The first American survey was ordered by the Constitution, and Article 1, Section 2, even specified the cross-tabs: “Number of free Persons, including those bound to Service for a Term of years”; “Indians not taxed”; and, infamously, “three fifths of all other persons”—that is to say, slaves. The new nation may have taken as its motto E pluribus unum, “From many, one,” but differences among Americans were written into the original political charter.

One hundred forty-nine years later, modern political surveying was born. The most famous presidential “straw poll” of the day was published for years in a magazine called Literary Digest. Its 1936 survey said the Republican Alf Landon would beat Franklin Roosevelt. Instead, Roosevelt ran up the biggest landslide in history. But George Gallup, Archibald Crossley, and Elmo Roper, competing market researchers who did political work on the side, had called it for Roosevelt. They used, Sarah Igo explains in her very thoughtful book, “statistical techniques that permitted a tiny cross-section of citizens of different regions, classes, and races to stand in for the whole.” It seemed to bestow on them an almost magic power: to divine how the average man thought.

By the 1940 presidential election, the three researchers claimed a grandiose civic function. “The political wisdom of the common people can now be settled,” Gallup pronounced, “on the basis of a mountain of factual data.” They gave their articles titles like, “We, the People, Are Like This,” and made confident assertions like, “The average American takes the attitude that conscription is . . . necessary.” This “average American” took on an almost living, breathing presence.

Such rhetoric obscured a paradox. Producing that one essential American required an understanding of the nation as a patchwork: so many people in this income group, so many...

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