Generating consensus and dissent on massive discussion platforms with a semantic-vector model

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>O</a:mi> <a:mo>(</a:mo> <a:mi>N</a:mi> <a:mo>)</a:mo> </a:mrow> </a:math> model to drive the aggregation of semantically similar ideas. The system consists of users represented as nodes in a <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>d</b:mi> <b:mo>=</b:mo> <b:mn>2</b:mn> </b:mrow> </b:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>β</c:mi> </c:math> . Our results show that <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>β</d:mi> <d:mo>></d:mo> <d:mn>0</d:mn> </d:mrow> </d:math> drives the system toward a ferromagneticlike phase (global consensus), while <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>β</e:mi> <e:mo><</e:mo> <e:mn>0</e:mn> </e:mrow> </e:math> induces an antiferromagneticlike 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.