Running the traders on some r or $\varphi$ might also be useful if we want a logical inductor that try to decide a particular statement $\varphi$ rather than try to decide all statements at the same time. If you want to decide $\varphi$ you could first run the traders on $\varphi$ and later run the traders on ${\varphi }_i$ with a probability proportional to $P_n\left({\varphi }_i\right)$'s influence on $P_n\left(\varphi \right)$. But I think it would be difficult to prove formally that such an approach would improve the inductors speed at deciding $\varphi$, and I don't know if it would work in practice.