Complete intro
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Andrew Stryker
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---
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We are five weeks into a presidential administration that is clearly making
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a break with past administrations. Many prominent observers are calling this
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an authoritarian _autogolpe_, or self-coup.
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We are six weeks into a presidential administration that is clearly making
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a break with past administrations. Many prominent observers like [Paul
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Krugman][PK] and [Robert Reich][RR] are calling this an authoritarian
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_autogolpe_, or self-coup. Of course, both of these observers are left of
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center, so being skeptical of these claims is a natural--and even
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prudent--reaction. After all, we have experienced 250 years of democratic
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government. On the other hand, maybe they are correct. Many of the stories
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company out of Washington seem alarming and the sheer number of stories is
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overwhelming. The Department of Government Efficiency (DOGE) shutting down
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agencies such as USAID. DOGE asking federal workers to justify the work they
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performed last week in an email or risk termination. Deciding how to think
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about this moment in light of emotionally charged claims and commentary is
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completely understandable.
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In this post, I will do my best to walk through this moment rationally. To do
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this, we will take a [Bayesian approach][Wiki-Bayesian]. I'll get into the
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details below, but for now think of Bayesian analysis gives a rigorous
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framework for combining disparate pieces of information. In this case, we will
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combine pieces of evidence that events support or refute the hypothesis that
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the administration is staging an autogolpe.
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Let’s frame the situation using Bayes’ theorem. We want to update our belief in the hypothesis AA (“an authoritarian self-coup is underway”) in light of evidence EE (the various reported actions). Bayes’ theorem tells us:
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# Bayesian Overview
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There are a few concepts that we need for this analysis:
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- Initial probability of a coup in the United States. We can label this as
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\( P(A) \), where \(A\) is for autrocatic, self-coup or autogolpe. We label
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the probability of _not_ an autogolpe as \( P( \neg A ) \). We will refer
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to this initial probability as the _prior_ probability or just prior.
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- Evidence that supports or refutes the conclusion that the administration
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is conducting an autogolpe. We think of evidence as objective and verifiable.
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For example, Trump posting a picture of himself as a king on Instagram.
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- The probability that the evidence is consistent with an autogolpe,
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\( P( E \mid A) \). This is our _intrepration_ of the evidence. Our
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interpretation is inherentally _subjective_. Perhaps Trump was only
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joking when he made the Instagram post. Perhaps Trump was very serious.
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The point is that as ae outsider we can only interpret the evidence. That is
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to say, there is _uncertainty_. We use probability values to
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represent the uncertainty. This term is a _likelihood_.
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- The probability that the evidence is _not_ consistent with an autogolpe,
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\( P( E \mid \neg A) \). We also refer to this term as a likelihood.
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- The probability that we are in the middle of autogolpe given the evidence,
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\( P( A \mid E ) \). We call this the _posterior_ probability as this
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the probability after accounting for the evidence.
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What we doing here is defining a framework for explicitly stating our beliefs.
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Prior to inauguration day, what was the probability that we would have an
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autogolpe in the United States? Maybe a 1% chance. That is, \( P( A ) \). How
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likely is it that the Instagram post implies an autogolpe? Maybe 70% chance.
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That is, \( P( E \mid A ) \).
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Our last step is a way to put this information together. This is where we
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use the Bayesian approach is define that probability that the administration
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is staging an autogolpe as:
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\[
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P(A \mid E) = \frac{P(E \mid A) \, P(A)}{P(E \mid A) \, P(A) + P(E \mid \neg A) \, P(\neg A)}
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\]
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That is, the probability that we are experiencing an autogolpe is equal to
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a ratio. The numerator is the probability that the evidence is consistent with
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an autogolpe times our prior. The denominator is the sum of two quantities.
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The first is numerator and the second is probability that the evidence is
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_not_ consistent with an autogolpe times the 1 minus the prior. That is, the
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probability that we would _not_ have an autogolpe prior to the evidence.
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With these quantities defined, let's work through a few examples to make this
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clear.
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# Initial Example
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To work an example, we need to start the probability that an autogolpe would
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happen in the United States. Prior to inauguration, we might have said a very
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small chance. The United States has gone almost 250 years without a coup, so
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the value should be low. There are recent example of a democratic government
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transforming into a dictatorship (e.g., Hungary), so the value should be not
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be zero. Let's say, our prior probability, \( P(A) \), is 1%.
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Next, let's assess one piece of evidence.
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The president the Secretary of Defense fired the Chairman of the Joint Chiefs
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of Staff, two Service Chairs, and three JAGS. There is precedent for firing
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the Chairman of the Joint Chiefs of Staff, for example Presidents Obama and
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Truman fired Generals McCrystal and MacCarther, respectively. However, there
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is not precedent for a mass firing of military leadership like this.
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Under the hypothesis this that we are experiencing an autogolpe, the likelihood
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that we would see evidence like this is quite. Replacing top military officers
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is consistent with the behavior of an administration staging a coupe. So,
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let's say there \( P( E \mid A ) = 0.8 \), or a 80% chance.
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Under the alternate hypothesis that we are witnessing a coup, the probability of
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this event is rather low. Let's say \( P( E \mid \neg A ) = 0.05 \) or 5%.
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We can put this together
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The likelihood
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that this is evidence that is consistent with an autogolpe might be 90%. The
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the likelihood that is not
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```{r init}
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prior <- 0.1
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prob_support <- 0.8
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prob_refute <- 0.05
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( prob_support * prior ) / ( prob_support * prior + prob_refute * (1 - prior))
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```
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[PK]: https://paulkrugman.substack.com/p/autogolpe
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[RR]: https://robertreich.substack.com/p/say-what-it-is-a-coup
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[Wiki-Bayesian]: https://en.wikipedia.org/wiki/Bayesian_inference
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