Every Opinion Dynamics Model Is a Class of Equivalent Models

While more and more opinion dynamics models have been developed along the years, many researchers have wondered on the possibility of finding some unified model or framework. At the same time, some research from psychometrics has showed how social simulations may be affected by the non-linear transformations due to scale change, which can introduce massive uncertainties on models’ outcome. In this article we explore scale transformations by showing how different models can actually become the same model under a scale transformation. Meaning that one model M1 studied on scale S1 is identical to another model M2 when studied on a scale S2. As an example, we show the equivalence of various models developed by Hegselmann and Krause by using both mathematical equivalence and simulations. This study shows how each model can be thought as a class of equivalent models. Such an approach is useful both for unifying different models and, especially, for studying how some of these models could be combined with empirical data.