Math Against Tyranny

More about the Electoral College.


This article about the electoral college originally appeared in the November 1996 issue of Discover. Some of our readers thought it would be a good idea to feature it again this election year. We agree. The editors 

When you cast your vote this month, you’re not directly electing the president—you’re electing members of the electoral college.  They elect the president.  An archaic, unnecessary system?  Mathematics shows, says one concerned American, that by giving your vote to another, you’re ensuring the future of our democracy. 

“One morning at two o’clock,” Alan Natapoff recalls, “I realized that I was the only person willing to see this problem through to the end.” The morning in question was back in the late 1970s. Then as now, Natapoff, a physicist, was spending his days doing research at MIT’s Man-Vehicle Laboratory, investigating how the human brain responds to acceleration, weightless floating, and other vexations of contemporary transport. But the problem he was working on so late involved larger and grander issues. He was contemplating the survival of our nation as we know it.

Natapoff’s self-chosen labor has taken him more than two decades. But now that the journal Public Choice is about to publish his groundbreaking article, he can finally relax a bit; he might even take a vacation. In addition to this nontechnical article, which skimps on the math, he’s worked out a formal theorem that demonstrates, he claims, why our complex electoral system is “provably” better than a simple, direct election. Furthermore, he adds, without this quirky glitch in the system, our democracy might well have fallen apart long ago into warring factions.

A champion should be able to win at least some of the tough, close contests by every means available–bunting, stealing, brilliant pitching, dazzling plays in the field–and not just smack home runs against second-best pitchers. A presidential candidate worthy of office, by the same logic, should have broad appeal across the whole nation, and not just play strongly on a single issue to isolated blocs of voters.

“Experts, scholars, deep thinkers could make errors on electoral reform,” Natapoff decided, “but nine-year-olds could explain to a Martian why the Yankees lost in 1960, and why it was right. And both have the same underlying abstract principle.”

These insights came quickly, but it was many years before Natapoff devised his formal mathematical proof. His starting point was the concept of voting power. In a fair election, he saw, each voter’s power boils down to this: What is the probability that one person’s vote will be able to turn a national election? The higher the probability, the more power each voter commands. To figure out these probabilities, Natapoff devised his own model of a national electorate–a more realistic model, he thought, than the ones the quoted experts were always using. Almost always, he found, individual voting power is higher when funneled through districts–such as states–than when pooled in one large, direct election. It is more likely, in other words, that your one vote will determine the outcome in your state and your state will then turn the outcome of the electoral college, than that your vote will turn the outcome of a direct national election. A voter therefore, Natapoff found, has more power under the current electoral system.

Why worry how easily one vote can turn an election, so long as each voter has equal power? One person, one vote–that’s all the math anyone needs to know in a simple, direct election. Natapoff agrees that voters should have equal power. “The idea,” he says, “is to give every voter the largest equal share of national voting power possible.” Here’s a classic example of equal voting power: under a tyranny, everyone’s power is equal to zero. Clearly, equality alone is not enough. In a democracy, individuals become less vulnerable to tyranny as their voting power increases.

James Madison, chief architect of our nation’s electoral college, wanted to protect each citizen against the most insidious tyranny that arises in democracies: the massed power of fellow citizens banded together in a dominant bloc. As Madison explained in The Federalist Papers (Number X), “a well-constructed Union” must, above all else, “break and control the violence of faction,” especially “the superior force of an . . . overbearing majority.” In any democracy, a majority’s power threatens minorities. It threatens their rights, their property, and sometimes their lives.

Lots more math and history. Worth the read, although it’s long!

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