Informational Cascades: A Test for Rationality?

ABSTRACT: 

In this presentation I focus on a logical analysis of the social phenomenon known as an 'informational cascade'.  In an informational cascade we observe how sequential inter-agent communication leads to epistemic failures and can prevent a group from tracking the truth.  By observing the decisions of previous people in a sequence, an individual may rationally decide to follow her predecessors and ignore her own private evidence, hence adding fuel to a cascade. This phenomenon is just one in a series that can illustrate a clear case of when social features interfere with agent's truth-tracking abilities.
However, one might still argue that by higher-order reflection (and in particular, by becoming aware of the dangers inherent in the sequential deliberation protocol), "truly rational" agents might be able to avoid the formation of cascades. Indeed, in some cases a cascade can be prevented simply by making agents aware of its very possibility. However, as I'll show in this presentation, this is not always the case. There are situations in which no amount of higher-order reflection and meta-rationality can stop an informational cascade from happening. To prove this, I will model an example of an informational cascade, and check the correctness of the individual reasoning of each agent involved. Formally, I make use of two alternative logical settings: an existing probabilistic dynamic epistemic logic, and a non-probabilistic logic for counting evidence. Based on this analysis, I can 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, the power of 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). This presentation is based on the results of joint work with with A. Baltag, Z. Christoff and J. U. Hansen on "Logical Models of Informational Cascades".