Shaping axisymmetric 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 1 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 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.