Democracy is not “self-evident,” and schools must teach Americans the complexities of collective choice. This essential civics education includes understanding the philosophical judgments required for democracy to function coherently and sustain itself.

Yes, the Declaration of Independence’s proclamation that all humans are “created equal” should be embraced as irrefutable. So too should its principle that all humans have “certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”

We can even accept as incontrovertible that governments derive “their just powers from the consent of the governed” and that, if tyranny contravenes this fundamental tenet, “it is the Right of the People” to overthrow that tyranny and “institute new Government” that will adhere to popular sovereignty.

But what is most emphatically not self-evident is how the procedures of democracy should be structured so that the will of the people prevails.

When Thomas Jefferson drafted the Declaration, he was unaware of the insights about the mathematics of democratic choice that were to be developed in France a few years later. In 1785, the Marquis de Condorcet showed that there is no necessarily straightforward way to determine the collective preference of voters given three or more alternatives. It is possible that a majority of voters will prefer A over B, B over C, and C over A, creating a cycle with no obvious resolution.

Ever since Condorcet proved this truth, scholars have developed ways to make democratic choice coherent despite the existence of such cycles. One proposal is for the winning alternative to be the one preferred more often by voters against each rival alternative when examining how voters compare every pair of alternatives. This method is called a “Borda count” after Condorcet’s mathematical colleague who advocated it. Another proposal is that the winning alternative be the one least objectionable because the fewest voters wish another alternative had been selected. This other method is called “minimax”; it chooses the alternative whose worst comparison with another option is least unfavorable.

Americans, however, have not been educated to comprehend the problem for democracy of Condorcet cycles, the various proposals for solving this problem, and the relevant considerations for evaluating the pros and cons of these proposals, including the values served by a system of self-government. Because Americans have been taught that the basic features of self-government are self-evident, their schooling has not equipped them with the intellectual tools necessary to make informed judgments about the best way to select an outcome when citizens are divided in their preferences among three or more options.

The math involved is not too hard to teach to high school students, certainly no more challenging than algebra or trigonometry. But it is not something that is easily picked up on one’s own. If it’s not included in the curriculum each student receives in preparation for adult citizenship, the electorate will lack the capacity to decide what sort of democratic procedures it wants for determining its collective will.

Making this decision is not just a matter of math. It also requires a philosophical choice among competing conceptions of democracy. Indeed, even when preferences are not cyclical, there are different ways to conceptualize the ideal of majority rule. Condorcet argued that genuine majority rule occurs when the winning alternative is the one that a majority prefers over each other option. But others have argued, contra Condorcet, that this conception of majority rule lets a weak compromise prevail when it would be better to force a choice between two opposing alternatives, each of which is more popular than the compromise option.

Which version of majority rule is better for America really matters, especially now. When politics are hyperpolarized, as they currently are, Condorcet’s search for an outcome that a majority favors over what’s offered by two antagonistic camps is more likely to help depolarize political contestation than procedures that structure politics as a binary choice between left and right. 

As America prepares to commemorate the Declaration’s semiquincentennial, it must figure out how to educate its citizens on the mathematics and philosophy of social choice, including Condorcet’s seminal contributions. Otherwise, polarization may destroy democracy, so that there is no more self-government to celebrate when it comes time for the Declaration’s tricentennial in 2076.