###### The utility of a subdivision of the legislative power into different branches … is, perhaps, at the present time admitted by most persons of sound reflection.But it has not always found general approbation; and is, even now, sometimes disputed by men of speculative ingenuity, and recluse habits.

—Joseph Story. *Commentaries on the Constitution of the United States*. 1833.

“We habitually underestimate the effect of randomness,” wrote Leonard Mlodinow of MIT in his 2008 book on the subject: *The Drunkard’s Walk: How Randomness Rules Our Lives*—so much so, in fact, that “even when careers and millions of dollars are at stake, chance events are often conspicuously misinterpreted as accomplishments or failures.” But while that may be true, it’s often very difficult to know just *when* chance has intervened; it’s a hard thing to ask people to focus on things that never happened—but could have. Yet while that is so, there remains some identifiable ways in which chance interjects itself into our lives. One of them, in fact, is how Americans pass their laws—an argument that has not only been ongoing for two centuries, but that America is losing.

When, in 1787, the United States wrote its constitution, Edmund Randolph introduced what has since been called “the Virginia Plan”—the third resolution of which asserted that “the national legislature ought to consist of two branches.” Those two branches are now called the Senate and the House of Representatives, which makes the American system of government a *bicameral *one: that is, one with two legislative houses. Yet, although many Americans tend to think of this structure as, apparently, created with the universe, in fact it is not one that has been widely copied.

“Worldwide,” wrote Betty Drexhage in a 2015 report to the government of the Netherlands, “only a minority of legislatures is bicameral.” More recently the Inter-Parliamentary Union, a kind of trade group for legislatures, noted that, of world governments, 77 are bicameral—while 116 have only one house. Furthermore, expressing that ratio without context over-represents bicameral legislatures: even in countries that have two legislative houses, few of them have houses that are equally powerful, as the American House and Senate are. The British House of Lords, for example—the model for the Senate—has not been on a par politically with the House of Commons, even theoretically, since 1911 at the latest, and arguably since 1832.

Yet, why should other countries have failed to adopt the bicameral structure? Alternately, why did some, including notable figures like Benjamin Franklin, oppose splitting the Congress in two? One answer is provided by an early opponent of bicameralism: the Marquis de Condorcet, who wrote in 1787’s *Letters from a Freeman of New Haven to a Citizen of Virginia on the Futility of Dividing the Legislative Power Among Several Bodies* that “‘increasing the number of legislative bodies could never increase the probability of obtaining true decisions.’” Probability is a curious word to use in this connection—but one natural for a mathematician, which is what the marquis was.

The astronomer Joseph-Jerôme de Lalande, after all, had “ranked … Condorcet as one of the ten leading mathematicians in Europe” at the age of twenty-one; his early skill attracted the attention of the great Jean d’Alembert, one of the most famous mathematicians of all time. By 1769, at the young age of 25, he was elected to the incredibly prestigious French Royal Academy of Sciences; later, he would work with Leonhard Euler, even more accomplished than the great d’Alembert. The field that the marquis plowed as a mathematician was the so-called “doctrine of chances”—what we today would call the study of probability.

Although in one sense then the marquis was only one among many opponents of bicameralism—his great contemporary, the Abbé Sieyes, was another—very few of them were as qualified, mathematically speaking, to consider the matter as the marquis was; if, as Justice Joseph Story of the United States would write later, the arguments against bicameralism “derived from the analogy between the movements of political bodies and the operations of physical nature,” then the marquis was one of the few who could knowledgeably argue from nature to politics, instead of the other way. And in this matter, the marquis had an ace.

Condorcet’s ace was the mathematical law first discovered by an Italian physician—and gambler—named Gerolamo Cardano. Sometime around 1550, Cardano had written a book called *Liber de Ludo Alea*; or, *The Book on Games of Chance*, and in that book Cardano took up the example of throwing two dice. Since the probability of throwing a single number on one die is one in six, the doctor reasoned, then the probability of throwing two of the same number is 1/6 *multiplied by *1/6, which is 1/36. Since 1/36 is much, much less likely than 1/6, it follows that it is much less likely that a gambler will roll double sixes than it is that the same gambler will roll a single six.

According to J. Hoffman-Jørgensen of the University of Aarhus, what Cardano had discovered was the law that the “probability that two independent events occurs simultaneously equals the product of their probabilities.” In other words, the chance of *two *events happening is exponentially less than the chance of either one of those two* *events—which is why, for example, a perfecta bet in horse racing pays off so highly: it’s much more difficult to choose two horses than one. By the marquis’ time the mathematics was well-understood—indeed, it could not have been *not *known to virtually anyone with any knowledge of mathematics, much less one of the world’s authorities on the subject.

The application, of course, should be readily apparent: by requiring legislation to pass through two houses rather than one, bicameralism thereby—all by itself—exponentially lessens the chance of legislative passage. Anecdotally, this is something that has been, if imperfectly, well-known in the United States for some time: “Time and again a bill threatening to the South” prior to the Civil War, as Leonard Richards of the University of Massachusetts has pointed out, “made its way through the House only to be blocked in the Senate.” Or, as labor lawyer Thomas Geoghegan once remarked—and he is by no means young—his “old college teacher once said, ‘Just about every disaster in American history is the result of the Senate.’” And as political writer Daniel Lazare pointed out in *Slate *in 2014, even today the “US Senate is by now the most unrepresentative major legislature in the ‘democratic world’”—because there are two senators from every state, legislation desired by *ninety percent *of the population can be blocked. Hence, just as the Senate blocked anti-slavery legislation—and much else besides—from passage prior to the Civil War, so too does it continue to function in that role today.

Yet, although many Americans may know—the quotations could be multiplied—that there is something not quite right about the bicameral Congress, and some of them even mention it occasionally, it is very rare to notice any mention of the Marquis de Condorcet’s argument against bicameral legislatures in the name of the law of probability. Indeed, in the United States even the very notion of statistical knowledge is sometimes the subject of a kind of primitive superstition.

The baseball statistician Bill James, for example, once remarked that he gets “asked on talkshows a lot whether one can lie with statistics,” apparently because “a robust skepticism about statistics and their value had [so] permeated American life” that today (or at least, in the 1985 James wrote) “the intellectually lazy [have] adopted the position that so long as something was stated as a statistic it was probably false and they were entitled to ignore it and believe whatever they wanted to.” Whether there is a direct relationship between these two—the political import of the marquis’ argument so long ago, and the much later apprehension of statistics noted by James—is unclear, of course.

That may be about to change, however. James, for example, who was once essentially a kind of blogger before the Internet, has gradually climbed the best-seller lists; meanwhile, his advice and empirical method of thinking has gradually infected the baseball world—until last year the unthinkable happened, and the Chicago Cubs won the World Series while led by a man (Theo Epstein) who held up Bill James as his hero. At the same time, as I’ve documented in a previous blog post (“Size Matters”), Donald Trump essentially won the presidency because his left-wing opponents do not understand the mathematics involved in the Electoral College—or cannot, probably due to the fact of their prior commitment to “culture,” effectively communicate that knowledge to the public. In other words, chance may soon make the argument of the marquis—long conspicuously misinterpreted as a failure—into a sudden accomplishment.

Or perhaps rather—great again.