Logical models of informational cascades

In this paper, we investigate the social herding phenomenon known as "informational cascades", in which sequential inter-agent communication might lead to epistemic failures at group level, despite availability of information that should be sufficient to track the truth. We model an example of a cascade, and check the correctness of the individual reasoning of each agent involved, using two alternative logical settings: an existing probabilistic dynamic epistemic logic, and our own novel logic for counting evidence. Based on this analysis, we conclude that cascades are not only likely to occur but are sometimes unavoidable by "rational" means: in some situations, the group's inability to track the truth is the direct consequence of each agent's rational attempt at individual truth-tracking. Moreover, our analysis shows that this is even so when rationality includes unbounded higher-order reasoning powers (about other agents' minds and about the belief-formation-and-aggregation protocol, including an awareness of the very possibility of cascades), as well as when it includes simpler, non-Bayesian forms of heuristic reasoning (such as comparing the amount of evidence pieces).