David Greenberg, a professor of history, journalism and media studies at Rutgers University, is the author of “Nixon’s ­Shadow: The History of an Image,” among other works of political history.

One night a few months ago, my 7-year-old son — who during the Republican primaries developed a mildly obsessional interest in presidential history — asked me to rank the American chief executives in order of greatness. With bedtime looming, I resolved to make it quick. Rattling off the successes (George Washington, Abraham Lincoln, Franklin D. Roosevelt) proved easy, as did listing the failures (James Buchanan, Andrew Johnson, Herbert Hoover, Richard Nixon). But filling in the middle drove me crazy. Should William McKinley place higher or lower than Gerald Ford? Martin Van Buren above or below Rutherford B. Hayes? Yawning, and under pressure from my eager son, I randomly plugged in Millard Fillmore, Chester A. Arthur and the Harrisons and called it a night.

Why is there such a robust appetite for something so silly? “ ‘Ranking the Presidents’ has always been a favorite indoor sport of history-minded Americans,” the political scientist Clinton Rossiter wrote in his classic 1956 work, “The American Presidency” — a line Robert W. Merry quotes in his diverting new book, “Where They Stand: The American Presidents in the Eyes of Voters and Historians.” The exercise plays to the 7-year-old within each of us, the part of our psyche that delights in making Top 25 lists, ticking off our desert-island discs and thumbing through “The New Bill James Historical Baseball Abstract.” We have a primal need to impose order on theinchoate, to quantify theunquantifiable....