A Novel Interpretation for Opinion Consensus in Social Networks With Antagonisms

Abstract

We take a new perspective for the consensus in DeGroot-type social networks with antagonistic interactions between some pairs of agents. We observe the analogies between social networks and electrical networks. A line with positive (or negative) conductance in the electrical network well corresponds to the cooperative (or antagonistic) interaction in the social network. Then, we introduce a refined definition of effective conductance (EC), which comes from electrical networks, into social networks as a characterization of the overall relationship between a pair of agents. The EC considers the effects of both direct and indirect interactions between the agents. Some EC-based consensus criteria are established by analytical and statistical approaches, showing that the sign of EC is a useful indicator of consensus. The opinion consensus can be generally interpreted as every pair of agents being overall cooperative despite antagonistic interactions, i.e., the corresponding EC being positive. The obtained results provide new insights into the consensus mechanism with clear intuition. Case study of a 15-agent network is provided as an illustration.

From classical to modern opinion dynamics

“…Some recent interesting work related to antagonism includes the following: Yang et al [70] mapped social networks onto electrical networks, with each interaction node between agents being mapped to a link in an electrical network and with the resistance (or rather conductivity) of each link representing the interaction/influence weight of the agents on each other. She used the effective conductance (EC) concept to measure the direct and indirect relationships of a given pair of agents whose interactions are defined by a DeGroot-type update rule: o…”

“…In the update rule it is assumed that w ij = w ji ∈ R. Hence, this model also assumed antagonistic interactions with no assumption on the structure of the graph, and a positive EC that would indicate, overall, the direct and indirect nature of the interactions between a pair of agents. The consensus criteria for this model were considered as well; for more details please see [70] and references therein. Meng [71] considered an antagonistic dynamic on a network with agents that are separated into leaders and followers, and with a topology that switched between M finite digraphs; note that leader/follower roles could also change as a function of changing network topology.…”

Collective Decision Making using Attractive and Repulsive Forces in Markovian Opinion Dynamics

“…Although a form of repulsion in opinion dynamics was explored in [14], we suggest the addition of a repulsive force specifically adapted to the framework in [9], [10] and [11]. Furthermore, we propose to divide the network into collaborative and conflicting agent groups, as has been explored in different ways in [15], [16] and [17]. Our partition consists of two interaction topologies, where the first describes the attractive forces between agents in each group, while the second expresses the way in which repulsive forces act upon agents from different groups.…”

Decision Modeling in Markovian Multi-Agent Systems

“…A form of repulsion in opinion dynamics was explored in [15], but we suggest the addition of a repulsive force specifically adapted to the framework in [10]- [12]. Furthermore, we propose to divide the set of interacting agents into attractive and repulsive groups, as was explored in different ways in [16], [17] and [18]. Our partition stems from the two interaction types that we consider, where the first describes the attractive forces between agents in each group, while the second expresses the repulsive forces between agents from different groups.…”