For the third time in a century (and the fifth time in US history) we have another election in which the candidate who won the popular vote did not gain enough electoral votes to win the presidency. This probably leaves you scratching your head, wondering how that’s even possible? After all, the number of electors each state has is based on the size of that state’s population, right? If a candidate gets the most votes in that state, that candidate wins all of the electors for that state. If you sum up all those votes the winning candidate should have the biggest total in both the popular vote and the electoral vote counts. Right? Yet, we have two recent examples where the candidate who *won* the popular vote *LOST* the electoral vote. (Gore in 2000, and Clinton this year.)

You don’t need to have a degree in math or political science to understand how this can happen. It looks complicated because there are so many states involved and the outcomes in those states are determined not just by votes cast, but by the percentage of voters who actually vote. If we look at a simpler system, and just assume everyone who can vote does, electoral math – and weird outcomes like we’ve just seen – are much easier to understand.

##### An Example

Let’s imagine a country that has just 6 states. One state has a population of 100, the other five have populations of 10 each. Each state is allotted one electoral vote for every 10 people. (We round up to the next 10, so a state with 13 people would be treated as though it had 20 and thus get 2 electoral votes.) Electors are awarded on a winner-take-all basis: whoever wins the most votes in that state, even if only by a single popular vote, wins all of the electoral votes.

State | Population | Electors |
---|---|---|

Big State | 100 | 10 |

Small State 1 | 10 | 1 |

Small State 2 | 10 | 1 |

Small State 3 | 10 | 1 |

Small State 4 | 10 | 1 |

Small State 5 | 10 | 1 |

Now, suppose you have an election to decide between candidate Jim and candidate Nancy for the next president. Even if all of the Small States vote unanimously for Jim, giving him 50 popular votes, he’ll only get 5 electoral votes. But if Jim loses in the Big State, even by only a few votes, Nancy gets all 10 of that state’s electoral votes, and thus beats Jim. All Nancy needs to do to win is get 51 votes (Jim would presumably get the other 49.)

Candidate | Big State Tally | Small State Tally | Popular Total | Electoral Total |
---|---|---|---|---|

Nancy | 51 | 0 | 51 | 10 |

Jim | 49 | 50 | 99 |
5 |

Nancy’s electoral tally is 10, but Jim’s is only 5. Yet, the popular vote *CLEARLY* favored Jim, giving him a total of 99 (50 from the Small States plus 49 from the Big State) with Nancy only receiving 51. Nancy wins with the most electoral votes even though she lost the poplar vote. Jim could lose by a very wide margin in the Big State — as much as 26 to 74 — and still win the popular vote (76 to 74), but lose the electoral college the way we’ve laid this out. This system is quite obviously biased in favor of the state with the most (voting) people.

##### Unbiasing the Bias

Let’s see if we can fix that the same way representation in the US’s legislative branch (Congress) was fixed. We’ll start by giving every state just one more electoral vote. We end up with Big State having 11 votes and each Small State having 2. Together the small states have 10 votes, which is better than before but still not enough to overcome Big State’s voting “power”.

So, let’s give every state two additional electoral votes and see what happens.

State | Population | Electors |
---|---|---|

Big State | 100 | 12 |

Small State 1 | 10 | 3 |

Small State 2 | 10 | 3 |

Small State 3 | 10 | 3 |

Small State 4 | 10 | 3 |

Small State 5 | 10 | 3 |

Now each Small State has 3 electoral votes for a total of 15, and the Big State has 12. Recalculating the tallies …

Candidate | Big State Tally | Small State Tally | Popular Total | Electoral Total |
---|---|---|---|---|

Nancy | 51 | 0 | 51 | 12 |

Jim | 49 | 50 | 99 |
15 |

Nancy now has 12 electoral votes, but Jim has 15, so Jim wins both the popular vote *and* the electoral college. We can all agree this is a fair and decisive outcome.

Or, is it?

In fact, this doesn’t eliminate the bias at all; it just shifts it to the smaller states. Sure, it gives the Big State 20% more voting “power”, but it gives each of the Small States 200% more voting power.

Let’s go back to our example and change the vote counts so that Nancy gets 80 votes in the large state and Jim only 20. Nancy still gets no votes in the Small States like before and Jim gets all of the popular votes there and so wins those electoral votes.

Candidate | Big State Tally | Small State Tally | Popular Total | Electoral Total |
---|---|---|---|---|

Nancy | 80 | 0 | 80 |
12 |

Jim | 20 | 50 | 70 | 15 |

Nancy wins the overall popular vote with a tally of 80 to Jim’s 70 (20 from Big State plus 5 x 10 from the Small States), but loses the electoral college to Jim with only 12 votes to his 15. In fact, Nancy could completely trounce Jim in the Big State, even winning it unanimously in the popular vote, and get 4 votes in every small state, giving her a whopping 120 votes to Jim’s 30. Jim would *still* win the most electoral votes and thus win the election.

##### A more recent, up-close-and-personal example

Our example isn’t all that far off from what the electoral map actually looked like in the first US election, held in 1788^{1}. In that election, John Hancock (Federalist) soundly defeated George Clinton (anti-Federalist). This map shows how the distribution of slave states and free states or industrial vs agrarian states was more or less even for both candidates. Worth noting, 51 out of the 96 total electoral votes rested with just 5 of the `13 states. That is, more than half the electoral college — clearly enough to carry any election — rested with less than half of the states. If electoral votes were simply one-state-one-vote, the 8 smaller states would have the greater power. Left to a one-(land-owning)-man-one-vote system, the more populous states have the upper hand. Rather than pick one or the other, the Framers of the Constitution came up with a system that *combined* these two extremes.

In the 2016 election cycle, Donald Trump won the most electoral votes and thus won the presidency even though Hillary Clinton won the popular vote by nearly three million more than Trump. Let’s look at how electoral math figured into this by looking at one of the two, electorally-large blue bastions, New York, which has 29 electoral votes, and a handful of small (by population), red states that have a total of 29 electoral votes between them. The following table^{2} depicts just such a collection.

Red State | Clinton | Trump | Electoral |
---|---|---|---|

Idaho | 189,765 | 409,055 | 4 |

Iowa | 653,669 | 800,983 | 6 |

Montana | 177,709 | 279,240 | 3 |

Nebraska | 284,494 | 495,961 | 5 |

South Dakota | 117,548 | 227,721 | 3 |

West Virginia | 188,794 | 489,371 | 5 |

Wyoming | 557,93 | 174,419 | 3 |

Totals | 1,667,772 | 2,876,750 | 29 |

Both the popular vote and electoral vote tallies indicate Trump to be the clear winner among these states. New York, on the other hand went unambiguously for Clinton with 4,547,562 votes to Trump’s 2,814,589. Clinton absolutely demolished Trump in New York’s popular vote and thus gained its 29 electoral votes. But, take a look at what happens when you add the New York popular vote with that of the red states:

State(s) | Clinton | Trump |
---|---|---|

Blue (NY) | 4,547,562 | 2,814,589 |

Red | 1,667,772 | 2,876,750 |

Totals | 6,215,334 | 5,691,339 |

In the overall totals, *Clinton wins over half a million more votes than Trump* in this subset of states — a margin of about 4.4% — yet they come out dead even in the electoral count.

Let’s throw in just one more small red state — Alaska, for example, which has only three electoral votes — Clinton still beats Trump by nearly half a million votes, yet loses the electoral count 32 to 29. Or, try this with Maine, which splits its electoral votes: Two went to Clinton, one to Trump. Clinton wins this electoral match-up by just one point, which hardly reflects the popular tally in which she wins by over a half million.

##### What are those “bonus” electoral votes really worth?

Suppose we paired up as many red and blue states as we could and subtracted two electoral votes from each of these states. In our example (before throwing in Alaska), we would discount New York’s two “bonus” electoral votes along with another two votes from one of the red states. That leaves 12 bonus from the other six red states. Now, divide the difference in the popular vote count (around 500,000) by these remaining 12 electoral votes and you find that they are worth just under 44,000 popular votes *EACH*. (This number would vary, of course, depending on actual voter turn out in a given election.) In other words, without this electoral bonus, for Trump to have matched Clinton in terms of the popular vote in these red states, he would have had to win an additional 87,000+ votes in each state, *on average.* If you subtract that number from the vote tallies for Trump in each of the red states and then recalculate the totals (including New York), Clinton beats Trump by more than a million popular votes, yet still ties him in the electoral count, 27-27^{3}.

I said on average rather generously. In fact, electoral votes aren’t “averaged”, so if we want to be truly strict about this, we’ll insist that Trump would have needed at least 87,000 more votes per state, for each of those six states. Where the popular margin was clearly in his favor, as it was in this sample, he still wins both the popular and electoral counts. If we include Alaska and apply this arithmetic, we have roughly 34,000 popular votes per bonus electoral vote. Subtracting twice this number (~68,000) as we did before, from Alaska’s popular count for Trump actually has *Clinton* winning Alaska in both the popular vote and electoral counts, 30-27.

If we apply this same arithmetic to all 50 states, Trump’s electoral edge of 77 electoral votes versus Clinton’s popular margin of 2,865,075 means each of those “bonus” electoral votes had the equivalent of 37,200 popular votes for Trump. Since he didn’t have to actually win those votes, he in effect won the election at a *discount* of sorts.

##### Is there a better way?

One solution that is regularly (and often) proposed is to do away with the electoral college completely and have just a popular vote. This would work fine when there is a clear choice or when a large enough part of the electorate is behind one of the candidates to make the vote clearly decisive. When voters are more or less evenly split, the system becomes highly vulnerable to ballot-box stuffing, voter intimidation and other types of fraud, or even counting errors or the rare loss of ballots from just one polling station. The electoral system makes this sort of rigging extremely difficult, and is highly fault-tolerant against slip-ups whether they are deliberate or accidental. It is also unlikely to produce a tie, in which case the Constitution says the election is decided by a vote in the House of Representatives. This has happened twice, the last time being nearly 200 years ago. In every election since the electoral college has delivered a very clear decision.

Another solution is to eliminate the additional two electoral votes per state. This sounds especially appealing when you realise that the whole reason we even do this relates indirectly to slavery being legal early in our history. I’m not going to go into the specifics of this, here. It’s sufficient to say that taking away those two electors from each state just puts us back to the first scenario where states with larger populations have the electoral edge. (Click here for a more detailed explanation of the link between slavery and the electoral college.)

Vote-splitting — allocating a states electoral votes in proportion to the popular vote — is yet another popular idea. Where there are only two candidates this amounts to nothing more than the system I described at the beginning of the example. Furthermore, suppose a state had only two electoral votes. How would you split these between two candidates when one of them had a significant majority in the popular vote? If there were more candidates, there would still be two major ones, leaving the other, minor candidates to function as little more than spoilers. It doesn’t really solve the problem; it merely “kicks the can” down the road a bit further. (You can begin to see why the Framers left this up to the states.)

##### You Can’t Fix “Stupid” … or “Lazy”

I believe that the real problem isn’t the electoral college; it is the electorate — the voting public — themselves. Any system that puts such important decisions to a vote as we do REQUIRES participation in that system for it to work properly. That means that eligible voters MUST VOTE, at the very least. When too few show up, the system becomes unstable, “wobbly” and decisions like electing a new president become about as random as flipping a coin. The electoral result will still be quite definite, but it is just as likely to disagree with the popular vote as it is to agree with it.

The electoral college is designed to ensure a decisive victory one way or the other. In fact, it quite purposely punishes poor voter turn-out by often handing the election to the least popular candidate. And, for those who say, “But I did vote! For a third-party candidate.”, I would answer that the electoral college also punishes poor understanding and willful ignorance. To vote in the general election you must understand or at least accept that, like it or not, there are two main candidates and only one of them will win. Voting for a third party candidate because you think you shouldn’t have to choose between the “lesser of two evils” will almost certainly result in your vote helping to elect the greater of the two.

##### Summing it Up

This last example is a simplified version of precisely what happened in the 2016 election. Instead of just six states, we have 50 (plus DC) and there are far more combinations of state populations and electoral vote tallies. But, the underlying mathematics is the same. You only need to know how to add numbers and compare them to see which is larger. It is tempting to say that anyone who can’t understand such basic arithmetic probably shouldn’t be voting. It is much more accurate to say that those who don’t vote can’t count.