Fig. 4.

Comparison of the model dynamics ([1] and [2]) for the three hypotheses on political elite response mechanism. Plotted as a function of time in years starting in 1959 are (A–C, Top) $x_r$ (red) and $x_d$ (blue); (A–C, Middle) ${\alpha }_r,{\alpha }_d,{\gamma }_r,{\gamma }_d,\left|b_r\right|,\left|b_d\right|$ (black is overlay of solid red, solid blue, and dashed blue); and (A–C, Bottom) $\left|x_r\right|-\left|x_d\right|$ (purple). For all simulations, $x_r\left(1959\right)=0.3$, $x_d\left(1959\right)=-0.3$, and ${\tau }_x=1$ y. (A) Positive feedback from self-reinforcement (hyp. A): comparison of symmetric versus asymmetric increase in ${\alpha }_r$ and ${\alpha }_d$ over time. $b_r=0.05$, $b_d=-0.05$, ${\gamma }_r={\gamma }_d=0$, and ${\alpha }_d\left(t\right)=\left(0.01\right)\left(t-1959\right)+0.3$. Solid lines correspond to the symmetric conditions ${\alpha }_r\left(t\right)={\alpha }_d\left(t\right)=\alpha \left(t\right)$. While $\alpha \left(t\right)<1$, $x_r$ and $x_d$ remain near the center, and when $\alpha \left(t\right)>1$, they diverge symmetrically away from the center. Dashed lines correspond to the asymmetric conditions ${\alpha }_r\left(t\right)=\left(0.02\right)\left(t-1959\right)+0.3$. In this case $x_r$ diverges sooner and ultimately more significantly than $x_d$ since ${\alpha }_r>1$ sooner than ${\alpha }_d>1$. (B) Positive feedback from reflexive partisanship (hyp. B): comparison of symmetric versus asymmetric increase in ${\gamma }_r$ and ${\gamma }_d$ over time. Conditions are identical to those for A except that the roles of ${\alpha }_r$ and ${\gamma }_r$ are swapped and the roles of ${\alpha }_d$ and ${\gamma }_d$ are swapped. For the symmetric conditions (solid lines), $x_r$ and $x_d$ diverge symmetrically away from the center. For the asymmetric conditions (dashed lines), the asymmetry in the divergence of $x_r$ and $x_d$ is not as significant as in A. (C) Additive response (hyp. C): comparison of symmetric versus asymmetric increase in $\left|b_r\right|$ and $\left|b_d\right|$ over time. ${\alpha }_r={\alpha }_d={\gamma }_r={\gamma }_d=0$, and $b_d\left(t\right)=-\left(\left(0.01\right)\left(t-1959\right)+0.05\right)$. Solid lines correspond to the symmetric conditions $b_r\left(t\right)=\left|b_d\left(t\right)\right|$ and dashed lines to $b_r\left(t\right)=\left(0.02\right)\left(t-1959\right)+0.05$. $x_r$ and $x_d$ linearly track $b_r$ and $b_d$, respectively.