Probability Trump is guilty of something: G
Probability that Mueller finds enough evidence to convict: C | G (notation for conditional probabilities)
U(proof of guilt vs. ambiguity)
Cost of early self-pardon: P
So, four basic terms. It may seem odd to include the first. We don't know for certain whether or not Trump is being blackmailed by Russia, but doesn't he? Um, maybe not. Remember that a) he's fucking stupid, and b) because he's fucking stupid, he is easy to manipulate. So, he really might not know whether or not he's guilty. Actually, he might sincerely believe he is innocent of everything, so he might sincerely believe G=0, which will blow all of this math up, but, well, let's go through with it anyway. Why? It's what I do when I'm not just ranting.
C is sort of a measure of Mueller's competence as an investigator, combined with the efficacy of the legal system. Personally, I think the legal system is fucking bullshit, but I'm a political scientist, not a lawyer. (Hey, kids! Don't be lawyers!) Regardless, this combines the evidence that Mueller is likely to get with how a legal proceeding would work if it happened. Remember, no legal proceeding will ever happen. If Mueller ever actually found anything, or if any investigator ever found anything, Trump absolutely would pardon himself. There is zero chance of Trump ever facing a trial for anything. Presidents, in this country, are above the law, at least when they are as shameless as Trump and have a party that, contrary to Trump's latest tweet, will defend him against anything. C is there because of the third term.
That third term is tricky. It is a "utility function," in econo-jargon. Economists translate outcomes into units of comparable value so that every dollar, every car, every computer, every cup of coffee etc. can be compared on the same scale. Everything is converted to units of utility. "Utils." Yes, a "util." How many "utils" is it worth for Trump not to be embarrassed? Trump is all about status. It is the only thing that really matters to him. Here is a question that I sometimes pose, to demonstrate the basic shallowness of The Donald. Would he rather be dirt-poor and have you think he is rich, or be rich and have you think he is dirt poor? By that, I mean that his actual lifestyle would match his actual financial circumstances. Eating out of dumpsters if poor, the whole deal. You know he'd rather have you think he is rich, even if it means eating out of dumpsters, sleeping in a cardboard box etc.
Keeping that in mind about how image-conscious Trump is, what happens if Mueller gets the goods on Trump? He immediately pardons himself, but Trump is humiliated, and Trump hates that. That's what the third term is about. On the other hand, it's still embarrassing to pardon himself early because it is basically an admission of guilt. That's why his people are now denying that he is even thinking about it. It's all about image. I still say that has contained impact like every other Trump "scandal" because his party will cover for him, contrary to his latest bullshit tweet, but a self-pardon followed by shutting down the investigation is still a cost.
So, there's the deal. By letting this thing go on, Trump is making the following gamble. He is running the risk of getting caught (G*C), which is associated with something really bad, U(proof of guilt), rather than choosing to keep things at least somewhat ambiguous and paying a definite but small cost, P.
GC*U(proof of guilt)>U(ambiguity)-P
The problem is that I've left something out. Did you notice? And it's what Trump has been saying all along is the reason Mueller shouldn't look into his finances... It's why he claims he won't release his taxes. Mueller can and will find unrelated, embarrassing stuff. There is no question about that. It will come out, with probability 1. Put certain embarrassment on the left-hand side of the inequality from unrelated aspects of the investigation (remember that Lewinsky had nothing to do with Whitewater) and this inequality can't be true anymore, even if Trump were certain of his own innocence.
Trump's best move now is to pardon himself immediately. He won't, because he is reckless, arrogant and stupid, but that's why he is being investigated. Of course, it didn't stop him from becoming President, so...
There is also the fact that Trump already admitted to firing Comey over the Russia investigation, which is clearly obstruction of justice to anyone who isn't an asshat lawyer, but like I said, Trump's a moron, and he really needs to pardon himself.
