Incorporating memory into bounded confidence models of probabilistic social learning

In social learning models, truth-seeking agents learn both individually from direct evidence and socially by pooling beliefs with others. That learning can be undermined by two types of unreliable agents: zealots, who do not learn and promote the same fixed opinion and free riders, who lack access to evidence yet still influence others. In this paper, we explore how learning rules that incorporate memory can mitigate the effects of unreliable agents. To do so, we construct an agent-based model of social learning in which agents apply a probabilistic bounded confidence (BC) model that evaluates the similarity between themselves and others based on samples of recent beliefs rather than current beliefs only. When compared to a memoryless BC benchmark, BC with memory proves significantly less sensitive to the choice of similarity threshold governing agent interactions, to the extent that a fixed threshold is effective for avoiding all types of zealots. It is also less susceptible to high levels of distrust in evidence. The BC with memory model is then extended to social learning about multiple hypotheses, and we show that the robustness results generalise to the case in which beliefs are multi-dimensional probability distributions.