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][1]?


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, some subjects may render conclusions out of [**loss aversion**][2] or **fear**. 

Side observation: Note that a model where the agent instead maximizes the **[utility][3]** it derives from a given belief is mathematically equivalent, i.e. loss (negative utility) and regret minimization are often 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**][4] 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 estimate, approximate and optimize the above expectation. 

###Confirmation bias still applies

The above is **not** to say that bias in $\pi$ (e.g. evidence selection based on confirmation bias) does not play a role. This Bayesian (subjective) model just happens to allow for the subject's perceived **loss** or **utility** to contribute and compound further how conspiracy theories shape the agent's behavior.

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


  [1]: https://en.wikipedia.org/wiki/Bayes_estimator
  [2]: https://en.wikipedia.org/wiki/Loss_aversion
  [3]: https://en.wikipedia.org/wiki/Utility
  [4]: https://en.wikipedia.org/wiki/Condition_number