Blazars are highly variable active galactic nuclei that emit radiation at all wavelengths from radio to gamma rays. Polarized radiation from blazars is one key piece of evidence for synchrotron radiation at low energies, and it also varies dramatically. The polarization of blazars is of interest for understanding the origin, confinement, and propagation of jets. However, even though numerous measurements have been performed, the mechanisms behind jet creation, composition, and variability are still debated. We performed simultaneous gamma-ray and optical photopolarimetry observations of 45 blazars between 2008 July and 2014 December to investigate the mechanisms of variability and search for a basic relation between the several subclasses of blazars. We identify a correlation between the maximum degree of optical linear polarization and the gamma-ray luminosity or the ratio of gamma-ray to optical fluxes. Since the maximum polarization degree depends on the condition of the magnetic field (chaotic or ordered), this result implies a systematic difference in the intrinsic alignment of magnetic fields in parsec-scale relativistic jets between different types of blazars (flat-spectrum radio quasars vs. BL Lacs) and consequently between different types of radio galaxies (FR I versus FR II).