Anyway, Bayesian statistics are built on the idea that probabilities are just about how much information we have. If a coin is covered up, there is a 50% chance that it is "heads," because I just don't know which side is up, and given my information, there is an equal chance of heads or tails, unless I have some reason to believe otherwise. As I encounter new information, I update my "priors" to incorporate new information.
If you play poker, you use Bayesian updating. In a game like Texas hold 'em, you estimate the likelihood that you will get a card that you need to complete your hand from a community card at each stage, updating your estimates as each new community card is dealt. You also have a prior estimate of the likelihood of a hand beating yours based on raw probabilities, and attempt to update those beliefs based on your opponents' bets. Bayesian updating.
Of course, if you observe a pattern that a player always bluffs, that player is easy to beat, which brings me to the subject of liars.
Trump's wiretapping claim has been pretty thoroughly debunked by now, but the thing is, it was obvious all along that it was bullshit, not just because it was outlandish, but because Trump said it.
Which of the following two conditional statements is more appropriate?
A) Probability(X is true | Trump says X) = Probability(X is true)
B) Probability(X is true | Trump says X) < Probability(X is true)
Um....
Uh....
Yeah. Hard one, right? Statement A says that the probability of a statement being true is independent of whether or not Trump says it. Statement B says that your estimate of a statement's probability of being true goes down when Trump says it because he's such a fucking liar. And let's keep in mind his PolitiFact scorecard. (Usual caveats about PolitiFact...)
This is the dude who rose to the presidency by claiming that Barack Obama was secretly born in Kenya, and along the way, told such doozies as that Ted Cruz's father killed Kennedy, the Chinese government invented the idea of global warming to inhibit US economic growth, and I could go on, and on, and on, and on, and on.... but I've got real work to do today. The point is that we have never, in the history of this country, seen a liar as shameless and brazen as Donald Trump.
Now be honest. Donald Trump makes a statement. Can you really say that you aren't even a little bit in category B?
Realistically, there is no informational content in Trump's words. He is an idiot child, and I wrote a post a while back arguing that the proper term for him is actually "bullshitter" rather than "liar" if we take the distinction made by Harry Frankfurt.
Still, there is a lesson here for how we discuss and cover Trump's claims, particularly his outlandish ones. The closest thing to progress I have seen has been that journalists decided to cover the wiretap claim by pointing out that Trump didn't provide evidence. True, but what they should have done is also provide context, that context being the number of times in the past that he has made claims like the batshit crazy ones about Ted Cruz's father. Note how pointing out that one neatly sidesteps the partisan issues of Trump's birtherism.
Trump is the most dishonest politician we have ever seen. It isn't close. Still, remember that the correct answer is model A not B. Trump's wiretap claim was just so obviously insane on its face that his inability to provide credibility meant that we could discount it.
