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A long line of work in social psychology has studied variations in people'ssusceptibility to persuasion -- the extent to which they are willing to modifytheir opinions on a topic. This body of literature suggests an interestingperspective on theoretical models of opinion formation by interacting partiesin a network: in addition to considering interventions that directly modifypeople's intrinsic opinions, it is also natural to consider interventions thatmodify people's susceptibility to persuasion. In this work, motivated by thisfact we propose a new framework for social influence. Specifically, we adopt apopular model for social opinion dynamics, where each agent has some fixedinnate opinion, and a resistance that measures the importance it places on itsinnate opinion; agents influence one another's opinions through an iterativeprocess. Under non-trivial conditions, this iterative process converges to someequilibrium opinion vector. For the unbudgeted variant of the problem, the goalis to select the resistance of each agent (from some given range) such that thesum of the equilibrium opinions is minimized. We prove that the objectivefunction is in general non-convex. Hence, formulating the problem as a convexprogram as in an early version of this work (Abebe et al., KDD'18) might havepotential correctness issues. We instead analyze the structure of the objectivefunction, and show that any local optimum is also a global optimum, which issomehow surprising as the objective function might not be convex. Furthermore,we combine the iterative process and the local search paradigm to design veryefficient algorithms that can solve the unbudgeted variant of the problemoptimally on large-scale graphs containing millions of nodes. Finally, wepropose and evaluate experimentally a family of heuristics for the budgetedvariation of the problem.

Opinion Dynamics with Varying Susceptibility to Persuasion via Non-Convex Local Search