Voter and Majority Dynamics with Biased and Stubborn Agents

Abstract

We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the {\em preferred opinion}. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is $\Theta (\log N)$, where $N$ is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.

References in corpus (2)

• Does a Single Zealot Affect an Infinite Group of Voters ?
• On the Role of Zealotry in the Voter Model

Cited by in corpus (6)

• Recent advances in opinion propagation dynamics: A 2020 Survey
• Forecasting elections results via the voter model with stubborn nodes
• Divergence and Consensus in Majority Rule
• Phase Transitions in Biased Opinion Dynamics with 2-choices Rule
• Voter-like dynamics with conflicting preferences on modular networks
• Mean First Passage Time of the Symmetric Noisy Voter Model with Arbitrary Initial and Boundary Conditions