Rotations of the electric vector position angle (EVPA) in blazars are often close to an integral multiple of 180°. There are many examples of this in the literature, and we strengthen the evidence by showing that, in the RoboPol monitoring program, nπ rotations occur more frequently than otherwise expected by chance. We explain this using 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 EVPAjet at both the beginning and the end of the burst, so the net rotation across the burst must be nπ. Several examples of this model 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. Shock-in-jet calculations can provide a physical model for our toy model and in addition they automatically give the required orthogonality. The model is illustrated with data from the literature on OJ 287. We suggest that the large rapid EVPA rotation seen in OJ 287 might be a phase effect and not representative of a physical rotation.