Opinion Dynamics on Discourse Sheaves

TL;DR

This paper introduces a new mathematical framework using discourse sheaves and Laplacians to model and analyze opinion dynamics and communication processes on social networks.

Contribution

It develops a novel sheaf Laplacian and diffusion dynamics model that captures complex communication modes like lying and selective opinion modulation.

Findings

Model captures various communication modes including lying.

Framework addresses controllability and reachability in opinion dynamics.

Provides a new algebraic approach to network diffusion processes.

Abstract

We introduce a novel class of Laplacians and diffusion dynamics on discourse sheaves as a model for network dynamics, with application to opinion dynamics on social networks. These sheaves are algebraic data structures tethered to a network (or more general space) that can represent various modes of communication, including selective opinion modulation and lying. After introducing the sheaf model, we develop a sheaf Laplacian in this context and show how to evolve both opinions and communications with diffusion dynamics over the network. Issues of controllability, reachability, bounded confidence, and harmonic extension are addressed using this framework.