  Rotations of the electric vector position angle (EVPA) in blazars are often
close to an integral multiple of 180$^\circ$. There are multiple examples of
this in the literature, and our analysis here, of the optical polarization data
from the RoboPol monitoring program, strengthens the evidence by showing that
$n\pi$ rotations occur more frequently than expected by chance. We explain this
with a model consisting of two polarized emission components: a "jet" that is
constant in time, and a "burst" that is variable. The EVPA of the combination
is $\rm EVPA_{jet}$ at both the beginning and the end of the burst, so the net
rotation across the burst must be $n\pi$. Examples are analyzed on the Stokes
plane, where the winding number for the Stokes vector of the combination gives
the value of $n$. The main conclusion is that the EVPA rotation can be much
larger than the physical rotation of the emission region around the axis of the
jet, but this requires the EVPAs of the jet and the burst to be nearly
orthogonal. A shock-in-jet calculation by Zhang et al. can provide a physical
model for our toy model, and in addition automatically gives the needed
orthogonality. The model is illustrated with data on OJ287 published by
Myserlis et al., and we suggest that the large rapid EVPA rotation seen there
might be a phase effect and not representative of a physical rotation.
