HKC07 - Bayesian conspiracy theorists? Equivocal signals and persistent polarization

Conspiracy beliefs are the subject of a rich literature in psychology, which explains them through personal dysfunction. The corresponding economics literature is scant. We offer a demand-side model of belief in specific conspiracy theories with no biases, misspecification, or strategic manipulation. A conspiracy, by its nature, generates equivocal evidence about its own existence, because the same strength that produces more to detect also produces better concealment. We model belief in a specific conspiracy theory as learning about the strength 𝑞 of a cabal, a stand-in for the secretly coordinating actors of any conspiracy theory. In the baseline the cabal influences events with probability 𝑞 and conceals that influence with probability 𝑞, so public evidence arrives at rate 𝑞(1−𝑞) and cannot distinguish a weak cabal from a strong, wellconcealed one. Bayesian agents converge to two-point beliefs on the pair of observationally equivalent states, with weights given by the ratio of their prior densities there, and their optimal actions diverge accordingly. Divergence requires only that concealment improve elastically with strength over some range, not exact symmetry. It is also invisible to standard belief elicitation: agents with indistinguishable measured priors can be driven to opposite camps by identical public information. Polarization, opposite responses to common information, and stable adherence follow from Bayes’ rule alone. The model provides a complementary account to the one offered by the psychology literature.