Impeaching the Black Swan

I have no idea how the impeachment proceedings against Donald Trump will play out. Neither does anyone else. The most important thing to remember when reading media coverage of the impeachment process is that the writer has no idea how the impeachment process is likely to go. This goes for everybody.

The standard conventional wisdom has been that impeachment will backfire on the Democrats in a replay of 1998, when the Republicans impeached Clinton but made him more popular. There is no real reason to believe this. I'm not saying it won't happen. I'm just saying there's no evidence it will. There's only reason to expect an exact repeat of 1998, and I'm using the word "reason" loosely, is that a lot of political journalists covered 1998 and therefore assume this will go the same way. That assumption has nothing to do with logic or evidence.

Impeachments of a sitting president are so rare that it's impossible to generalize about them. This has only happened three times in the last 230 years, and one of those times the president resigned before the process finished playing out. Every single instance of impeachment is an outlier. They are all black swans.

There haven't been enough presidents of the United States, or even presidential elections, to constitute a valid statistical sample. But we fudge that, and run the numbers anyway, not always admitting how unreliable the results are. But no one can pretend that three is a statistical sample. That's ridiculous. No one tries to extrapolate anything from a baseball player's batting average after only three at-bats, or should. But this is more like a situation where only three games of baseball have ever been played. Predictions based on that are folly.

Would you read a sex-advice book written by someone who's only had sex three times? 'Or someone who started having sex three times, and finished twice? Pontificating about how impeachments turn out is the same way. No one has enough experience to know what's likely, or what's normal, and what isn't.

Over-generalizing from limited experience is a common mistake and a basic part of many political journalists' approach to their work. If you've ever heard a political journalist talking about some candidate's "Sister Souljah" moment, you've been given a good example. The journalist takes a thing that happened one time during Bill Clinton's 1992 primary run and treats it as something that must happen in all campaigns always. Woe betide the Democratic candidate without his or her Sister Souljah moment. But in fact there is no reason to expect the Sister Souljah incident to be repeated.

There are some people who try to argue that a 2019 impeachment will be a replay of Watergate in 1974 rather than of Clinton in 1998. But there's no reason to think that, either. It's no more likely than a replay of 1998. This doesn't have to be a replay of anything. Something totally different could happen. If there were such a thing as smart money in this case, and there's not, it would probably be on previously unforeseen outcome.

All three of the previous presidential impeachments were weird and therefore hard to compare to one another in any meaningful way. This one is also strange. The first impeachment was of a president who'd been vice-president before the president was assassinated, which had never happened before either, and he was not from the murdered president's party but the opposing party, because of a national unity ticket during the Civil War, and ... you get the idea. Totally unrepeatable circumstances. Watergate was also very strange. The Clinton impeachment was maybe the most "normal," in the sense of the impeached president's wrongdoing being the least unusual (which is not an excuse for illegality but a comment on its statistical distribution), but that arguably makes the Clinton impeachment unusual in its own right, another freak occurrence. Impeachments are so weird that you learn nothing from one experiment that you can generalize to the next. Nate Silver isn't going to help you out of this one.

The circumstances we're faced with are extremely strange, and so is the current occupant of the White House. Trump doesn't fit many precedents or norms. He's a kind of black swan president himself, who sometimes gets treated in the press as if normal probabilities don't apply to him. Trump won despite being behind in the poll and despite losing the popular vote by a bigger margin than any electoral-college winner ever had, so there's a sense in the press that the normal political expectations don't apply and that Trump's awful poll numbers, for example, won't hurt his chances at reelection. (This is another version of the generalizing-from-one-result error. Trump won a massively unlikely victory last time, so some people expect him to win next time. It's a bit like expecting someone who just turned an unassisted triple play to do it again tomorrow.)

It's not simply that we lack the experience to know what will happen or what will likely happen. We don't have the experience to foresee everything that can happen.

If you've only rolled a pair of dice three times, most of the possible outcomes have never occurred. There are eleven basic outcomes, from rolling a two to rolling a twelve. After three rolls, you haven't seen most of those. In fact, you may not have seen the most likely outcomes yet. Seven is the most likely result, coming up once in every six throws. But if you've only thrown the dice three times, the odds of seeing at least one seven are only between 42 and 43%, less than half. You are more likely not to have seen a seven than to have seen one.

That doesn't mean seven can't or won't happen on the next roll of the dice. It remains just as likely as it ever was, as do all the other results you haven't rolled yet. (Similarly, if you have only seen three at-bats of baseball, you may not have seen a hit, or a strikeout, or a walk, which doesn't make them any less likely in at-bat number four.) Expecting the next throw of the dice to produce the same result as the throw just before it, and discounting the possibility of an outcome you haven't previously seen, is obviously a mistake.  But that is exactly how many people are discussing impeachment.

The current thinking is that the party that impeaches the president will be punished by the voters, because that's the conventional wisdom about what happened last time. (We can debate that, too, but for purposes of this argument I won't.) No one talks about any political risk for the party defending its president, or facing a backlash from voters for shielding a president who's committed crimes, because that's never happened before. But "never happened before" in this case means "has not turned up in a minuscule and not necessarily representative sample of three freakishly-strange events." That something didn't happen in the first three tries doesn't make it impossible. It doesn't even necessarily make it unlikely.

In the same way, the three results you have seen aren't necessarily the high-probability ones. You might have rolled snake-eyes or boxcars in the first three rolls, either of which only happens once every 36 times. A thing that happens only three percent of the time is something that could and does happen. To bring things back to American political history: in 1804 the United States had only had three vice-presidents. One of those three had shot another Founding Father dead. That didn't mean that future veeps had a 33.3% likelihood of killing a Cabinet secretary in a duel (which would get us up to sixteen killer vice-presidents at this point). It just meant that three examples is nowhere close to being enough to get a sense of what's normal. (Presidents Washington, Adams, and Jefferson weren't exactly a representative sample themselves.)

We don't have enough of a historical track record to know what's likely, or even the full range of what's possible. As the late, great William Goldman said about the film business, nobody knows anything.

Alea jacta est, kids. Buckle up.

cross-posted at Dagblog. Please post comments there, not here.