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