Mean value for the variance of the imaginary part of $\delta \hat{\mathbf{p}}$ (left), real part of $\delta \hat{\mathbf{p}}$ (center), and their ratio (right), as a function of the polarization fraction normalized to the maximal polarization fraction p_max, for our toy model made of N independent layers with a magnetic field having both an ordered and a random component close to equipartition. The number of layers is varied between 5, 7 and 9 to emphasize uncertainties, with the corresponding ratio f_M = σ_B/B₀ of turbulent to ordered magnetic field varying from 0.7 (thinner lines) to 1.1 (thicker lines) in steps of 0.1 (all values compatible with Planck data). Simulations are produced at 1° of resolution (N_side = 128) and then smoothed to 4° (N_side = 32) as in our study.