Bias and Identifiability in the Bounded Confidence Model
This work addresses parameter estimation challenges in opinion dynamics models, which is crucial for connecting these models to real-world data to understand consensus and polarization phenomena, though it is incremental in nature.
The study analyzed maximum likelihood estimators for the confidence bound and convergence rate parameters in bounded confidence opinion dynamics models, finding that the confidence bound estimator has small-sample bias but is consistent, while the convergence rate estimator shows persistent bias, with joint estimation facing identifiability issues in certain parameter regions.
Opinion dynamics models such as the bounded confidence models (BCMs) describe how a population can reach consensus, fragmentation, or polarization, depending on a few parameters. Connecting such models to real-world data could help understanding such phenomena, testing model assumptions. To this end, estimation of model parameters is a key aspect, and maximum likelihood estimation provides a principled way to tackle it. Here, our goal is to outline the properties of statistical estimators of the two key BCM parameters: the confidence bound and the convergence rate. We find that their maximum likelihood estimators present different characteristics: the one for the confidence bound presents a small-sample bias but is consistent, while the estimator of the convergence rate shows a persistent bias. Moreover, the joint parameter estimation is affected by identifiability issues for specific regions of the parameter space, as several local maxima are present in the likelihood function. Our results show how the analysis of the likelihood function is a fruitful approach for better understanding the pitfalls and possibilities of estimating the parameters of opinion dynamics models, and more in general, agent-based models, and for offering formal guarantees for their calibration.