  A long line of work in social psychology has studied variations in people's
susceptibility to persuasion -- the extent to which they are willing to modify
their opinions on a topic. This body of literature suggests an interesting
perspective on theoretical models of opinion formation by interacting parties
in a network: in addition to considering interventions that directly modify
people's intrinsic opinions, it is also natural to consider interventions that
modify people's susceptibility to persuasion. In this work, we adopt a popular
model for social opinion dynamics, and we formalize the opinion maximization
and minimization problems where interventions happen at the level of
susceptibility.
  We show that modeling interventions at the level of susceptibility lead to an
interesting family of new questions in network opinion dynamics. We find that
the questions are quite different depending on whether there is an overall
budget constraining the number of agents we can target or not. We give a
polynomial-time algorithm for finding the optimal target-set to optimize the
sum of opinions when there are no budget constraints on the size of the
target-set. We show that this problem is NP-hard when there is a budget, and
that the objective function is neither submodular nor supermodular. Finally, we
propose a heuristic for the budgeted opinion optimization and show its efficacy
at finding target-sets that optimize the sum of opinions compared on real world
networks, including a Twitter network with real opinion estimates.
