If the jet supplies energy to the lobes alternately then the larger scale structure of the source will appear more symmetric. The problem with this model is that hotspots are often observed in both lobes. In order to keep both hotspots lit the jet must flip on a timescale less than the synchrotron loss time of the hotspots. This is short compared to both the time for the energy from the core to reach the hotspots and the difference in light travel times from the core and hotspots to the observer. Thus there should have been many flips of the jet since the energy presently being deposited in the hotspots set off from the core, and there should now be no correlation seen between the present core jet direction and the hotspots. The existence of these correlations rules out the flip-flop model (at least for the sources in the observed samples).
If the jet is slightly asymmetric then relativistic beaming will still give an apparently one-sided jet. Superluminal motion (see, for example, Zensus & Pearson 1987) shows that the small scale jets are relativistic and strongly beamed in many cases. The approximate symmetry in the large scale structure of radio sources implies that the jet power differs by less than a factor of a few between the two sides of the source. This is insufficient to overwhelm relativistic beaming and the jet will be an orientation indicator. One can no longer infer, however, that the large scale structure should be exactly symmetric. Any correlations with the jet sidedness must be due to orientation, but the jet power asymmetry will add scatter and might induce correlations between other parameters that depend on the power deposited on each side of the source.
If the jet asymmetry is intrinsic, then the depolarization asymmetry is presumably due to the extra power being deposited in the lobe to which the jet is pointing. This will not of itself lead to a depolarization asymmetry, although it might give a polarization asymmetry. No such asymmetry is found by GCL.
The depolarization asymmetry then has to be caused by an excess of depolarizing material on the counterjet side. Three models can be distinguished (i) internal matter (ii) a cocoon or sheath (iii) foreground material. In the first two cases the simplest models involving more entrainment or a stronger sheath give the asymmetry in the incorrect sense. The lack of depolarization associated with the large RMs seen in Cygnus A (Dreher, Carilli & Perley 1987) and 3C295 (Perley & Taylor 1991) indicates that the Faraday rotation is foreground, ruling out internal depolarization. An excess of foreground material is then either an orientation or environmental effect.