  Political campaigns involve, in the simplest case, two competing campaign
groups which try to obtain a majority of votes. We propose a novel mathematical
framework to study political campaign dynamics on social networks whose
constituents are either political activists or persuadable individuals.
Activists are convinced and do not change their opinion and they are able to
move around in the social network to motivate persuadable individuals to vote
according to their opinion. We describe the influence of the complex interplay
between the number of activists, political clout, budgets, and campaign costs
on the campaign result. We also identify situations where the choice of one
campaign group to send a certain number of activists already pre-determines
their victory. Moreover, we show that a candidate's advantage in terms of
political clout can overcome a substantial budget disadvantage or a lower
number of activists, as illustrated by the US presidential election 2016.
