Generating consensus and dissent on massive discussion platforms with an $O(N)$ semantic-vector model

TL;DR

This paper introduces an $O(N)$ semantic-vector model to control consensus and dissent in large discussion platforms, enabling better management of collective idea evolution.

Contribution

It presents a novel dynamical system based on a standard $O(N)$ model that uses semantic vectors to influence consensus and dissent in massive discussion networks.

Findings

Positive coupling promotes global consensus.

Negative coupling induces maximum dissent.

Framework allows controllable balance between cohesion and diversity.

Abstract

Reaching consensus on massive discussion networks is critical for reducing noise and achieving optimal collective outcomes. However, the natural tendency of humans to preserve their initial ideas constrains the emergence of global solutions. To address this, Collective Intelligence (CI) platforms facilitate the discovery of globally superior solutions. We introduce a dynamical system based on the standard $O(N)$ model to drive the aggregation of semantically similar ideas. The system consists of users represented as nodes in a $d=2$ lattice with nearest-neighbor interactions, where their ideas are represented by semantic vectors computed with a pretrained embedding model. We analyze the system's equilibrium states as a function of the coupling parameter $\beta$. Our results show that $\beta > 0$ drives the system toward a ferromagnetic-like phase (global consensus), while $\beta < 0$ induces an antiferromagnetic-like state (maximum dissent), where users maximize semantic distance from their neighbors. This framework offers a controllable method for managing the tradeoff between cohesion and diversity in CI platforms.