  The election control problem through social influence asks to find a set of
nodes in a social network of voters to be the starters of a political campaign
aiming at supporting a given target candidate. Voters reached by the campaign
change their opinions on the candidates. The goal is to shape the diffusion of
the campaign in such a way that the chances of victory of the target candidate
are maximized. Previous work shows that the problem can be approximated within
a constant factor in several models of information diffusion and voting
systems, assuming that the controller, i.e., the external agent that starts the
campaign, has full knowledge of the preferences of voters. However this
information is not always available since some voters might not reveal it.
Herein we relax this assumption by considering that each voter is associated
with a probability distribution over the candidates. We propose two models in
which, when an electoral campaign reaches a voter, this latter modifies its
probability distribution according to the amount of influence it received from
its neighbors in the network. We then study the election control problem
through social influence on the new models: In the first model, under the
Gap-ETH, election control cannot be approximated within a factor better than
$1/n^{o(1)}$, where $n$ is the number of voters; in the second model, which is
a slight relaxation of the first one, the problem admits a constant factor
approximation algorithm.
