With the 2012 Presidential Election right around the corner, you’ll likely hear the number 270 tossed around quite a bit. It’s the required number of electoral votes a candidate must earn to be named president. Seems pretty cut and dry. Now throw the popular vote into the equation and you’ve piqued a mathematician’s interest.
Prof. Charles Wessell, assistant professor of mathematics at Gettysburg College, has been interested in the Electoral College for much of his career, particularly how the system provides the possibility of a candidate winning the presidency with less than half of the popular vote. Historically, it has happened several times. On three occurrences, a candidate not only obtained less than half of the popular votes, he even won the election with fewer popular votes than his opponent (1876, 1888, 2000).
Wessell has done the math forwards and backwards and found numerous ways to accumulate the hallowed 270 electoral votes with less than a majority of the popular vote. In fact, for Wessell, it’s a bit elementary. The real joy of Electoral College math is in the extremes.
In a two-candidate election, what is the minimal percentage of the popular vote possible for a winning candidate?
The answer requires examining the work of a fellow mathematics scholar and “a vague understanding of algebra,” said Wessell, who has lectured on the topic and was recently highlighted in the September issue of Math Horizons, published by Mathematical Association of America.
To tackle the question, Wessell turned to the work of mathematician George Pólya, who crafted the paper, “The minimum fraction of the popular vote that can elect the President of the United States,” featured in a 1961 issue of The Mathematics Teacher. Exploring Article II, Section 1, Clause 2 and 4 of the Constitution as a word problem, Pólya calculated a minimal popular vote percentage within an assumed 1960 framework.
The framework, a few simplifying assumptions added to the equation to produce a more manageable working model, states that there must be 537 possible electoral votes (same as in 1960); there must be only two candidates (occasionally three candidates have run in presidential elections); each state must award all of its electoral votes to the winning candidate in that state (winner takes all); and the number of votes cast in a state must be exactly proportional to the number of U.S. representatives from that state (states may be over or underrepresented).
Pólya’s results: With slightly 22.08 percent of the popular vote, a candidate can collect the required 270 electoral votes for presidency within the 1960 framework.
And how could a candidate achieve this? Win as many of the small states as possible, by as small of a margin as possible – one vote. As for the states a candidate lost, he or she would need to utterly tank, earning zero total popular votes.
Polya’s findings are impressive, but Wessell wanted to do better. Is it possible to win by earning 18, 17, or 16 percent of the popular vote?
Wessell discovered that since the decision variable for the problem could only take two variables, zero or one, a losing state or a winning state, he could use Binary Integer Linear Programming (BILP) to solve the problem within the established 1960 framework and produce a lower result.
Wessell’s conclusion: With only 17.56 percent of the popular vote, a candidate can win the presidency within the 1960 framework (utilizing actual voting totals from each state for that election). When working out the percentages for all other elections, including 2012, Wessell found that the popular vote for a winning candidate was typically as low as 18 to 21 percent.
Will we see this mathematically anomaly on November 6? Probably not.
Founded in 1832, Gettysburg College is a highly selective four-year residential college of liberal arts and sciences with a strong academic tradition that includes Rhodes Scholars, a Nobel laureate and other distinguished scholars among its alumni. The college enrolls 2,600 undergraduate students and is located on a 200-acre campus adjacent to the Gettysburg National Military Park in Pennsylvania.
Contact: Mike Baker, assistant director of communications, 717.337.6521.
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