The Election of Donald Trump and the Law of Small Numbers: A Statistical Note on the Choice of Incompetent Presidents.

The Election of Donald Trump and the Law of Small Numbers:

A Statistical Note on the Choice of Incompetent Presidents.

Burton Weltman

Making too much out of too little.

Statisticians have long warned us not to violate what they call the Law of Small Numbers, which is the mistake of making too much out of too little, and drawing big conclusions from a small sample of evidence.  At the same time, psychologists have told us that we are hardwired to do just that, and are programmed to reach hasty conclusions that would not survive reasoned reflection.  Without someone or something to make us stop and think, we all too often make decisions that we later regret.  And all of this, they tell us, is a result of evolution.

The tendency to reach hasty conclusions was, in fact, an evolutionary advantage for our puny ancestors, little rat-like mammals scurrying around trying to avoid being eaten by large predators.  For them, for example, seeing a potential predator in a given place more than once was probably a good reason to avoid that place forever more.  Taking extra precautions such as this was a key to survival for them.  But, the fact of the matter was that the appearance and reappearance of that predator in that place was often more likely a matter of chance than a pattern of behavior.  There was probably nothing to fear, but better safe than sorry was the order of the day.  The extra precaution was wise, albeit it was not statistically necessary.

We humans today are still operating under that primitive imperative of better safe than sorry, and we almost inevitably jump to broad conclusions based on limited data.  But what was a wise thing for our ancestors to do may be unwise for us.  Concluding, for example, that since your buddy was able to pick five winners in five horse races, you should place your life’s savings on his sixth tip, is probably unwise.  The sample of five winners in five races is just too small to reach a reasonable conclusion that your buddy knows what he is doing.  Unless, of course, you know that he has inside information and that the fix is in for the sixth race.

Making a silk purse out of a sow’s ear.

So, what does that have to do with the presidential election of Donald Trump?  Just this.  If you look at our system of electing Presidents in the United States, and read what commentators have been saying about it since the adoption of our Constitution, it is hard not to conclude that it is an extremely inefficient process.  At its best, the process has not worked at least since the first quarter of the nineteenth century to select the best and most qualified people to be our Presidents.  And with the degeneration of our political parties in recent years, and their declining influence, and with the increasing influence of big money and the mass media in the election of our Presidents, the process has gotten even worse in recent decades.  It is, at best, a random process, giving us maybe a fifty-fifty chance of having a decent or a disastrous President.

Under these circumstances, we have actually been very lucky in this country that we have had so few disastrous Presidents in our history.  Yet, we are surprised when someone as disastrous as Donald Trump gets elected.  We should not be surprised.  Our surprise is a function of our being fooled by the Law of Small Numbers.  Since a good majority of our Presidents have been at least decent, with disastrous Presidents seemingly as exceptions rather than the rule, we think we have a system of elections that works reasonably well.  Well, we don’t.  And it has once again been proven to us in spades.

There are many specific reasons why Trump was elected.  It was seemingly a perfect storm of things that went wrong or went against Hillary Clinton’s campaign, and went right or in favor of Trump’s.  But there are also many things wrong with our system of electing Presidents which contributed to his victory, from the undemocratic Electoral College to the extraordinary length of our election campaigns.

Some of these things will likely never be fixed, including the Electoral College, but some things can.  In particular, we need strong political parties that are organized from the bottom on up, and a strong program of public financing of election campaigns.  For information and ideas about public campaign financing, you can consult the website of Democracy Matters, a grass roots organization dedicated to taking big money out of our politics.  With stronger political parties and public financing, we can minimize the influence of demagoguery through the mass media of the sort that Trump successfully engaged in during the last election, and we can minimize the undemocratic influence of billionaires and big corporations on our elections.

These things are doable.  And we should, at least, learn from this last election not to trust in the illusion of conclusions that violate the Law of Small Numbers.  Given the nature of our electoral system, and the odds of the game, something like Trump was to be expected.  We can do better.




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