Shortly after the first experimental findings, Kinsler and Whittaker provided a phenomenological explanation for the subaverage behavior. The main idea in that work was recognizing that the exciton lineshape is commonly a Gaussian, and the photon lineshape is a Lorentzian. With given widths, the convolution between a Gaussian and a Lorentzian (i.e., Voigt function) has a linewidth narrower than the convolution of two Lorentzians (i.e., direct average of the linewidths). However, it does not provide the scaling relation between the polariton linewidth with the number of molecules N , nor does it explain the experimentally observed asymmetry between the UP and LP linewidths. Savona et al. proposed a microscopic model of disordered quantum wells embedded in a microcavity. By solving the nonperturbative coupled equations of motion of the exciton and cavity photon system numerically, they successfully recovered the experimental results by Whittaker et al. in terms of motional narrowing, explaining both the subaverage behavior and why the upper UP is always broader than the LP -due to inter-branch scattering, in which the multiple scattering to all orders is emphasized . Nevertheless, a lot of theoretical controversies are generated and remain unresolved . For example, it is mentioned in Ref. that the motional narrowing effects are more pronounced in a 1D system than in a 2D system, while Ref. made the opposite statement. And it is not clear the necessity of includ-ing the full dispersion band, as well as considering the polariton multiple scatterings. Therefore, it is of great importance to establish a minimal physical model and theory to clarify the above-mentioned ambiguities.