We have measured the ratio of doubly to singly charged parent ions of benzene, naphthalene, anthracene, and pentacene using monochromatized synchrotron radiation up to 30 eV above the corresponding threshold. Our measurements show a striking similarity between the ratio of doubly charged to all parent ions and the ratio for helium. Moreover, the magnitudes of the ratios for these molecules scale linearly with their lengths with an amazing accuracy. A high ratio, i.e., a high relative double-photoionization probability, makes a molecule an important source of low-energy electrons that can promote radiation damage of biomolecules [B. Boudaïffa et al., Science 287, 1658 (2000)].