Propagation of measurement error in opinion dynamics models: The case of the Deffuant model

Opinion dynamics models have an enormous potential for studying current phenomena such as vaccine hesitancy or diffusion of fake news. Unfortunately, to date, most of the models have little to no empirical validation. One major problem in testing these models against real-world data relates to the difficulties in measuring opinions in ways that map directly to representations in models. Indeed, measuring opinions is a complex process and presents more types of measurement error than just classical random noise. Thus, it is crucial to know how these different error types may affect the model's predictions. In this work, we analyze this relationship in the Deffuant model as an example. Starting from the psychometrics literature, we first discuss how opinion measurements are affected by three types of errors: random noise, binning, and distortions (i.e. uneven intervals between scale points). While the first two are known to most of the scientific community, the third one is mostly unknown outside psychometrics. Because of that, we highlight the nature and peculiarities of each of these measurement errors. By simulating these types of error, we show that the Deffuant model is robust to binning but not to noise and distortions. Indeed, if a scale has 4 or more points (like most self-report scales), binning has almost no effect on the final predictions. However, prediction error increases almost linearly with random noise, up to a maximum error of 40%. After reaching this value, increasing the amount of noise does not worsen the prediction. Distortions are most problematic, reaching a maximum prediction error of 80%. Error propagation is already established in other fields, such as statistics and engineering. We believe its application in opinion dynamics will contribute to the expansion and development of this field. Indeed, as we show here, it allows researchers to test models’ reliability and prediction quality even before testing the model against real world data.