A neighbor stopped me on the street the other day to share a moment of panic.

“If the presidential election were held yesterday, Donald Trump would have won,” she said, citing a report on the previous evening’s 11 o’clock news.

“You know,” I replied, “why don’t we take a poll on election day instead of voting? We’d inconvenience a thousand or so people with early morning phone calls, but the rest of us could go about our business undisturbed.”

I can never get enough of the deer-in-the-headlights expression that always accompanies this suggestion.

(If, perchance, you think this is a good idea, stop watching Fox News immediately.)

It was an Italian mathematician named Luca Pacioli who fathered the  agony and the ecstasy that we know as public opinion polling.

The year was 1494 and Pacioli, perhaps looking for some excitement after the whole Columbus-discovering-America affair, got in over his head trying to solve this problem:

Two players engage in a best 3-out-of-5 dice-rolling contest. After three rounds, the first player is up 2 to 1, but the game is called off. How, Pacioli wondered, should the prize be distributed?

Nobody officially won, but certainly the first player had a better chance of winning than the second, if the game had progressed. And, that was the glitch.

Pacioli was looking to mathematics to predict an event that hadn’t happened yet. But mathematicians of the day, who firmly followed Aristotle’s teachings, believed math could not do that. They wanted no part of Pacioli’s quixotic quest.

Pacioli died and the problem lingered, unsolved, until 1654 when Pierre de Fermat, a French lawyer and mathematician, proved that three-quarters of the prize should go to player one and one-quarter to player two. The proof was intuitively simple, and eventually dislodged the inertia of thousands of generations of mathematical Luddites.

Within a few decades mathematicians developed statistics, probability, the bell curve, statistical inference, and actuarial tables. But it was Jacob Bernoulli, a 17th-century Swiss mathematician, who laid down the law behind modern polling.

The Law of Large Numbers.

In conversational terms, the law says that if you have a huge barrel of jelly beans, some of which are red and the rest blue, you can estimate the percentage of red and blue jelly beans in the barrel by counting the red beans in a random sample.

Bernoulli’s math worked flawlessly for either/or events, such as a jelly bean being either red or not red, but another 200 years would pass before Russian mathematician Pafnuty Chebyshev extended Bernoulli’s work to situations in which the barrel contained jelly beans with any number of arbitrary colors.

If you think of the colors as being opinions, such as which presidential candidate a jelly bean is likely to vote for, it’s Chebyshev’s work that turned the Law of Large Numbers into justification for public opinion measurement. Nevertheless, Bernoulli’s original work remains as the heartbeat of those news-making polls.

I suspect television covers opinion polls relentlessly because of the medium’s fascination with law breakers. And every one of those polls breaks the Law of Large Numbers. The only question is to what degree.

Bernoulli would be the first to admit that Aristotle was partially correct. Math doesn’t predict the future with certainty. At best it offers a guesstimate of future results. How good that guesstimate is depends on how random your samples are.

And when it comes to random samples, it’s easier to break the law than follow it.

The instant you decide how to include people in your sample, the less random your sample becomes.

Call voters on a landline telephone? You’re excluding those who don’t have landlnes, or voters who don’t answer calls from strangers during dinner.

Go door to door?

Voters who work tend not to be home during the day. Upscale voters may spend their evenings at the opera or a popular eatery.

Stop voters on the street?

In Los Angeles you’ll get a colorful, albeit highly skewed, sample of Americans if you stick to people who are walking.

Since the best we can do is construct what’s called quasi-random samples—samples that are close enough to being random that they’d almost satisfy Bernoulli—television ought to report what would be a more telling measurement, in this case the odds that Trump will win, not merely the guess that he will.

And if Channel 4 would tell my neighbor not to worry, that the election wasn’t held yesterday, that wouldn’t be a bad idea, either.

Courtesy of Wikimedia Commons