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Social influence is largely recognized as a key factor in opinion formationprocesses. Recently, the role of external forces in inducing opiniondisplacement and polarization in social networks has attracted significantattention. This is in particular motivated by the necessity to understand andpossibly prevent interference phenomena during political campaigns andelections. In this paper, we formulate and solve a targeted interventionproblem for opinion displacement minimization on a social network.Specifically, we consider a min-max problem whereby a social planner (thedefender) aims at selecting the optimal network intervention within her givenbudget constraint in order to minimize the opinion displacement in the systemthat an adversary (the attacker) is instead trying to maximize. Our resultsshow that the optimal intervention of the defender has two regimes. For largeenough budget, the optimal intervention of the social planner acts on all nodesproportionally to a new notion of network centrality. For lower budget values,such optimal intervention has a more delicate structure and is ratherconcentrated on a few target individuals.

Targeting interventions for displacement minimization in opinion dynamics