(Abridged) We consider the polarization properties of optically thin synchrotron radiation emitted by relativistically moving electron--positron jets carrying large-scale helical magnetic fields. In our model, the jet is cylindrical, and the emitting plasma moves parallel to the jet axis with a characteristic Lorentz factor $Gamma$. We draw attention to the strong influence that the bulk relativistic motion of the emitting relativistic particles has on the observed polarization. We conclude that large-scale magnetic fields can explain the salient polarization properties of parsec-scale AGN jets. Since the typical degrees of polarization are $leq 15%$, the emitting parts of the jets must have comparable rest-frame toroidal and poloidal fields. In this case, most relativistic jets are strongly dominated by the toroidal magnetic field component in the observers frame, $B_phi/B_z sim Gamma$. We also discuss the possibility that relativistic AGN jets may be electromagnetically (Poynting flux) dominated. In this case, dissipation of the toroidal magnetic field (and not fluid shocks) may be responsible for particle acceleration.
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