Polyisocyanates with a random sequence of (R) and (S) pendant groups follow a chiral "majority rule" : the optical activity of the polymers is dominated by whichever enantiomer is in the majority. In earlier work, this effect was explained theoretically through a mapping of the polymer system onto the random-field Ising model. Here, the theory is extended to a wider class of heteropolymers. The theory predicts that the introduction of achiral pendant groups into the random sequence should have remarkably little effect on the sharpness of the majority-rule curve. It further predicts that correlations in the handedness of neighboring pendant groups should reduce the sharpness of the majority-rule effect, while anticorrelations should enhance the sharpness of this effect.