No political judgments here. It’s just really hard to define.

By Nathan Collins

Thousands of people gather to hear Democratic presidential candidate Senator Bernie Sanders in Manassas, Virginia. (Photo: Chip Somodevilla/Getty Images)

In a press conference last month following his upset victory in the Michigan primary, Bernie Sanders spoke optimistically of a “people’s revolution.” This populace uprising would, he argued, bring him victories on the West Coast and elsewhere. Whether that revolution materializes, Sanders’ claim raises an interesting question: What, exactly, do the people want?

Well, the people, as a group, don’t want anything. More precisely, it’s nearly impossible to find any specific candidate or political platform that even a small group of people can agree on. If that sounds like complete horse malarkey, it’s OK: Social scientists held out hope for the “will of the people” for a couple hundred years after the first signs of political problems appeared, until a young economist’s side project finally settled the matter.

That young economist was Kenneth Arrow, who went on to win the Nobel Prize in Economics for his work on what’s called general equilibrium theory. But when he was still a budding economist, an interest in group decision making led him to conclude that it was, in general, impossible to define what the people want.

The people, as a group, don’t want anything.

There are a couple reasons for this, political scientists and economists now realize. For one thing, you can get different results depending on the voting system. Majority rule, for example, will sometimes yield different winners than rank-choice voting, an increasingly popular method among cities and councils.

But it’s worse than that—sometimes, a voting system will fail to produce any winner at all, an idea that goes back to the 18th-century philosopher and social scientist Marquis de Condorcet. (A truly fascinating character, he was a politician and advocate for women’s rights well before he wrote his most famous work, a 1785 essay on voting and elections.)

Here’s how it works: Suppose that Max, Nick, and Nathan want pizza. Nathan prefers Hawaiian to pepperoni, and pepperoni to vegetarian; Max prefers pepperoni to vegetarian to Hawaiian; and Nick prefers vegetarian to Hawaiian to pepperoni. Take a close look at those preferences, and you’ll realize that two of them prefer pepperoni to vegetarian, two of them prefer vegetarian to Hawaiian, and two of them prefer Hawaiian to pepperoni. So if the three guys were to vote on it, they wouldn’t be able to make a decision. If they’re going to eat pizza, someone (probably Nick) has got to make a command decision.

Condorcet’s observation led to a succession of proposals, most notably rank-choice voting and its cousin, the Borda count, but both proposals turned out to have their own issues. The choice between two candidates in the Borda count, for example, can depend on voters’ preferences over other, seemingly irrelevant candidates.

The culmination of the debate came in 1950, when Arrow published what’s now known as Arrow’s Impossibility Theorem. In the paper, he shows there’s only one way to make group choices that avoid the problems with majority rule and the Borda count, respect all possible preferences, and satisfy the no-brainer condition that if everyone prefers option A over option B, and no one prefers B to A, the group should choose A.

Unfortunately, that way is dictatorship.

This doesn’t mean that it’s impossible for the people to want something. Indeed, the people really may want a revolution. It’s hardly unprecedented. But exactly what they want out of that revolution, well, that’s another matter—just look at the last 240 years of American history.

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