# Bayesian models of conspiracy theorists

Have there been any studies or are there any theories in cognitive psychology that try to model the belief in conspiracy theories through the lens of Bayesian decision theory?

For reference, in Bayesian decision theory a rational agent often behaves so as to minimize its expected (projected) loss. This expected loss is subjective and involves:

1. An estimated probability over a set of events (or possible explanations)
2. The loss the subject individually assigns to or perceives associated with a given event (or explanation)

Under this model a rational agent can make decisions as per:

$$d^* = \underset{d}{\operatorname{argmin}} \mathrm{E}^\pi\left[L\left(\theta,d\right)| \text{D}\right]$$

where we have:

• $$L$$ is the (subject's) loss function
• $$\pi$$ is the subject's posterior or prior beliefs over a set of parameters / events / explanations $$\theta$$
• $$d$$ is the decision the agent is trying to make
• $$\text{D}$$ is the observed data (e.g. available evidence to the subject)

### Fear and loss aversion

I have often been intrigued about this connection since one could argue that if a subject assigns a high loss to a specific belief (e.g. a conspiracy theory that the subject is particularly afraid of), the subject may choose to believe it or at least behave as if it was true, even if there is little evidence to support it. Moreover, it illustrates how some subjects may render biased conclusions out of fear and loss aversion.

Side observation: Note that a model where the agent instead maximizes the utility it derives from a given belief is mathematically equivalent. Loss (negative utility) and regret minimization are often just used as a canonical model for both.

### Ill-conditioned optimization

From a computational standpoint, the optimization (minimization) of the expected loss can be ill-conditioned if the probability $$\pi$$ collapses (little evidence supporting an explanation) but the assigned loss $$L$$ is large, which could lead different agents to believe, act and behave very differently depending on how they approximate and optimize the above expectation.

To illustrate this point it's like a conspiracy theorist initially thinking: "I know there is little direct evidence for theory X, but what if it's true?".

### Confirmation bias still applies

Note that the above still allows a straight bias in $$\pi$$ (e.g. evidence selection based on confirmation bias) to play a role. This Bayesian and subjective model just happens to allow for the subject's perceived loss or utility to also contribute to how a given conspiracy theory may shape the agent's behavior, conclusions or beliefs. Most interestingly perhaps, it shows that the computation can be ill-conditioned so small differences in how different agents aggregate evidence and model their losses can lead them to draw different conclusions.

Note: I'm not familiar with the psychology of conspiracy theories, so apologies if I am missing a trivial connection in the literature.

• You're ignoring here the importance of who says it for something to be believed. See the "second key insight" in ncbi.nlm.nih.gov/pmc/articles/PMC6282974 – Fizz May 20 at 2:47
• Also "belief in conspiracy theories is positively associated with intuitive rather than analytic thinking (Swami, Voracek, Stieger, Tran, & Furnham, 2014)." – Fizz May 20 at 2:53
• +1 Thanks @Fizz for the first reference. On your second point, couldn't one caveat that, while an individual may not "consciously" think what to believe or do "analytically", this type of Bayesian computation may approximate well how the agent integrates evidence and fears? Needless to say, we are always talking about models here and they may be a good fit whether or not an individual states or arguably follows any logical argument. – Amelio Vazquez-Reina May 20 at 15:52