Discrete Opinion models as a limit case of the CODA model

Opinion Dynamics models can be, for most of them, divided between discrete and continuous. They are used in different circumstances and the relationship between them is not clear. Here we will explore the relationship between a model where choices are discrete but opinions are a continuous function (the Continuous Opinions and Discrete Actions, CODA, model) and traditional discrete models. I will show that, when CODA is altered to include reasoning about the influence one agent can have on its own neighbors, agreement and disagreement no longer have the same importance. The limit when an agent considers itself to be more and more influential will be studied and we will see that one recovers discrete dynamics, like those of the Voter model in that limit

💡 Research Summary

The paper investigates the relationship between continuous‑opinion/discrete‑action (CODA) models and traditional discrete opinion dynamics such as the Voter model. In the standard CODA framework each agent holds a continuous internal belief p_i (or its log‑odds λ_i) and translates that belief into a binary action: “agree” if p_i > 0.5, “disagree” otherwise. Updates are performed by observing the actions of neighboring agents and applying a Bayesian‑like rule, which treats all neighbors symmetrically. The authors argue that this formulation ignores a realistic psychological factor: agents often consider the influence they themselves exert on their neighbors. To capture this, they introduce a self‑influence parameter α∈