Sunday, May 21, 2017

The statistics of impeachment

It really is astonishing just how quickly Trump has flamed out as President.  I still remain skeptical that he will be impeached, though, and it is worth thinking about base-level statistics.

We have had 44 past presidents.  (Do we have to get into the Grover Cleveland issue?  Please, no.)  Of those, two were actually impeached, and one resigned before being impeached.  Andrew Johnson was impeached for, um... firing Edwin Stanton as Secretary of War.  Nixon resigned before being impeached.  Was there a firing involved in that?  I forget...  Apparently Trump did too.  Oh, and Clinton was impeached for lying to Ken Starr about an affair with Monica Lewinsky, which he was investigating because, um... uh... because he was given a mandate to find something for which Republicans could impeach Clinton.  While articles of impeachment were passed in the House for both Johnson and Clinton, both were acquitted in the Senate because in neither case could the Senate muster the 2/3 supermajority required to convict.  Nixon could have been convicted, which was why he resigned before the House even got to the point of passing articles of impeachment.

So:

Presidents removed by impeachment:  0%

Presidents impeached:  2/44, or roughly 4.5%

Presidents implicitly forced out by threat of impeachment:  1/44, or roughly 2.3%

Notice who isn't in here.  People like Warren Harding.  The Harding administration was about as corrupt as they came, and it wasn't necessarily that Harding himself was corrupt, but he was either stupid, or just willing to look the other way as the Teapot Dome scandal, and others played out around him.

Anyway, though, the problem here is in terms of what we call "Bayesian" probability.  I've referenced this before.  These numbers are just base probabilities, or, "priors."  The estimates of Trump's likelihood of getting tossed out or resigning are higher because, well, that dude is seriously corrupt, and very stupid about it.  He has already publicly admitted to exactly what got Nixon thrown out, and we are just getting started with the investigation.

With Bayesian probabilities, we start with a prior, and "update" the prior as we incorporate new information.  So, how much do we update those base probabilities?

Nixon did get forced out.  He is the closest analog.  Does that mean the probability goes close to 1?  Based on a sub-sample of 1?  No.  We can't put that much leverage on a single case.  We also have the party problem.  Nixon's own party eventually turned on him because Republicans back then were willing to do so.  They're not anymore, and I have written a few posts explaining why, based partially on the memory of Nixon and the aftermath of Watergate.

Regardless, there isn't a lot of history to guide us here, beyond base probabilities.  Then again, we are already well outside the bounds of historical norms here.  That's becoming our national motto.

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