Information overload for (bounded) rational agents

Abstract

Bayesian inference offers an optimal means of processing environmental information and so an advantage in natural selection. We consider the apparent, recent trend in increasing dysfunctional disagreement in, for example, political debate. This is puzzling because Bayesian inference benefits from powerful convergence theorems, precluding dysfunctional disagreement. Information overload is a plausible factor limiting the applicability of full Bayesian inference, but what is the link with dysfunctional disagreement? Individuals striving to be Bayesian-rational, but challenged by information overload, might simplify by using Bayesian networks or the separation of questions into knowledge partitions, the latter formalized with quantum probability theory. We demonstrate the massive simplification afforded by either approach, but also show how they contribute to dysfunctional disagreement.

Keywords: Bayesian inference; decision-making; disagreement; entrenchment; rationality.

Figure 1.

Alice and Bob are interested in whether Brexit may increase the price of imported cheese, C. Alice considers C with questions related to immigration, while Bob considers C with finance questions. As a result, Alice and Bob develop meanings for the C question which are different, even though they think they are considering the same question. (Online version in colour.)

Figure 2.

We plot information cost given one scheme minus information cost given another scheme, labelled Diff (in bits). The superior scheme has lower information cost. Horizontal axes represent the number of questions (n) and outcomes per question (k); complexity increases with both n and k. Note, m = 3 for Bayesian networks translates to three questions per knowledge partition in QPT. (Online version in colour.)