At sunrise on the day before the Republican National Convention begins, in Cleveland, a hundred women will take off their clothes and pose for the photographer Spencer Tunick outside the convention hall. Naked, they’ll be holding up big, round mirrors to the sky, to catch the light. “Women will decide the outcome of this election,” Tunick says. He insists that his installation is not a political protest. “This is a work Republican women can participate in,” he says, bipartisanly.

This year’s Conventions will be held back to back, like a doubleheader, or two root canals in a row. The week after the Republicans meet in Cleveland, the Democrats will meet in Philadelphia. First Trump, then Clinton. But, what with the anti-Trumpers and the pro-Sandersers, some people are worried that all hell might break loose, which is unusual, since people more commonly worry that the Conventions will be boring. “At first blush, the Republican National Convention at Cleveland next week promises to be a very dull show,” H. L. Mencken wrote in 1924, when the incumbent, Calvin Coolidge, was the all but assured nominee. “Some dreadful mountebank in a long-tailed coat will open . . . with a windy speech; then another mountebank will repeat the same rubbish in other words.” And, while that really is what happens, lately more than ever (since 1952, no Convention has gone past the first ballot) the Conventions are never boring, if only because of the high jinks, not to mention the low jinks. In Chicago in 1864, the Democrats installed a giant sign made of coiled gas pipe. It was supposed to read “McClellan, Our Only Hope,” but the gas jets broke and the thing just flickered and died, hopelessly. Roscoe Conkling was so sure he’d get the nod in 1876 that he picked his Vice-President and a motto—“Conkling and Hayes / Is the ticket that pays”—only to be defeated by his erstwhile running mate, ever after known as Rutherfraud B. Hayes.

Until 1932, when F.D.R. decided to show up to accept his nomination, the candidates themselves skipped the Conventions, citing modesty, a precedent set a century before by Henry Clay. Asked by letter if he would be willing to be nominated by the short-lived National Republicans, at their one and only Convention, Clay wrote back to say yes but that it was impossible for him to attend the Convention “without incurring the imputation of presumptuousness or indelicacy.” When Grover Cleveland received a telegram at the White House informing him that he had been renominated by a Democratic Convention meeting in St. Louis, he said, “Heavens, I had forgotten all about it.” Many a journalist might not have minded if the candidates had maintained the tradition of keeping away. “Interviewing a candidate is about as intimate as catching him on television,” Norman Mailer wrote from the Republican Convention in Miami in 1968, to which some G.O.P. genius had flown in a pachyderm. “Therefore the reporter went to cover the elephant.”

It’s not all a bamboozle, especially not this election. The White House is at stake, and more, too: the state of the union. The worry, this time around, isn’t that the Conventions will be boring; it’s that they’ll be interesting, frightfully.

The Presidential-nominating Convention is an American invention. It is the product of a failure of the Constitution. Kings are born; Presidents are elected. How? This is a math problem and it’s a political problem, and it’s been solved but never resolved. The first nominating Convention was held in 1831. It was an attempt to wrest power away from something known as the legislative caucus, which was itself an attempt to wrest power away from the Electoral College. The first primary was held in 1901. It was an attempt to wrest power away from the nominating Convention. This year, there’s been a lot of talk about how the system is “rigged” by “the establishment.” It was exactly that kind of talk that got us the caucus, the Convention, and the primary, institutions built in the name of making American democracy more representative and more deliberative. But the more representative the body the less well it is able to deliberate: more democracy is very often less.

How to elect a President was vexed from the start. At the constitutional convention in Philadelphia in 1787, the men who framed the federal government made a great many compromises, but “the Convention were perplexed with no part of this plan so much as with the mode of choosing the President,” as the Pennsylvania delegate James Wilson later explained. Some delegates believed that Congress should elect the President. This allowed for popular participation in government while avoiding what Hamilton called the “excess of democracy.” But having Congress elect the President violated the principle of the separation of powers. Wilson proposed that the people elect the President directly, but Madison pointed out that the Southern states “could have no influence in the election on the score of the Negroes.” That is, the South had a lot of people, but a third of them were slaves; in a direct election, the North, which had a lot of people but very few slaves, would have had more votes. Wilson therefore suggested the Electoral College, a proposal that built on a mathematical compromise that had taken the delegates most of the summer to devise. Under the terms of the three-fifths compromise, each state was granted one representative in Congress for every thirty thousand people, except that slaves, who could not vote, counted as three-fifths of a person. Wilson’s proposal applied this formula to the election of the President: the number of each state’s electors in the Electoral College is the sum of its congressional delegation, its two senators plus its number of representatives. Substituting electors for voters conferred on the slave states a huge electoral advantage, once the first census was taken, in 1790. Virginia and Pennsylvania had roughly equivalent free populations, for instance, but Virginia, because of its slave population, had six more seats in the House than did Pennsylvania, and therefore six more electors in the Electoral College. This bargain helps to explain why the office of the President of the United States was, for thirty-two of the first thirty-six years of its existence, occupied by a slave-owning Virginian.

In the first two Presidential elections, George Washington ran unopposed. But by 1796, when Washington announced that he would not run for a third term, the polity had divided into parties, a development that the Electoral College was not designed to accommodate. One Federalist complained that he hadn’t chosen his elector “to determine for me whether John Adams or Thomas Jefferson is the fittest man for President. . . . No, I choose him to act, not to think.” To better delegate their electors, Federalists and Republicans in Congress began meeting in a caucus where they decided their party’s Presidential nominee.

Early American Presidential elections were not popular elections, not only because the vote was mainly restricted to white male property owners but also because delegates to the Electoral College were elected by state legislatures. The legislative caucus worked only as long as voters didn’t mind that they had virtually no role in electing the President, a situation that lasted for a while since, after all, most people living in the United States at the time were used to having a king. But a new generation of Americans objected to this arrangement, dubbing it “King Caucus.” “Under what authority did these men pretend to dictate their nominations?” one citizen asked in 1803. “Do we send members of Congress to cabal once every four years for president?” New states entering the union held conventions to draft state constitutions, in which they adopted more democratic arrangements. This put pressure on old states to revise their own constitutions. By 1824, eighteen out of twenty-four states were holding popular elections for delegates to the Electoral College. Between 1824 and 1828, the electorate grew from fewer than four hundred thousand people to 1.1 million. Men who had attended the constitutional convention in 1787 shook their gray-haired heads and warned that Americans had crowned a new monarch: “King Numbers.”