Candidate A Gets 11 Votes; Candidate B Gets 70 Million Votes; The Winner: Candidate A!

June 1, 2012 — -- There are a number of structural problems with American democracy. Gerrymandering, in which partisan state lawmakers do their best to create squiggly congressional districts that stretch octopus-like to encompass enough supportive voters, is one of them. The role of money in campaign finance is another, as the Citizens United Supreme Court decision of 2010 illustrates once again.

Among the worst is the hoary United States Electoral College, which every four years seriously threatens to negate the will of the voters.

Sometimes taking ideas to an extreme lays bare their absurdities or at least underscores their weaknesses. Such is the case with the Constitutionally-mandated rules of the college, which allows for the possibility indicated in the headline to this piece. (If you understand why the number 11 appears above, you should probably skip reading. If not, take it as a simple puzzle to consider before reading on.)

Let me first state a few basic points. As many know, presidential elections in this country are decided by vote of the Electoral College, not by popular vote. This means that the outcome of the presidential election is determined by only 538 people, the electors in the college. The number 538 is the sum of 435, the number of representatives in the House, plus 100, the number of senators in the Senate, plus 3 electors for the District of Columbia.

Winner Take All

If a candidate receives more popular votes than his or her opponent in any given state, he or she wins all of that state's electoral votes, which is to say the sum of the number of that state's representatives plus 2, the number of its senators.

There are a couple of nuances that needn't concern us here, but the important point is that to be elected president one needs a majority of the votes of the 538 electors in the Electoral College. This magic number is 270.

The popular vote refers simply to the number of votes cast, and the candidate who receives the larger number is deemed the winner of the popular vote. The problem is that the winner in the Electoral College is not always the candidate who wins the popular vote as several U.S. presidential elections have demonstrated. Most recently, George Bush won the 2000 election even though Al Gore received about half a million more popular votes than he did. Because of outcomes like these, there have been repeated but so-far futile calls to abolish the Electoral College.

Do the Math

This is, as mentioned, well-understood by most people who follow presidential politics, but we can cutely accentuate the underlying problem with the college in this way:

Two candidates, A and B, are running for president. A gets 11 votes nationwide, B gets more than 70 million votes nationwide, yet A wins the election. (To provide a smidgeon of retroactive justice, we can reverse the 2000 presidential results by taking A to be Al and B to be Bush.)

How is this outcome logically possible? Well, since the number of electors in the Electoral College that are granted to a state is the sum of the number of representatives plus 2, the number of senators, we know that populous states, which have more representatives, will have more electors. Specifically, the 11 states with the most electors in the college are California (55), Texas (38), New York (29), Florida (29), Pennsylvania (20), Illinois (20), Ohio (18), Georgia (16), Michigan (16), North Carolina (15), and New Jersey (14).

The conclusion follows if, in each of these 11 most populous states, only one voter goes to the polls and he or she votes for A. No one in these states votes for B. Absurdly unlikely to be sure, but not logically impossible. Because each state is governed by the winner-take-all rules of the Electoral College, candidate A takes all the electoral votes from these 11 states, and a little addition shows the sum to be 55 + 38 + 29 + 29 + 20 + 20 + 18 + 16 + 16 + 15 + 14 = 270. A wins a majority in the Electoral College and is thus elected president of the U.S. It doesn't matter that in the other 39 states no one votes for A, but B receives a huge total of more than 70 million votes.

The Electoral College and Its Failings

There are a number of other problems with the Electoral College and one or two dubious points in its favor. Arrow's Theorem, a result in mathematical decision theory, shows that every electoral system has flaws and anomalies, but those of the Electoral College are, in my opinion, too egregious and too frequently occurring to countenance for much longer.

John Allen Paulos, a professor of mathematics at Temple University in Philadelphia, is the author of several best-selling books, including "Innumeracy," "A Mathematician Reads the Newspaper" and "A Mathematician Plays the Stock Market." He's on Twitter and his "Who's Counting?" column on ABCNews.com appears occasionally here.