Figure 4.

(Top left panel) Polarization ${ẑ}_{\mathcal{U}}^{\ast }=1-{ŷ}_{\mathcal{U}}^{+\ast }$ of the unbiased agent population as a function of the average signal mix ${\widehat{x}}_{\mathcal{U}}^{\ast }$ in the steady state calculated as $\mathrm{erfc}\left.\left({\widehat{x}}_{\mathcal{U}}^{\ast }-1/2\right)/\left(\sqrt{2}\sigma \left({\widehat{x}}_{\mathcal{U}}^{\ast }\right)\right)\right)$/2, with $\sigma \left({\widehat{x}}_{\mathcal{U}}^{\ast }\right)$ given by Eq. (5) . (Top right panel) Expected accuracy (Eq. (6)) as a function of the initial signals’ informativeness $p$. (Bottom left panel) Expected accuracy (Eq. (6)) as a function of the fraction $f$ of biased agents. (Bottom right panel) Behaviour of the accuracy-maximizing value $f^{\ast }$ and of the corresponding accuracy $\mathcal{A}\left(G\mid f=f^{\ast }\right)$ as functions of $k$ . In the first three panels the model’s parameters are $n=10^3$, $q=1$, $k=8$, while the parameters in the last panel are $n=10^3$, $q=1$, $p=0.53$. In all cases we assume $X=+1$ without loss of generality.