A Constraint Opinion Model
Fabio Gadducci, Carlos Olarte, Frank Valencia
TL;DR
The paper generalizes the classical DeGroot opinion dynamics by introducing Constraint Opinion Models in which both opinions and influences are represented as soft constraints drawn from a semiring. This enables modeling of partial information, uncertainty, and multi-topic beliefs, while preserving tractable update rules and yielding convergence results under suitable conditions. A new polarization distance based on Hausdorff distance between constraint solution sets is proposed to quantify disagreement. The authors illustrate rich expressive scenarios including extreme vs. moderate preferences, topic-wise discussion, and conditional influences, and provide a reproducibility tool at a public GitHub repository.
Abstract
This paper introduces a generalised opinion model that extends the standard DeGroot model by representing agents' opinions and influences as soft constraints rather than single real values. This allows for modelling scenarios beyond the scope of the DeGroot model, such as agents sharing partial information and preferences, engaging in discussions on multiple topics simultaneously, and representing opinions with different degrees of uncertainty. By considering soft constraints as influences, the proposed model captures also situations where agents impose conditions on how others' opinions are integrated during belief revision. Finally, the flexibility offered by soft constraints allows us to introduce a novel polarisation measure that takes advantage of this generalised framework.