From cafce77e622df527d8019a06e3edf697c98b48a1 Mon Sep 17 00:00:00 2001 From: Andrew Stryker Date: Sun, 2 Mar 2025 22:18:15 -0800 Subject: [PATCH] Complete intro --- content/posts/autogolpe-bayesian.Rmd | 114 ++++++++++++++++++++++++++- 1 file changed, 110 insertions(+), 4 deletions(-) diff --git a/content/posts/autogolpe-bayesian.Rmd b/content/posts/autogolpe-bayesian.Rmd index 0ff4214..c7b2d69 100644 --- a/content/posts/autogolpe-bayesian.Rmd +++ b/content/posts/autogolpe-bayesian.Rmd @@ -6,13 +6,119 @@ xparams: math: true --- -We are five weeks into a presidential administration that is clearly making -a break with past administrations. Many prominent observers are calling this -an authoritarian _autogolpe_, or self-coup. +We are six weeks into a presidential administration that is clearly making +a break with past administrations. Many prominent observers like [Paul +Krugman][PK] and [Robert Reich][RR] are calling this an authoritarian +_autogolpe_, or self-coup. Of course, both of these observers are left of +center, so being skeptical of these claims is a natural--and even +prudent--reaction. After all, we have experienced 250 years of democratic +government. On the other hand, maybe they are correct. Many of the stories +company out of Washington seem alarming and the sheer number of stories is +overwhelming. The Department of Government Efficiency (DOGE) shutting down +agencies such as USAID. DOGE asking federal workers to justify the work they +performed last week in an email or risk termination. Deciding how to think +about this moment in light of emotionally charged claims and commentary is +completely understandable. +In this post, I will do my best to walk through this moment rationally. To do +this, we will take a [Bayesian approach][Wiki-Bayesian]. I'll get into the +details below, but for now think of Bayesian analysis gives a rigorous +framework for combining disparate pieces of information. In this case, we will +combine pieces of evidence that events support or refute the hypothesis that +the administration is staging an autogolpe. -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: +# Bayesian Overview + +There are a few concepts that we need for this analysis: + + - Initial probability of a coup in the United States. We can label this as + \( P(A) \), where \(A\) is for autrocatic, self-coup or autogolpe. We label + the probability of _not_ an autogolpe as \( P( \neg A ) \). We will refer + to this initial probability as the _prior_ probability or just prior. + + - Evidence that supports or refutes the conclusion that the administration + is conducting an autogolpe. We think of evidence as objective and verifiable. + For example, Trump posting a picture of himself as a king on Instagram. + + - The probability that the evidence is consistent with an autogolpe, + \( P( E \mid A) \). This is our _intrepration_ of the evidence. Our + interpretation is inherentally _subjective_. Perhaps Trump was only + joking when he made the Instagram post. Perhaps Trump was very serious. + The point is that as ae outsider we can only interpret the evidence. That is + to say, there is _uncertainty_. We use probability values to + represent the uncertainty. This term is a _likelihood_. + + - The probability that the evidence is _not_ consistent with an autogolpe, + \( P( E \mid \neg A) \). We also refer to this term as a likelihood. + + - The probability that we are in the middle of autogolpe given the evidence, + \( P( A \mid E ) \). We call this the _posterior_ probability as this + the probability after accounting for the evidence. + +What we doing here is defining a framework for explicitly stating our beliefs. +Prior to inauguration day, what was the probability that we would have an +autogolpe in the United States? Maybe a 1% chance. That is, \( P( A ) \). How +likely is it that the Instagram post implies an autogolpe? Maybe 70% chance. +That is, \( P( E \mid A ) \). + +Our last step is a way to put this information together. This is where we +use the Bayesian approach is define that probability that the administration +is staging an autogolpe as: \[ P(A \mid E) = \frac{P(E \mid A) \, P(A)}{P(E \mid A) \, P(A) + P(E \mid \neg A) \, P(\neg A)} \] + +That is, the probability that we are experiencing an autogolpe is equal to +a ratio. The numerator is the probability that the evidence is consistent with +an autogolpe times our prior. The denominator is the sum of two quantities. +The first is numerator and the second is probability that the evidence is +_not_ consistent with an autogolpe times the 1 minus the prior. That is, the +probability that we would _not_ have an autogolpe prior to the evidence. + +With these quantities defined, let's work through a few examples to make this +clear. + +# Initial Example + +To work an example, we need to start the probability that an autogolpe would +happen in the United States. Prior to inauguration, we might have said a very +small chance. The United States has gone almost 250 years without a coup, so +the value should be low. There are recent example of a democratic government +transforming into a dictatorship (e.g., Hungary), so the value should be not +be zero. Let's say, our prior probability, \( P(A) \), is 1%. + +Next, let's assess one piece of evidence. +The president the Secretary of Defense fired the Chairman of the Joint Chiefs +of Staff, two Service Chairs, and three JAGS. There is precedent for firing +the Chairman of the Joint Chiefs of Staff, for example Presidents Obama and +Truman fired Generals McCrystal and MacCarther, respectively. However, there +is not precedent for a mass firing of military leadership like this. + +Under the hypothesis this that we are experiencing an autogolpe, the likelihood +that we would see evidence like this is quite. Replacing top military officers +is consistent with the behavior of an administration staging a coupe. So, +let's say there \( P( E \mid A ) = 0.8 \), or a 80% chance. + +Under the alternate hypothesis that we are witnessing a coup, the probability of +this event is rather low. Let's say \( P( E \mid \neg A ) = 0.05 \) or 5%. + +We can put this together + +The likelihood +that this is evidence that is consistent with an autogolpe might be 90%. The +the likelihood that is not + +```{r init} +prior <- 0.1 +prob_support <- 0.8 +prob_refute <- 0.05 + +( prob_support * prior ) / ( prob_support * prior + prob_refute * (1 - prior)) + + +``` + +[PK]: https://paulkrugman.substack.com/p/autogolpe +[RR]: https://robertreich.substack.com/p/say-what-it-is-a-coup +[Wiki-Bayesian]: https://en.wikipedia.org/wiki/Bayesian_inference