Winning presidential elections, as Hillary Clinton has just been rudely reminded, isn’t just about what you vote, but where you vote. At the present moment, Clinton has a narrow but definite lead in the popular vote, but has already conceded the race, treating us all to 4 years of Donald Trump (or worse, Mike Pence).

Anyone familiar with elections will be pretty confused by this outcome, as while very few democracies employ methods which guarantee that a majority means a win, the systems only go wrong very occasionally. In Italy, for example, a whole succession of reforms have been enacted over the past few decades to make sure that even a barely clear plurality can function as a majority once it gets into office.

And for the past two hundred odd years, the Electoral College has worked remarkably well, only delivering an outcome different from the popular vote four times, and none of those in the 20th Century. The election of John Quincy Adams was definitely a fix-up, but Andrew Jackson won the next time round and got to commit genocide anyway. The compromise of 1877 ended Reconstruction in exchange for giving Rutherford B. Hayes the White House – probably not worth it – and dodgy dealing by party insiders cost Grover Cleveland re-election in 1888, but for over a century, the Electoral College worked fine.

Then the 2000 election happened, and amid all the hanging chads and the Supreme Court and Ralph Nader ruining everything for everyone, Al Gore chose the integrity of institutions over his own ambitions, and gracefully stepped aside.

All of which is the lede to an exciting data journalism question – why has the Electoral College, after over a century of smooth operation, started playing up all of a sudden? No elections in 112 years to two from five is a big step change. So, why?

The answer lies in the design of the Electoral College itself. The framers of the constitution had very little interest in popular sovereignty, and so broadly disregarded it, but were very concerned about the conflict between urban and rural interests (see Hamilton’s ‘Cabinet Battle #1’). The Electoral College was intended to ensure that no candidate could win without appealing to a broad swathe of the nation, by limiting the weight of votes from each state to the same as their voice in the Congress. There was no way to win the presidency with the support of New England elites alone.

Which brings us to the reason that Electoral College has broken down. The College forces candidates to pick up states rather than votes, and the margins in those states don’t matter in the slightest, which means that winning by three million votes in California (as Hillary Rodham Clinton has done) is no different from winning by three votes. From a terrifyingly practical perspective, almost three million voters have added literally nothing to the Democratic Party’s campaign for president this year.

And this is the problem – it doesn’t matter how many votes you get, it matters how efficiently your votes are distributed. You can pile them up in California (or indeed Texas, which Clinton lost  by only 9 points compared with Obama’s 16 in 2012), if you don’t get that 50 per cent +1, you may as well not have bothered.  So, to return to the top of this article, how do you win the Electoral College?

The key is to understand the distribution of Electors – every state is guaranteed three (a congress person, plus two senators) by the constitution, and a bonus three for D.C., which still isn’t a state for Reasons. That means that however small your state is, you have a guaranteed floor on your electoral influence. Let’s draw a contrast. 563,767 people live in Wyoming, according to the 2010 US Census, which is the basis for the divvying up of electoral votes. That gets them 3 electoral votes, as that’s the fewest you can have. 897,936 people live in Delaware, they also have 3 electoral votes, because those 330,000 odd additional people don’t matter. At the other end of the scale, the people of D.C. get 3 electoral votes to share between 601,767 of them, although admittedly no senators or congresspeople. In Texas, meanwhile, more than 25m people make do with just 38 votes between them, less than a third as much representation per head as those fat cats in D.C. get when picking a president.

So, how do you win the Electoral College?

Let’s try out a few scenarios, starting with the 2012 election, which has better data than this one. What’re the fewest votes you could get overall, and still win the Electoral College, if your voters were perfectly efficiently distributed across the various states.

Image: 270towin.com

This map looks nothing like any map you’ve ever seen, even on The West Wing. Louisiana, Oregon, and Delaware are all on the same page. Vermont and Utah in perfect harmony. But this is the most efficient way to win the presidency – winning 50 per cent +1 of the popular vote in each of the states that has the most electors per voter. Unsurprisingly, this route sweeps the West and Midwest, focusing on the low population states and three of the four biggest Electoral College prizes, California, Texas, and New York.

If we take this route, and assume that our candidate picks up no votes at all in the red states, while winning 50 per cent +1 of the votes in all their target states, as well as working with the turnout numbers from 2012, we get this outcome in the popular vote.

Democrat: 30,806,956

Republican: 96,042,343

But the Democrat wins 270 – 268 in the Electoral College.  Despite winning less than a quarter of the popular vote. Now this is obviously the most extreme example, so let’s try some others.

How few Electoral College votes can you get while still winning the popular vote?

 

Image: 270towin.com

 

If everyone in D.C. votes Democrat, everyone in the beige states stays home, and one person in each of the eleven largest states shows up and votes Republican, on a truly bizarre turnout, the Democrat loses with 99.99% of the popular vote.

These are both pretty silly examples, so let’s think about some slightly more realistic ones.

What’s the worst route to the presidency?

Image: 270towin.com

 

If you’re a Clinton fan, of either vintage, this probably looks pretty familiar. You’ve sewn up the Mid West, more or less, done not too badly in the South by modern standards, and lost a few log cabin Republicans. But this is the least efficient route to the presidency – you’re picking up 37.5m voters as minimum to make this map, and that’s if you win these states by a single vote each, and lose every other state without a single vote.

Seven million votes between the easiest and the hardest perfectly efficient routes to the presidency. That is the distorting power of the Electoral College.

The Electoral College exerts its own terrifying logic, entirely intended by the framers, of ensuring that no candidate can win with the cities alone. What Hamilton, Jay, Madison, Franklin, et al did not foresee, nor could they have, was the scale of the cities. More people live in Queens than in Maine or Hawaii. There are as many people in Utah as in Brooklyn,  and living in 93 times as much space. The Five Boroughs combined are more populous than the whole state of Virginia. The Electoral College does what it can to adapt – Florida was only worth 25 electoral votes in 2000 – but the three vote floor continues to discriminate against cities and concentrations of political opinion.

Perfect efficiency

So, what would have happened if the Clinton campaign had been able to freely move voters from their homes to swing states and districts in order to change the election?  Let’s imagine that the Clinton campaign redistributed all of that ~270,000 popular vote lead with perfect efficiency.

Image: 270towin.com

 

And finally, what could Hillary have done if she had distributed her 3m spare California voters to the other states even 50 per cent efficiently this year?

Image: 270towin.com

 

[Caveat: It is very, very, very difficult to simulate the multivariate calculus outcomes that are presented by third parties. So we’ve ignored them.]