The Funky Math of the Electoral College

You might already know we have a pretty weird system for electing presidents. Candidates can win with fewer votes, some states matter more than others, some votes matter more than others, and all due to an ad hoc political compromise between 18th century wigged gentlemen. Per their decision, we don’t vote for our leaders directly, but instead choose intermediaries, known as electors, who then (usually) vote for who we tell them to. Since each state is given two free electors regardless of how few people live there, voters from sparsely populated states like Wyoming are able to pack over three times the electoral punch than in large states like California. So it’s been for the past 57 presidential elections, and so it shall be this November when we decide whether Hillary Clinton or Donald Trump should be our next Commander in Chief. But the situation is even weirder than you think. According to Professor Steven Brams, a political scientist and game theorist at NYU who has been working on electoral decision problems since the 1970s, there is a non-obvious effect that gives more power to the large states than their large populations would suggest. His research indicates that campaign resources should be allocated to states according to their electoral votes to the three-halves power. Why this is so involves advanced combinatorial math, for the initiated only, but the outcome is that if one state has four times the electoral votes of another state, rather than give it quadruple the attention and ads, it’s in a campaign’s interest to give it eight times as much, all else being equal. (It may be a dubious proposition that this is in any way advantageous to the citizens of these large states, as they get bombarded with mailers and 30-second TV ads, but it is a reflection of how valuable their votes are to the campaigns competing for them.) This isn’t just an academic result, Brams told me. Studies show campaigns actually do allocate their resources this way. If anything, they over-invest in the large states. As 1964’s Republican nominee Barry Goldwater put it, you have to “go shooting where the ducks are.” Because most states’ electoral votes are bundled into winner-take-all blocs, a large state like Ohio with its 18 electors can easily become must-win for either side. One way to understand this phenomenon is to imagine an extreme case in which a number of large states merge into an even larger one. Let’s call it New Texaflohioginia. Let’s further envision that New Texaflohioginia is worth a total of 270 electoral votes, and that all the remaining states are worth a total of 268. In this thought experiment, a candidate could safely ignore anyone living in those smaller states since whoever manages to win New Texaflohioginia will get all 270 of its votes, enough to outweigh all the other states combined, and therefore enough to win the presidency. So which states have more influence per voter then, the big states or the smaller ones? It’s not an easy question to answer since there are factors pushing in opposite directions, and they interact in ways which are asymmetrical and complex. Small states get more electors per voter, while the big states form larger blocs which cluster their influence into unignorable masses. According to Brams, “you might think the small states would have an advantage because of the plus two votes they get, but the winner-take-all aspect swamps the small state effect.” But not everyone agrees with this analysis. Professor Andrew Gelman, a statistician and political scientist at Columbia University, points to a study of his which he says shows the real-life distribution of votes following a different pattern from the one predicted by Brams et al. In his view, the theory of a large state bias lacks empirical backing and thus the “small states are slightly overrepresented because of how they all get three electoral votes.” Even if academics aren’t in agreement on the knotty ways in which the votes of small and large states interact, there is one distinction that is widely agreed on: the one between swing states and non-swing states. The system “is motivating candidates to campaign in swing states, so a few states become very important and nobody else matters,” Gelman said. In a state like New York, for instance, democrats have won by an average of 26 percent in the last five presidential elections, and always by at least 20%. Since the outcome is generally not in question, an individual vote, or even a few thousand votes, cannot alter the result. What’s more, if a solidly blue state like New York does happen to be close in a particular election, that would almost certainly indicate a national landslide in favor of Republicans, as in 1984, when Ronald Reagan won New York--and every other state, excepting only Minnesota and the District of Columbia. Most states are lopsidedly red or blue in this way. Only a very few are competitive, and candidates limit their charm offensives to these few battleground states. “In most states your vote doesn’t count. You may as well not have voted at all,” Brams said. So which states do matter? For starters, Pennsylvania. Trump recently claimed that if he doesn’t win in that state, it will be because Clinton cheated. Given the current polls, that is highly dubious, but for a while its rust belt voters seemed receptive enough to the Republican nominee’s populist message. Florida too will certainly be at the top of both candidates’ wishlists. Its importance was amply demonstrated in 2000 when a mere few hundred votes were the difference in Florida’s electoral delegation swinging to George W. Bush instead of Al Gore, thereby winning him the presidency. Trump may now be regretting the way he insulted Florida’s popular Senator “little Marco” Rubio and ex-Governor Jeb “low energy” Bush. Then there’s Ohio. No Republican has ever won the presidency without winning Ohio, and Democrats have managed to overturn the will of Ohioans just once. According to the nonprofit organization FairVote, in 2012 Mitt Romney held more campaign events in Ohio than in all 30 of the smallest states combined. (Ohio still opted for Barack Obama.) The New York Times reports that Ohio Governor John Kaisich was offered--and turned down--the Republican VP slot. Hillary Clinton had more luck, luring the ex-governor of Virginia, another swing state, onto her ticket. Other swing states include Iowa, Nevada, Colorado, New Hampshire, North Carolina, and possibly Wisconsin and Michigan. If one purpose of our grueling year-long presidential campaigns is to create a national conversation about the major issues facing the country, then most Americans are not being invited into that discussion. The current system creates the incentive for candidates to moneyball the electoral college in all its kludgy non-egalitarian intricacies. These Byzantine strategeries are both opportunity and necessity for modern campaigns. As we gear up for an election so operatic and wacky it makes House of Cards look prosaic by comparison, it’s natural that the more urgent question of Clinton versus Trump remains at the forefront of our minds. But hovering above all the targeted ad dollars and campaign stops in the same old states, we might also pause to wonder: does democracy really need to be more complicated than “most votes wins”? However, the electoral college is written into the constitution and is not likely to be amended anytime soon. Let’s hope Pennsylvania, Ohio and Florida pick us a good president.

You might already know we have a pretty weird system for electing presidents. Candidates can win with fewer votes, some states matter more than others, some votes matter more than others, and all due to an ad hoc political compromise between 18th century wigged gentlemen. Per their decision, we don’t vote for our leaders directly, but instead choose intermediaries, known as electors, who then (usually) vote for who we tell them to. Since each state is given two free electors regardless of how few people live there, voters from sparsely populated states like Wyoming are able to pack over three times the electoral punch than in large states like California.

So it’s been for the past 57 presidential elections, and so it shall be this November when we decide whether Hillary Clinton or Donald Trump should be our next Commander in Chief.

But the situation is even weirder than you think.

According to Professor Steven Brams, a political scientist and game theorist at NYU who has been working on electoral decision problems since the 1970s, there is a non-obvious effect that gives more power to the large states than their large populations would suggest. His research indicates that campaign resources should be allocated to states according to their electoral votes to the three-halves power. Why this is so involves advanced combinatorial math, for the initiated only, but the outcome is that if one state has four times the electoral votes of another state, rather than give it quadruple the attention and ads, it’s in a campaign’s interest to give it eight times as much, all else being equal. (It may be a dubious proposition that this is in any way advantageous to the citizens of these large states, as they get bombarded with mailers and 30-second TV ads, but it is a reflection of how valuable their votes are to the campaigns competing for them.)

This isn’t just an academic result, Brams told me. Studies show campaigns actually do allocate their resources this way. If anything, they over-invest in the large states. As 1964’s Republican nominee Barry Goldwater put it, you have to “go shooting where the ducks are.” Because most states’ electoral votes are bundled into winner-take-all blocs, a large state like Ohio with its 18 electors can easily become must-win for either side.

One way to understand this phenomenon is to imagine an extreme case in which a number of large states merge into an even larger one. Let’s call it New Texaflohioginia. Let’s further envision that New Texaflohioginia is worth a total of 270 electoral votes, and that all the remaining states are worth a total of 268. In this thought experiment, a candidate could safely ignore anyone living in those smaller states since whoever manages to win New Texaflohioginia will get all 270 of its votes, enough to outweigh all the other states combined, and therefore enough to win the presidency.

So which states have more influence per voter then, the big states or the smaller ones? It’s not an easy question to answer since there are factors pushing in opposite directions, and they interact in ways which are asymmetrical and complex. Small states get more electors per voter, while the big states form larger blocs which cluster their influence into unignorable masses. According to Brams, “you might think the small states would have an advantage because of the plus two votes they get, but the winner-take-all aspect swamps the small state effect.”

But not everyone agrees with this analysis. Professor Andrew Gelman, a statistician and political scientist at Columbia University, points to a study of his which he says shows the real-life distribution of votes following a different pattern from the one predicted by Brams et al. In his view, the theory of a large state bias lacks empirical backing and thus the “small states are slightly overrepresented because of how they all get three electoral votes.”

Even if academics aren’t in agreement on the knotty ways in which the votes of small and large states interact, there is one distinction that is widely agreed on: the one between swing states and non-swing states. The system “is motivating candidates to campaign in swing states, so a few states become very important and nobody else matters,” Gelman said. In a state like New York, for instance, democrats have won by an average of 26 percent in the last five presidential elections, and always by at least 20%. Since the outcome is generally not in question, an individual vote, or even a few thousand votes, cannot alter the result. What’s more, if a solidly blue state like New York does happen to be close in a particular election, that would almost certainly indicate a national landslide in favor of Republicans, as in 1984, when Ronald Reagan won New York--and every other state, excepting only Minnesota and the District of Columbia.

Most states are lopsidedly red or blue in this way. Only a very few are competitive, and candidates limit their charm offensives to these few battleground states. “In most states your vote doesn’t count. You may as well not have voted at all,” Brams said.

So which states do matter? For starters, Pennsylvania. Trump recently claimed that if he doesn’t win in that state, it will be because Clinton cheated. Given the current polls, that is highly dubious, but for a while its rust belt voters seemed receptive enough to the Republican nominee’s populist message. Florida too will certainly be at the top of both candidates’ wishlists. Its importance was amply demonstrated in 2000 when a mere few hundred votes were the difference in Florida’s electoral delegation swinging to George W. Bush instead of Al Gore, thereby winning him the presidency. Trump may now be regretting the way he insulted Florida’s popular Senator “little Marco” Rubio and ex-Governor Jeb “low energy” Bush.

Then there’s Ohio. No Republican has ever won the presidency without winning Ohio, and Democrats have managed to overturn the will of Ohioans just once. According to the nonprofit organization FairVote, in 2012 Mitt Romney held more campaign events in Ohio than in all 30 of the smallest states combined. (Ohio still opted for Barack Obama.) The New York Times reports that Ohio Governor John Kaisich was offered--and turned down--the Republican VP slot. Hillary Clinton had more luck, luring the ex-governor of Virginia, another swing state, onto her ticket. Other swing states include Iowa, Nevada, Colorado, New Hampshire, North Carolina, and possibly Wisconsin and Michigan.

If one purpose of our grueling year-long presidential campaigns is to create a national conversation about the major issues facing the country, then most Americans are not being invited into that discussion. The current system creates the incentive for candidates to moneyball the electoral college in all its kludgy non-egalitarian intricacies. These Byzantine strategeries are both opportunity and necessity for modern campaigns.

As we gear up for an election so operatic and wacky it makes House of Cards look prosaic by comparison, it’s natural that the more urgent question of Clinton versus Trump remains at the forefront of our minds. But hovering above all the targeted ad dollars and campaign stops in the same old states, we might also pause to wonder: does democracy really need to be more complicated than “most votes wins”? However, the electoral college is written into the constitution and is not likely to be amended anytime soon. Let’s hope Pennsylvania, Ohio and Florida pick us a good president.

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