<p>Are there any theories in cognitive psychology that try to model the belief in conspiracy theories through the lens of <a href="https://en.wikipedia.org/wiki/Bayes_estimator" rel="nofollow noreferrer">Bayesian decision theory</a>?</p>
<p>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:</p>
<ol>
<li>An estimated probability over a set of events (or possible explanations)</li>
<li>The loss the subject individually assigns to or perceives associated with a given event (or explanation)</li>
</ol>
<p>Under this model a rational agent can make decisions as per:</p>
<p><span class="math-container">$d^* = \underset{d}{\operatorname{argmin}} \mathrm{E}^\pi\left[L\left(\theta,d\right)| \text{D}\right]$</span></p>
<p>where we have:</p>
<ul>
<li><span class="math-container">$L$</span> is the (subject's) loss function</li>
<li><span class="math-container">$\pi$</span> is the subject's posterior or prior beliefs over a set of parameters / events / explanations <span class="math-container">$\theta$</span></li>
<li><span class="math-container">$d$</span> is the decision the agent is trying to make</li>
<li><span class="math-container">$\text{D}$</span> is the observed data (e.g. available evidence to the subject)</li>
</ul>
<h3>Fear and loss aversion</h3>
<p>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. In other words, subjects may act and believe in a conspiracy theory out of <strong>fear</strong> and <a href="https://en.wikipedia.org/wiki/Loss_aversion" rel="nofollow noreferrer"><strong>loss aversion</strong></a>.</p>
<p>Side observation: Note that a model where the agent instead maximizes the <strong><a href="https://en.wikipedia.org/wiki/Utility" rel="nofollow noreferrer">utility</a></strong> 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.</p>
<h3>Ill-conditioned optimization</h3>
<p>From a computational standpoint, the optimization (minimization) of the expected loss can be <a href="https://en.wikipedia.org/wiki/Condition_number" rel="nofollow noreferrer"><strong>ill-conditioned</strong></a> if the probability <span class="math-container">$\pi$</span> is small (little evidence supporting an explanation) but the assigned loss <span class="math-container">$L$</span> is large (big implications if true). This could lead different agents to believe and act <em>very</em> differently depending on how they <strong>approximate</strong> and <strong>optimize</strong> the above expectation.</p>
<p>To illustrate this point, consider a conspiracy theorist arguing: <em>&quot;I know there is little direct evidence for [conspiracy theory] X, but <em>what if</em> it's true?&quot;</em>.  This tension could lead the conspiracy theorist to &quot;accept&quot; the theory and behave accordingly.</p>
<h3>Confirmation bias still applies</h3>
<p>Note that the above still allows a straight bias in <span class="math-container">$\pi$</span> (e.g. evidence selection based on confirmation bias) to heavily influence <span class="math-container">$d^*$</span>. This Bayesian and subjective model just happens to allow for the subject's perceived <strong>loss</strong> or <strong>utility</strong> to also contribute to how a given conspiracy theory may shape the agent's behavior, conclusions or beliefs.</p>
<p>Most interestingly, perhaps, this framework shows that the computation of beliefs and behavior can naturally be very <strong>ill-conditioned</strong>, so small differences in how different agents aggregate sparse evidence and model their losses can lead them to draw significantly different conclusions.</p>
<p><strong>Note</strong>: I'm not familiar with the psychology of conspiracy theories, so apologies if I am missing a trivial connection in the literature.</p>

CC BY-SA 4.0
2020-05-20T02:47:49.550Z
You're ignoring here the importance of who says it for something to be believed. See the "second key insight" in https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6282974/
got trolled too much this week
CC BY-SA 4.0
2020-05-20T02:53:27.333Z
Also "belief in conspiracy theories is positively associated with intuitive rather than analytic thinking (Swami, Voracek, Stieger, Tran, & Furnham, 2014)."
got trolled too much this week
CC BY-SA 4.0
2020-05-20T15:52:48.047Z
+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
<cognitive-psychology><decision-making><behavioral-economics>
Bayesian models of conspiracy theorists
Amelio Vazquez-Reina
# Bayesian models of conspiracy theorists

(Asked by: username_0 on 2020-05-16)

Are there any theories in cognitive psychology that try to model the belief in conspiracy theories through the lens of [Bayesian decision theory](https://en.wikipedia.org/wiki/Bayes_estimator)?

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

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. In other words, subjects may act and believe in a conspiracy theory out of **fear** and [**loss aversion**](https://en.wikipedia.org/wiki/Loss_aversion).

Side observation: Note that a model where the agent instead maximizes the **[utility](https://en.wikipedia.org/wiki/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**](https://en.wikipedia.org/wiki/Condition_number) if the probability $\pi$ is small (little evidence supporting an explanation) but the assigned loss $L$ is large (big implications if true). This could lead different agents to believe and act *very* differently depending on how they **approximate** and **optimize** the above expectation.

To illustrate this point, consider a conspiracy theorist arguing: *"I know there is little direct evidence for [conspiracy theory] X, but *what if* it's true?"*. This tension could lead the conspiracy theorist to "accept" the theory and behave accordingly.

### Confirmation bias still applies

Note that the above still allows a straight bias in $\pi$ (e.g. evidence selection based on confirmation bias) to heavily influence $d^\*$. 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, this framework shows that the computation of beliefs and behavior can naturally be very **ill-conditioned**, so small differences in how different agents aggregate sparse evidence and model their losses can lead them to draw significantly 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.

**Tags:** cognitive-psychology, decision-making, behavioral-economics

> **Comments:**
> **username_1**: You're ignoring here the importance of who says it for something to be believed. See the "second key insight" in https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6282974/  
> **username_1**: Also "belief in conspiracy theories is positively associated with intuitive rather than analytic thinking (Swami, Voracek, Stieger, Tran, & Furnham, 2014)."  
> **username_0**: +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.  

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## 0 answers

