On Conspiracy Coup theories and Bayesian Reasoning
A phenomenon occurred shortly after Donald Trump took office which involved huge numbers of people running out to stock up on canned goods and writing pieces about how Steve Bannon was testing the waters for a Coup via the Muslim Ban order.
Why did that occur? Suppose for example that you have a machine in a room that does a good job of running some missile silo. It's designed well, and it has run well for the last 30 years. Your confidence that it won't accidentally launch nuclear missiles is pretty high.
Now suppose the janitor comes to you and tells you that last night while he was cleaning things up he spilled a bunch of something into the console and while cleaning that up he flipped a bunch of the switches. Suppose there are 20 switches that if you put them into a particular randomly chosen configuration will start a nuclear launch countdown.
Now, the chance of getting accidentally into that configuration is but checking that it's not set to launch is the first damn thing you're going to do when you rush into that room.
The point is this:
Historical info about how reliable something is is useless to you when you have new information that something is amiss with the machine. You MUST reset your Bayesian prior over the reliability of the machine to include some probability on every possibility of what state it might be in, and then collect data on the machine and use your model of how it works to re-concentrate your posterior distribution on the internal state.
To decide what to focus on, you need to use Bayesian Decision theory to first check the things that have the largest expected costs associated. So even if it's a 1 in a million chance that you might be nuking the planet into oblivion... you gotta check it because the cost associated if you nuke the world is trillions and trillions of dollars (or utiles or whatever unit of cost you decide to use).
So, it's fully rational when a large shift in how things are going politically leads us to focus on the possibility that everything might be going to hell right away and we need to stock up on canned goods, ammunition, and cricket bats for the zombie hoard.
Fortunately, after seeing the output of the machine for a while, we can re-concentrate our prior. So, conspiracy nuts are not the ones who cry conspiracy when a big change occurs in the government. It's actually Rational to fear conspiracy if there's a big enough change. Conspiracy nuts are the ones who cry conspiracy well after the likelihood suggests otherwise and the expected cost associated with conspiracy should be calculated as negligible.
The "conspiracy nut" has two problems. Typically they start with concentrated priors on conspiracy, and second, they focus their model of how the world works on likelihoods associated with conspiracies (that is, their prior over models is to choose a model where any data can be seen as evidence of a conspiracy).