Cognitive biases can move opinion dynamics from consensus to chaos

Research in the area of how networks of people form consensus opinions has exploded recently, with statistical physics approaches and contributions from economists both suggesting that there is convergence to a fixed point in belief networks. We straightforwardly generalize the model used by economists to describe Bayesian updating so that the likelihood of a piece of data depends on ground truth and, potentially, the alignment of the receiver's beliefs with the sender's beliefs and the data point itself. Confirmation bias occurs when the data point is considered more likely when it aligns with the receiver's beliefs; a version of in-group bias occurs when the receiver further considers the data point to be more likely when the receiver's beliefs and the sender's beliefs are aligned. When the likelihood of the data point only depends on ground truth, so that receivers exhibit no confirmation bias or in-group bias, the network of people always converges to complete consensus. With confirmation bias, there can be polarization in the final state. When in-group bias is added, consensus and polarization are still possible; but when agents do their best to counteract confirmation bias, so is chaos. This is the first work to suggest that chaos might be a feature of opinion dynamics when cognitive biases, or attempts to counteract cognitive biases, are taken into account.