Transmission errors and influence maximization in the voter model

Abstract

In this paper we analyze the effects of mistakes in opinion propagation in the voter model on strategic influence maximization. We provide numerical results and analytical arguments to show that generally two regimes exist for optimal opinion control: a regime of low transmission errors in which influence maximizers should focus on hub nodes and a large-error regime in which influence maximizers should focus on low-degree nodes. We also develop a degree-based mean-field theory and apply it to random networks with bimodal degree distribution, finding that analytical results for the dependence of regimes on parameters qualitatively agree with numerical results for scale-free networks. We generally find that the regime of optimal hub control is the larger, the more heterogeneous the social network and the smaller the more resources both available to the influencers.

Shielding and Shadowing: A Tale of Two Strategies for Opinion Control in the Voting Dynamics

“…. N for the B-controller, both subject to budget constraints: [29] and other previous work on opinion control in the voter dynamics [23,42,9], we do not limit targeting to binary decisions (target a node with fixed weight or not target it at all) but allow for a continuous distribution of weight allocations.…”

“…Contributions to the literature mostly have focused on developing or evaluating numerical approaches, e.g. in the context of the political campaign problem for continuous opinion dynamics [19], the AB-model [2], the Glauber dynamics [26,24,28], and voting dynamics [23,42,29,[7][8][9]. Some very recent studies have also considered the co-evolution of control topologies and opinion dynamics at comparable time-scales, finding that active participation in influence maximization of many agents can enhance or hinder consensus formation in certain circumstances [6].…”

“…This is not necessarily the case for directed networks. Subsequent work has shown that noise or copying errors [9] and resistance to attempts of control [7] can shift optimal targeting to lower degree nodes in certain parameter regimes. Similar effects can also be observed if optimization is not aimed at achieving maximum vote shares in the stationary state, but rather at a finite time horizon [8].…”

Shadowing and shielding: Effective heuristics for continuous influence maximisation in the voting dynamics

“…Agents are assumed to hold one of two possible binary opinions (A or B) and opinion diffusion follows the classical voter model [27,28], with nodes copying the opinions of neighbours with a probability proportional to the weight of the link connecting them. Further to the standard model, external influence is introduced via zealots as external controllers [26,33,48]. We assume there are two external controllers respectively holding either of the two opinions.…”

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].…”