Resisting Influence: How the Strength of Predispositions to Resist Control Can Change Strategies for Optimal Opinion Control in the Voter Model

Abstract

In this paper, we investigate influence maximization, or optimal opinion control, in a modified version of the two-state voter dynamics in which a native state and a controlled or influenced state are accounted for. We include agent predispositions to resist influence in the form of a probability q with which agents spontaneously switch back to the native state when in the controlled state. We argue that in contrast to the original voter model, optimal control in this setting depends on q: For low strength of predispositions q, optimal control should focus on hub nodes, but for large q, optimal control can be achieved by focusing on the lowest degree nodes. We investigate this transition between hub and low-degree node control for heterogeneous undirected networks and give analytical and numerical arguments for the existence of two control regimes.

Effects of time horizons on influence maximization in the voter dynamics

“…Such a scenario may be appropriate when there is an effect of lock-in, e.g., if agents make one-off decisions about buying an expensive product or generally making decisions when further change is costly. However, as it has been realized by some authors [9,25,29,43], these models may not be appropriate in situations in which agents are subject to various sources of social influence, and decisions can be changed over time. Such decision making can be described by various types of dynamic models of opinion formation for which there is a rich interdisciplinary literature (see, c The author 2018.…”

“…Whereas most modeling effort has been devoted to understanding various facets of opinion dynamics, some recent studies have also started to consider influence maximization for such dynamic models of opinion formation. In this context, previous work has focused on exploring optimal control allocations that maximize influence in the stationary state of the kinetic Ising model [26][27][28], for the AB model [2] and for the voter dynamics [9,25,29,43].…”

“…Recent work [9,25,29,43] has also started to address the question of opinion control in the voter model. Up to our best knowledge, all work in the area has focused on maximizing vote shares in the stationary state, finding that albeit centrality measures cannot exactly predict optimal allocations [43] optimal control will generally focus on high-degree nodes on undirected networks [25,29], at least if the resistance of nodes to control is small [9]. However, the transient dynamics of the voting process can sometimes be long and influence maximization in real-world settings may be targeted at achieving best results in shorter time frames [17].…”

How Does Active Participation Affect Consensus: Adaptive Network Model of Opinion Dynamics and Influence Maximizing Rewiring

“…Recent literature has started to address questions of optimal allocation for the dynamic models of opinion formation, with studies focusing on the voter dynamics [37][38][39][40][41], Ising-like models [42], and variants of AB models [43]. While some studies point to a nuanced picture of optimal allocations depending on noise and details of the goal-functions of the optimizing parties [40,44], a common thread is that optimal allocations are often well approximated by targeting hub nodes [37,39].…”

Transmission errors and influence maximization in the voter model

“…Specifically, [22,24,25] have pointed out that heuristics targeting hub nodes perform very well on undirected heterogeneous networks, even though heuristics based on centrality metrics do not correspond to exactly optimal allocations for all types of networks [22]. This picture has been qualified by some of our recent work which has shown that targeting hub nodes is not necessarily optimal in all situations, e.g., not if agents have a large propensity to resist influence [35] or if time horizons of the influence maximizer are very short [36].…”