Math, Rationality, and All That.

Supposedly, a million is a statistics, but one is a tragedy, according to Stalin, but there is something a bit deeper than this trivialization of numbers.  I began thinking about this after reading this article by Chris Arnade, a math PhD turned bond trader turned photo grapher/social commentator.  The problem, I suspect, is not because of numbers but because of the expectations and deviations from them.  Or, in other words, a million as a mean has a less impact than one as a variance.  (But a million as a variance will have much bigger impact than one as mean).

In the article, Arnade writes of how people in the commentariat write dismissively of terrible things that happen to so many people:  the economically and socially depressed parts of United States, the dead workers at the collapsed garment factory in Bangladesh etc.  Yet, for many, these events do not stray from what “we” expect, accurately or inaccurately, to be taking place in these places.  Huge tragedies are not all that unexpected.  Closer to home, however, tragedies are uncommon, even when they involve single persons.  The so-called missing white woman syndrome is not because a single disappearance is a tragedy, but we simply do not expect tragedies to befall the proverbial “white women,” even on individual basis.  You can be sure that, if a hundred “white women “disappeared on a single day, it will be portrayed as a far greater tragedy than a single disappearance, nevermind the “million is a statistic” quote.

Statistically speaking, these seem a bit silly:  there is no good reason to expect that a tragedy involving hundreds in a faraway, allegedly “unsafe” country with lax workplace regulations and such, is necessarily more likely, probabilistically speaking, than one disappearing “white woman” in the first world.  But while we understand the means, that one environment is “safe” while the other is “not,” we lack a good understanding of the variances–how likely the real reality is to deviate, and by how far, from the sense of mean we have in our heads (even when these means are accurate!).  So we gauge probabilities of the improbable poorly, in a manner not unlike how the second order thinking dramatically reduces the variance as noted in the beauty contest game.

Interestingly, one might expect people like Arnade to get this problem intuitively–which he seems to.  Successful bond trading, after all, requires accurate gauging of the variances.  Being able to predict the mean helps you track the market.  Being able to better gauge the variances helps you beat the market.  It is, by necessity, a gamble:  betting on a low mean, high variance choice gives you a greater chance to win big (and more than a higher, but still low mean, but lower variance choice), but you also run a greater chance of losing big as well–at least, usually (unless the distribution is skewed, but that’s another matter).  The point is that this seeming “irrationality” is fully within the realm of mathematical expectations.

This, in turn, brings up another post Arnade brings up elsewhere (the post that led me to the BI article, in fact):  Trump’s supporters (and to a lesser degree Sanders voters and even many of Obama voters back in 2008) are gambling, and gambling big on a high variance, low mean bet.  I had mentioned this before, that a single question in a Pew survey captured the dramatic difference between Clinton and Trump.   Trump inspires both extreme hope and extreme fear, from expectations that things will change dramatically somehow under his presidency.  Clinton inspires only expectation that things will stay the same.  But this extends far beyond just elections:  poor people buy lotto tickets and take chance on God (I tend to think Pascal, Kierkegaard, and in a sense, Marx had gauged the religion exactly right:  religion is a gamble.)  So the poor bet on the variances with little regard for the mean.  Not in itself an irrational action–even if incomprehensible to the means-based thinkers–but, perhaps, understandable to those who trafficked in high finance where everything depends on understanding the variances properly.

PS.  Another, perhaps, much neater way of describing this is to borrow words from Tolstoy:  the happy families are all close to the mean, while the unhappy ones all feature high variance.  But the patterns in unhappy families can be gauged by examining the patterns in their deviations from the mean.  Sometimes, you DO get cases where all unhappy families are alike while there are no happy families (e.g. coin tosses:  EVERY observation is exactly 1/2 away from the mean–you get either exactly 0 or exactly one head at a time and NEVER 1/2 of a head).  The problems today, in  a sense, might be that while the mean has been growing, the tails have gotten fatter (of course, this is just another way of saying inequality has grown.)  When the variances grow, knowing the means is less valuable than knowing the variances and their patterns.

PPS.  Doggoneit, Arnade had made exactly the kind of argument that I do, based on variances!!!!   Math education has really made us the same people (and he is a fellow Louisianan…).

PPPS.  Arnade’s observations about the disappearance of social institutions is a critical change that has gotten too little an attention.  I had written about the changing nature of retail politics before.  Electoral and party politics used to be social events, “popular politics,” as McGerr called it.  Its heyday had already passed by mid-20th century, but its traditions were carried on by individual politicians until fairly recently, in the form of “home style” as Fenno described it.  But the trend towards polarization and ideologicalization of party politics dealt the final blow to that tradition in the last twenty years or so as well:  as Alford said, and I paraphrase, why go around shaking hands every weekend in your home district when everyone already knows that you are a Democrat/Republican and everyone knows what to expect from a Demcorat/Republican?  Socializing with the voters is increasingly a waste of time, compared to what can be done in Washington…except it has also turned politicians and the political process into a caricature without a human touch.

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