveys of
polarized radio sources. Stacking offers not only high sensitivity to the
median signal of a class of radio sources, but also avoids a detection
threshold in polarized intensity, and therefore an arbitrary exclusion of
source with a low percentage of polarization. Correction for polarization bias
is done through a Monte Carlo analysis and tested on a simulated survey. We
show that the non-linear relation between the real polarized signal and the
detected signal requires knowledge of the shape of the distribution of
fractional polarization, which we constrain using the ratio of the upper
quartile to the lower quartile of the distribution of stacked polarized
intensities. Stacking polarized intensity for NVSS sources down to the
detection limit in Stokes I, we find a gradual increase in median fractional
polarization that is consistent with a trend that was noticed before for bright
NVSS sources, but is much more gradual than found by previous deep surveys of
radio polarization. Consequently, the polarized radio source counts derived
from our stacking experiment predict fewer polarized radio sources for future
surveys with the Square Kilometre Array and its pathfinders.
