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Election Math Special

On Election Day Eve, we bring you a mathematical puzzler courtesy of Nathan Feldman, the new Rupert and Lillian Radford Professor of Mathematics at Washington and Lee.

How little of the popular vote can a presidential candidate get and still win the election?

That was one of a number of mathematic problems that Nathan posed and solved during his lecture, “Beauty & Surprise in Mathematics.” He began by noting that math and W&L go hand in glove. Not only was math the favorite subject of George Washington (a surveyor and map maker), but Robert E. Lee was an acting assistant professor of mathematics at West Point when he was a second-year student there.

After presenting three proofs of the Pythagorean theorem, and exploring the geometry of skateboarding and biking by examining the brachistochrone problem (look it up), Nathan turned to the U.S. presidential election.

Got your answer yet?

The fewest number of votes a candidate can get and still win a U.S. presidential election is . . . 11. That would happen if one person in each of the 11 most-populous states cast his or her ballot for the same candidate and no one else in those states votes, thereby awarding her or him 270 electoral ballots. And suppose that in addition to those 11 votes in those 11 states, every eligible voter in the remaining 39 states all cast a ballot for the other candidate: what would the winner’s winning percentage be? A whopping .000006 percent of the popular vote.

Now, suppose that the statewide voter turnout in every state is identical to the national voter turnout. It doesn’t matter what that percentage is; a candidate can win the election with as little as 21.8 percent of the popular vote. That can be done by winning 39 states with 12 electoral votes or less plus one state with 15 electoral votes.

And now, we trust, you’re ready to vote.