# How Would 2016 Have Looked if the Electoral College Was Mathematically Proportional?

The vote tallies are (mostly) in for the 2016 election cycle, and we’ve hit another anomalous event. Twice now in the 21st century, the winner of the Electoral College vote (and hence the presidency) lost the national popular vote. Prior to 2000, the last time a split vote happened was 1888 and, not surprisingly, the increasing frequency of its occurrence has led to yet more pontifications against the Electoral College per se.

The theoretical problems and benefits of the system are numerous and complex, and any thorough analysis is complicated by its historical, constitutional, and legal underpinnings. And, as dissections of the Electoral College (both pro and con) are becoming a near time-honored tradition, I don’t want to rehash well-traveled arguments.

But one point that has particular resonance in these discussions relates to fairness—a “one person, one vote” principle. Over the years, many have argued (e.g. recently over at Vox and The Washington Post) that the Electoral College violates this fairness principle by distorting the vote and thus disenfranchising large swaths of the electorate.

The argument goes something like this: the winner has to collect a majority, not of individual votes nation-wide, but of electors in the college. There are 538 in total, 1 per Congressional district and 1 for each member of the Senate (plus 3 for the District of Columbia). States vary widely in the number of Congressional districts, owing to differences in population density. California is the most populous state and has 53 Congressional seats (and hence 55 electors) while Wyoming, the least dense, has 1 district (and 3 electors total). Electors are roughly apportioned by population density (as are the corresponding Congressional Districts). But, since every state gets two Senate-derived votes irrespective of its size, voters in sparsely-populated states end up with more electors per voter, giving those voters an outsized influence on election outcomes.

It you peruse pro-reform sites you’ll sometimes see a statistic that comes out of this electoral quirk: voters in Wyoming have somewhere around a 3-fold greater “influence” in the electoral college than do California voters. This statistic and related ones are occasionally heralded as something of a Q.E.D. that the Electoral College produces inherently unfair distortions in the final election outcome.

But this struck me as more of an inference than anything dispositive. Is it really the case that a truly proportional system, where each vote counts “equally,” would have produced a different election outcome this year?

The big caveat in answering this question, of course, is that we can’t really predict with much accuracy how a voter’s behavior (or a politician’s behavior) would have changed in response to a different electoral system, were it in place. But let’s put that caveat aside.

And let’s put aside the argument over whether a proportional system—or which one—could replace the Electoral College outright, as proportionality can be satisfied in a number of ways (e.g. a direct national popular vote and an allocation of Electoral College electors proportional to each state-wide vote count would both involve proportional representation, in some sense).

What I was interested in answering was this: what would have happened in this election if the electoral college system itself were proportional? What if every voter represented an equal (fractional) number of electors, but each state’s winner-take-all system were still in place? In effect, I wanted to see whether voter distortions can be eliminated while still retaining an Electoral College-style system, and assess how this year’s election would have turned out under such a system.

I think the results reveal something interesting about the Electoral College and a subtler point about voter enfrachisement.

Math Time!

Okay, so let’s start by looking at what is meant by the outsized influence of small-state voters. A few other places have looked at this but it’s helpful to see it layed out. Below I’ve calculated the number of voters per elector, relative to the national average:

The states (plus the District of Columbia) are shown in descending order according to their population from the 2010 Census (which is what I used for all of the calculations). States above the 100% line have more electors per voter; those below have fewer. You can see the disproportionality pretty clearly: the less populous the state, the greater the “electoral strength” of its voters. Wyoming is sitting pretty at 258% relative to the national average, while California is down around 70%, giving Wyoming voters that 3-fold-plus distortional edge.

Okay, so let’s finagle some proportionality into this. The simplest way is to just remove the Senate-based electors from the equation:

The above chart shows how voter influence would look with only the 436 electors from Congressional districts (plus one for D.C.). That’s much closer, but still not quite right. Those little fluctuations are the result of slight population differences that occur before jumping from one electoral category to the next (necessary because we can’t physically split members of the electoral college into pieces—much as some may want to).

None of these adjustments are realistic anyway; the Constitution is quite clear on the mechanics of the Electoral College and any change—no matter how dull or fanciful—would likely require an amendment. So let’s just continue down the fanciful path and clear away all the bumps to make this absolutely proportional. If I arbitrarily set the electoral weight of the least populous state to 1 and then multiply up by population density, I can make all states equally proportional:

It doesn’t get much more “one person, one vote” than that! Voters in each state now have precisely the same per-elector weight as any other voter in the country. Just for comparison, here’s how the number of electors would change when shifting from the Electoral College to my Fantasy-Land College:

As you can see, the effect is to increase the number of electors in high-density states, and decrease them in the sparse states. Under this scheme, the ten most dense states gain about 40 votes altogether, and the ten least dense states lose about 20. Twelve states gain at least 1 vote, and sixteen states lose at least 1 vote. Adding up the total, this particular proportional scheme turns out to have 545.31 electors versus 538 in the actual college.

So, the states are now properly calibrated for full proportionality. Each voter commands the same fractional amount of an elector as a voter in any other state. Trump won 30 states (and Maine’s 2nd Congressional District), while Clinton won 20 states (plus D.C). If we take the victory map and plug in the proportional scheme, how does the modified college compare to the actual one? Here it is:

Actual Electoral College

Trump: 306

Clinton: 232

(1.32:1 Victory Ratio)

Proportional Electoral College

Trump: 309.24

Clinton: 240.08

(1.29:1 Victory Ratio)

(Note that for simplicity I added +3 to Clinton and +1 to Trump to compensate for Maine’s unique allocation scheme.)

Interesting! If we assume that voter and electioneering behavior were to be roughly similar, then adjusting voter power to equivalency within the Electoral College does almost nothing to change the final outcome of this year’s election. How is this so? Beyond the obvious observation that Trump won 10 more states than did Clinton, it turns out that the number of sparsely-populated red and blue states were not dramatically different: for example, of the states that have 10 or fewer electoral votes in the current system, 19 went red, while 12 went blue.

It’s worth pointing out that the assumption of unchanged behavior probably holds up pretty well under this scenario, given that—though the “points” awarded for each victory are different—the distribution of solid blue, solid red, and targetable swing states would by definition be precisely the same.

So What Does This Say About Voter Enfranchisement Under the Electoral College?

The results could have easily been quite different under a proportional Electoral College in a different election year (for instance, if one candidate had won a very large number of sparse states and the other won a very small number of the most populous states). But the broader lesson from this thought experiment is that the potential for contradictory results in the popular vote versus the Electoral College vote doesn’t happen because voters are unfairly weighted. In the scenario above, every voter is represented equally, the popular vote still would have gone for Clinton, and Trump still would have won by roughly the same electoral margin.

The potential for discrepancy arises because in the Electoral College we actually hold 50 separate elections rather than one, so vote total run-ups beyond the single vote needed for a state majority add no extra electoral value. Whether this characteristic ought to change is, however, for another time (and perhaps another post). But, I will note that the value of a Trump vote in very red state, or a Clinton vote in a very blue state, is not less than that of a swing state—since those extra votes are what keep these states out of play during an election cycle.

“One person, one vote” sounds pleasant to the ear and conforms to our instinctive predispositions to democratic fairness. It also happens to make for a nice bumper sticker slogan. But as an argument against the Electoral College, it simply doesn’t stand up to mathematical scrutiny.