A framework to analyze opinion formation models

Abstract

Comparing model predictions with real data is crucial to improve and validate a model. For opinion formation models, validation based on real data is uncommon and difficult to obtain, also due to the lack of systematic approaches for a meaningful comparison. We introduce a framework to assess opinion formation models, which can be used to determine the qualitative outcomes that an opinion formation model can produce, and compare model predictions with real data. The proposed approach relies on a histogram-based classification algorithm, and on transition tables. The algorithm classifies an opinion distribution as perfect consensus, consensus, polarization, clustering, or dissensus; these qualitative categories were identified from World Values Survey data. The transition tables capture the qualitative evolution of the opinion distribution between an initial and a final time. We compute the real transition tables based on World Values Survey data from different years, as well as the predicted transition tables produced by the French-DeGroot, Weighted-Median, and Bounded Confidence models, and we compare them. Our results provide insight into the evolution of real-life opinions and highlight key directions to improve opinion formation models.

Probabilistic Analysis of Agent-Based Opinion Formation Models

“…Every opinion distribution x ∈ [−1, 1] N can be related to two values, the average x and the average of the absolute values |x|. Then, an opinion distribution can be represented as a point in the Cartesian plane, whose abscissa is |x| and whose ordinate is x, resulting in the Agreement Plot [37].…”

“…Adding these features often results in rich and complex mathematical models, which are not in general amenable to theoretical analysis: the broad exploration of the model behaviour, properties, and capabilities relies on numerical approaches and simulation-based techniques [33,34,35,11]. A number of recently proposed techniques use numerical distributional measures to characterise opinion formation models and the opinion distributions they can produce: a histogram-based algorithm has been proposed to categorise opinion distributions and assess how the transitions between different opinion distribution categories in real populations are predicted by various agent-based models [36]; Bias, Diversity, and Fragmentation measures have been computed so as to classify opinion distributions and relate the model parameters with qualitative properties of the resulting opinions [11]; a graphical analysis can be employed to investigate how the model outcomes depend on the initial opinions, the agent parameters, and the underlying digraph [37]. Simulation-based techniques allow not only a thorough analysis of opinion formation models, but also a meaningful comparison of the behaviours of different models, and thus contribute to recent efforts towards common frameworks in which model behaviours can be studied, classified, and compared [38,36,39,40].…”

“…Our proposed technique can be applied to analyse any agent-based opinion formation model in which the opinion of each agent is a real number belonging to a bounded interval. The technique is exemplified by applying it to four opinion formation models: the classical Friedkin-Johnsen model [12,13] and Bounded Confidence model [10], as well as the recently proposed Classification-based model [43] and Backfire Effect and Biased Assimilation model [44]. In all these models, opinions are represented by real values between −1 and +1.…”

“…For the Classification-based (CB) model [43], each agent has three inner traits whose strength is quantified by three parameters: α i , capturing conformism, which induces agent i to agree with its neighbours; β i , capturing radicalism, which moves its opinion towards extreme values; γ i , capturing stubbornness, which prevents its opinion from changing. The three parameters take values in the interval [0, 1] and sum up to 1.…”

Opinion Dynamics and Unifying Principles: A Global Unifying Frame

“…This work subscribes to a series of papers dealing with the same goal of building tools to allow comparing the various models of opinion dynamics [9][10][11].…”