We have used the very large Jodrell Bank VLA Astrometric Survey/Cosmic Lens All-Sky Survey 8.4-GHz surveys of flat-spectrum radio sources to test the hypothesis that there is a systematic alignment of polarization position angle vectors on cosmological scales of the type claimed by Hutsemekers et al. (2005, Cat. <J/A+A/441/915>). The polarization position angles of 4290 sources with polarized flux density 1mJy have been examined. They do not reveal large-scale alignments either as a whole or when split in half into high-redshift (z>=1.24) and low-redshift subsamples. Nor do the radio sources which lie in the specific areas covered by Hutsemekers et al. (<J/A+A/441/915>) show any significant effect. We have also looked at the position angles of parsec-scale jets derived from very long baseline interferometry observations and again find no evidence for systematic alignments. Finally, we have investigated the correlation between the polarization position angle and those of the parsec-scale jets. As expected, we find that there is a tendency for the polarization angles to be perpendicular to the jet angles. However, the difference in jet and polarization position angles does not show any systematic trend in different parts of the sky.