  Shaping axi-symmetric planetary nebulae is easier if a companion interacts
with a primary at the top of the asymptotic giant branch. To determine the
impact of binarity on planetary nebula formation and shaping, we need to
determine the central star of planetary nebula binary fraction and period
distribution. The short-period binary fraction has been known to be 10-15% from
a survey of ~100 central stars for photometric variability indicative of
irradiation effects, ellipsoidal variability or eclipses. This survey technique
is known to be biased against binaries with long periods and this fact is used
to explain why the periods of all the binaries discovered by this survey are
smaller than 3 days. In this paper we assess the status of knowledge of binary
central stars discovered because of irradiation effects. We determine that, for
average parameters, this technique should be biased against periods longer than
1-2 weeks, so it is surprising that no binaries were found with periods longer
than 3 days. Even more puzzling is the fact that 9 out of 12 of the irradiated
binaries, have periods smaller than one day, a fact that is starkly at odds
with post-common envelope predictions. We suggest that either all common
envelope models tend to overestimate post-common envelope periods or that this
binary survey might have suffered from additional, unquantified biases. If the
latter hypothesis is true, the currently-known short-period binary fraction is
put in serious doubt. We also introduce a new survey for binary-related
variability, which will enable us to better quantify biases and determine an
independent value for the short period binary fraction.
