  This paper presents four examples of different ways that coordinated
influence operations exert pressure on the prominence of ideas on social
networks. We argue that these examples illustrate the four archetypical paths
to influence: promotion by strengthening, promotion by weakening, demotion by
strengthening, and demotion by weakening. We formalize this idea in a stylized
economic model of the optimal behavior of the influence operator and derive
some predictions about when we should expect each path to be followed. Finally
we sketch out how one might go about quantitatively estimating the key
parameters of (a variant of) this model and how it applies much more broadly
than in the international political influence examples that motivate it.
