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On a Voter Model with Context-Dependent Opinion Adoption

Luca Becchetti, Vincenzo Bonifaci, Emilio Cruciani, Francesco Pasquale

TL;DR

A context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion a in favor of opinion b depends on both a and b, is proposed and studied.

Abstract

Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading in social networks and structured populations. Its simplest version assumes that an updating agent will adopt the opinion of a neighboring agent chosen at random. The model allows us to study, for example, the probability that a certain opinion will fixate into a consensus opinion, as well as the expected time it takes for a consensus opinion to emerge. Standard voter models are oblivious to the opinions held by the agents involved in the opinion adoption process. We propose and study a context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion $a$ in favor of opinion $b$ depends on both $a$ and $b$. We discuss the relations of the model with existing voter models and then derive theoretical results for both the fixation probability and the expected consensus time for two opinions, for both the synchronous and the asynchronous update models.

On a Voter Model with Context-Dependent Opinion Adoption

TL;DR

A context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion a in favor of opinion b depends on both a and b, is proposed and studied.

Abstract

Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading in social networks and structured populations. Its simplest version assumes that an updating agent will adopt the opinion of a neighboring agent chosen at random. The model allows us to study, for example, the probability that a certain opinion will fixate into a consensus opinion, as well as the expected time it takes for a consensus opinion to emerge. Standard voter models are oblivious to the opinions held by the agents involved in the opinion adoption process. We propose and study a context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion in favor of opinion depends on both and . We discuss the relations of the model with existing voter models and then derive theoretical results for both the fixation probability and the expected consensus time for two opinions, for both the synchronous and the asynchronous update models.
Paper Structure (31 sections, 10 theorems, 81 equations, 1 algorithm)

This paper contains 31 sections, 10 theorems, 81 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Findings
  3. Related work
  4. Voter and voter-like models.
  5. Pull vs push.
  6. Other biased opinion dynamics.
  7. Model formulation
  8. Notation.
  9. Model.
  10. Quantities of interest.
  11. The unbiased setting
  12. Asynchronous variant
  13. On the $n$-clique topology.
  14. Synchronous variant
  15. Connections to lazy random walks.
  16. ...and 16 more sections

Key Result

Proposition 1

In the unbiased asynchronous case, the fixation probability is the same as for the standard asynchronous voter model. The expected consensus time is $T^{\mathrm{avoter}}/\alpha$, where $T^{\mathrm{avoter}}$ is the expected consensus time of the standard asynchronous voter model.

Theorems & Definitions (20)

  • Proposition 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof : Sketch of the proof
  • Theorem 3
  • proof
  • Theorem 4
  • Proposition 2
  • proof
  • ...and 10 more