What the Electoral College tells us about the Electorate

Voting systems should be designed so that the outcome of elections reflect the preferences of voters. This is much easier said than done, and dozens of voting systems have been proposed, each with their strengths and weaknesses. The Electoral College system awards electoral votes to a presidential candidate on a winner-take-all basis at the state level, with the exceptions of Maine and Nebraska. In a previous post, I describe one of the major weaknesses of this system. States are highly heterogeneous in their makeup, even states that are consistently Red or Blue by a large margin. This fact alone makes it highly questionable to award electoral votes with a winner-take-all system, aside from all of the other negative consequences of this system that I described in that article. Here I bring up an additional issue: the Electoral College obscures voter preferences since the electoral result can swing wildly with small changes in vote counts. The electoral results also may swing drastically with fixed votes but slight changes in state borders. Aside from granting the election winner the legal authority to govern, elections can provide valuable information about the electorate which leaders can point to as a mandate for their agenda. However, when an electoral system distorts voter preferences arbitrarily, as the Electoral College does, it becomes difficult (if not impossible) to use election results as a way to take the nation's pulse. Every politician, journalist, and citizen appears to have a unique interpretation of the 2016 election result, and there is at least a grain of truth in each of these explanations. Our election results are like an inkblot test, where everyone simply sees what they want to see, and each explanation may be at least partially justified by the data. This system can and should be changed. The National Popular Vote Interstate Compact is a de facto implementation of a popular vote system through state legislatures. Member states agree to cast their electoral votes for the national popular vote winner regardless of their state level winner. This is a step in the right direction, but I'll mention as I did previously that eliminating the Electoral College is just a half measure if you are interested in having a voting system that truly works for everyone. I'm preparing some materials on some of these other voting systems for future posts. But first things first, let's see if we can claim that the Electoral College result reflects what voters actually want.

The Efficiency Gap

The best strategy to win the Electoral College is to focus campaign efforts on states that are close races, and to ignore states which you expect to safely win or lose. To put it more quantitatively, you want to minimize your so-called wasted votes, where votes in states you lost (lost votes) as well as additional votes beyond what was necessary to win a state (surplus votes) are considered wasted. Take the 2016 presidential result in California: 3,916,209 people voted for Donald Trump, but all of California's electorate votes still would have gone to Clinton even if 0 people had voted for him. These 3,916,209 people votes are thus considered wasted votes for the Republicans. 7,362,490 people voted for Hillary Clinton, but only 3,916,210 were needed to win all of California's electoral votes. The surplus 3,446,280 are wasted votes for the Democrats. The efficiency gap is the difference in wasted votes for each party divided by the total number of votes in the election. The reason why these votes are considered to be wasted is because a party would be better off if its wasted voters had been in a swing state where they could have tipped that state one way or the other. To maximize your efficiency gap, you want to lose big in the states that you cannot win, and win narrow victories in the states that you can win. You don't need to win by large margins in any state though. It may seem strange at first that it's actually a bad thing to win a state by a large amount, but it makes sense. The Democrats would have been better off if the surplus voters in California had been in Florida, Michigan, Pennsylvania or any other close loss for Democrats. This cuts both ways, and surplus Republican votes in Texas would have been more valuable to Republicans in Virginia or New Hampshire. Below I've computed the wasted votes and the efficiency gap for the 2008, 2012, and 2016 elections. Note, since I use both county-level and state-level data, the state-level data is computed from the county-level data for consistency. Official results for the 2016 election are not yet available on the county level, and state-level tallies reported elsewhere for 2016 may therefore differ from the results shown here.

Year Wasted Dem. Votes (Millions) Wasted Rep. Votes (Millions) Efficiency Gap
2008 30.61 43.87 Dem. 10.24%
2012 28.13 40.96 Dem. 10.58%
2016 41.34 29.43 Rep. 9.65%

In 2008 and 2012, the Electoral College actually helped the Democrats, with very similar numbers for the efficiency gap as 2016. The major difference between President Obama's wins and President Trump's is that the Electoral College turned Obama's popular vote win into an electoral win by a much more substantial margin rather than allowing him to take the presidency with a popular vote loss. The total numbers of wasted votes in both elections are pretty shocking, and this gets hidden somewhat by just looking at the efficiency gap alone where large numbers of wasted votes for both parties essentially cancel each other out. 

The efficiency gap tells us what the difference is in the wasted votes between two parties, which is one way to measure how an election may have favored one group or another. However it does not necessarily tell us how effectively a party is in converting popular votes to electoral vote in the electoral college. In addition to the original efficiency gap, we can use a variant of the efficiency gap that is more intuitive and easier to visualize, which I'll call the electoral efficiency. If we ignore all third party votes, then the electoral efficiency simply is the difference between a party's percentage of electoral votes and its percentage of popular votes. In general, the electoral efficiency will not be the same magnitude as the efficiency gap, and these two measures would coincide only if each state had the same population and the same number of electors. For congressional races, each district has roughly the same population, and winning one district gets you one seat in contrast to the electoral college where winning one state wins you multiple electors. This makes it a little easier to apply the efficiency gap for analyzing gerrymanders in congress and state assemblies. In fact, the efficiency gap was central to the ruling of Whitford v. Gil, where the plaintiffs successfully argued that Wisconsin's state legislative districts are unconstitutionally gerrymandered. In a future post, I'll describe the similarities and differences in the arguments used in this and other gerrymandering cases and arguments against the Electoral College in more detail. Since there is a recent court ruling on the books where the efficiency gap played a key role, it is worth using for the electoral college as well, as long as it is clear that the gerrymandering cases and the electoral college are not completely analogous. Below, I've plotted the Democratic popular vote share vs. electoral vote share for 2008, 2012, and 2016. The back line represents a proportional result, where the shares of electoral and popular votes are the same. The electoral efficiency is just the vertical distance from a given election result to the black line. Outcomes that fall below the blue line mean the Electoral College hurt Democrats, while outcomes above the blue line favor Democrats.

Since electoral votes are allocated on a winner-take-all basis, we should not expect to see proportional results in general, but a large electoral efficiency favoring either party represents a distortion of voter preferences. All three elections were quite distorted, and supporters and detractors of each election winner can find some evidence to make nearly any case they want about the results. President Obama's popular vote wins were pretty solid by election standards, but nowhere near as significant as his electoral vote percentage. His supporters pointed to his large electoral win margin as evidence of a broad mandate for his agenda, while his opponents pointed to his smaller popular vote margin to counter this notion and argue for a more limited mandate. Today, President Trump's opponents point to his popular vote loss as evidence of strong opposition to his agenda. President Trump himself has subscribed to various conspiracy theories attributing his popular vote loss to fraud and has claimed his electoral victory is a mandate for his agenda. These contradictions in our election results do not bring any clarity, just confusion.

Since the Electoral Collegee distorts the election outcome, it is a bit tricky to determine whether or not an election was "close." Looking only at the electoral results makes it appear that President Trump's electoral win was close by historical standard. On the other hand, looking only at Hillary Clinton's popular vote win makes it appear that the election was close in the other direction. A technique we can use to determine the closeness of a race is to consider some hypothetical election outcomes, where we shift voters from one party to another by the same percentage in each state. We then recompute the electoral results to determine the hypothetical winner under this uniform shift. This can be repeated for shifts of many different magnitudes, and we can generate a whole curve of outcomes for a given election. While these results are hypothetical, it is a very useful technique, as we will be able to see if small changes in the popular vote could have led to large changes in the electoral vote. This exercise tells us if an election was close or not, and it can further reveal how a particular election may have favored one party or another. A similar concept is used to attempt to identify partisan gerrymandering in congressional elections. Again, even though these are hypothetical scenarios, they allow us to answer important questions about an election. For example, if a block of voters shifted their votes from one candidate to the other, would their change in preference be reflected in the election outcome? We can shift as many votes as we want, but this only remains sensible up to a certain point. While many voters have their mind made up from the start, there are always many late-deciding voters who don't choose their candidate until election day, so considering small shifts in the vote is reasonable. I've considered shifts of no more that plus or minus 8% from the actual result, which may sound like a lot, but opinions changed wildly throughout this election cycle. The real clear politics polling average, which is an estimate of the popular vote outcome based on aggregated polling data, varied from 1% favoring President Trump to 8% favoring Hillary Clinton over the course of the last few months leading up to the election. Further, most of the interesting results from this technique are found by shifting votes by no more that one or two percent from the actual result.

Below, the dots represent the Democratic popular vote share (with third party votes excluded) vs. the electoral vote share in 2008, 2012, and 2016. The black line represents an election outcome where the Democratic popular vote share is the same as its electoral vote share.  The electoral efficiency is the vertical distance from any outcome to the black line. The jagged lines are hypothetical outcomes, the result of shifting votes from one party to another by the same percentage in any state. 

The first thing to note is the difference in popular vote share to electoral vote share at 50%. In 2008, if there was a uniform nationwide shift of popular support from President Obama to Senator McCain so that if the popular vote was evenly split, the electoral vote would have gone to President Obama by a slight margin. The same is true for 2012, but to an even greater degree. Under these scenarios, President Obama could have won the presidency while losing the popular vote. There was actually some concern that this would happen in 2012, and at the time President Trump called for a march on Washington to protest this outcome, which ultimately did not occur. These elections showed a slight partisan advantage favoring Democrats, but if Senator McCain had won the popular vote by the same margin as President Obama did, he also would have enjoyed a nice boost in his win margin from the Electoral College. The same is true for Mitt Romney in 2012. From this analysis it appears that President Obama's wins were fairly comfortable, although not as dominant as the Electoral College made it seem. We can also say that while the Electoral College amplified President Obama's wins, it likely would have done the same for his opponents if they had the same level of nationwide support. This means that the 2008 and 2012 elections showed some degree of partisan symmetry, and they would have given a boost to whichever party had won. The Republicans were clearly disadvantaged however, since a narrow popular vote loss for President Obama could still have elected him in both years.

In 2016, the Republicans clearly enjoyed a partisan advantage. For the Democrats, 50% of the popular vote would have only earned them about 43% of the electoral vote. They had a significant uphill battle in the Electoral College, but a fairly small uniform nationwide swing in favor of the Democrats in 2016 would have quickly flipped the Rust Belt states that President Trump narrowly won. This slight shift would have caused a substantial and highly disproportionate swing in the Electoral College in favor of Hillary Clinton. Small changes in overall voter preferences would have led to a huge difference in the electoral result and election outcome. Looking at a 6.5% electoral win margin by President Trump hides how razor-thin his victory actually was, boiling down to narrow victories of tens of thousands of votes in a handful of important swing states. Note that this analysis assumes that support shifts from one candidate to the other uniformly nationwide. It is rare for support to shift exactly uniformly however, and in fact it is possible to gain in the electoral vote share while losing in overall popular vote share. For example, Hillary Clinton could have afforded to lose millions of supporters in California if it won her the 10,000 or so additional votes she needed to flip Michigan. This points back to the reason why swing states are the only states that matter in the Electoral College, which I discussed previously.

As an interesting aside, when similar techniques are used to examine gerrymandering in congressional districts, instead of comparing a party's share of popular votes to its share of electoral votes, we compare a party's vote share to its share of congressional seats won. The deficit in vote share to seat share at 50% support has been proposed as a measure of partisan asymmetry and has been considered in the Supreme Court case LULAC v. Perry, which was a gerrymandering case in Texas. The Supreme Court Justices viewed this metric as useful but not definitive, which I generally agree with. Technical details of this metric can be found here, and a discussion of its usefulness from a legal perspective can be found here. Both link to pdfs.

Partisan asymmetry and sensitivity to small changes in voter preferences are highly undesirable features in a voting system because it makes it very difficult to use the electoral result as a way to take the pulse of the electorate. President Trump seems to have noted this himself, appearing confused and agitated that historically large demonstrations against him occurred after his inauguration. This analysis showed that the 2016 result was quite sensitive to small changes in nationwide voter preferences, but that is not the only way we can try to evaluate the sensitivity of an election result. In the next section, instead of considering changes in the vote itself, we'll look at small changes to state borders. As it turns out, the 2016 result was highly sensitive to geography as well.

The Electoral Shuffle

Many states have interesting histories, but their borders are fairly arbitrary. Multiple distinct communities may be contained within the boundaries of a state, and therefore it doesn't make much sense to aggregate the votes of a state in a winner-take-all electoral system. The borders of states should not influence the outcome of the election for the office of president, but in fact they do. Below we see counties that lie on their state border, colored blue for counties going to Clinton, and red for counties going to Trump.

While on average, citizens of a particular state may lean in one direction or the other, it is not reasonable to consider the preferences of voters in a state to be homogenous. Aggregating votes by winner-take-all state-level elections additionally has the effect of making electoral results sensitive to small changes in state boundaries. This means that while keeping voter preferences fixed, the electoral result can change drastically. Kevin Wilson has created an interactive map where you can redraw state boundaries and see how the electoral result changes. Here is one such map, that actually flips the winner of the election:

So what happened here? Florida and Michigan flip and the Electoral College goes to Clinton. This is possible by taking Escambia, Okaloosa, and Santa Rosa counties in the panhandle of Florida and counting their votes in neighboring Alabama. Alabama was won solidly by Trump, but since the Electoral College is winner-take-all, adding more Trump votes to this state doesn't change the outcome of the Alabama election. On the other hand, moving these votes is enough to flip Florida to Clinton. Similarly, moving Monroe County in Michigan in to Ohio is enough to flip Michigan for Clinton and win her the election. The popular vote totals stay exactly the same, the only difference is that four counties, with a total of 0.32% of the national popular vote, were counted to their neighboring state. The efficiency gap now favors the Democrats by a slight margin of 1.02%. Voter preferences did not change, we simply shuffled four counties around to decrease the number of wasted votes for Democrats. We can get another scenario where Clinton wins the Electoral College by moving more votes, but one fewer county. Here we again move Monroe County in Michigan to Ohio, but instead of flipping Florida, we can move Lake County, Illinois to Wisconsin, and Camden County, New Jersey to Pennsylvania. This map moves 0.45% of the total votes cast nationwide, and leads to an efficiency gap favoring Democrats by a slight margin.

President Trump could have also benefited from a little shuffling of this kind. In this map, three counties with a total of 1.05% of the national popular vote can be shuffled to win Trump three additional states: Nevada, by moving Clark County to California, New Hampshire, by moving Cheshire County to Massachusetts, and Virginia, by moving Fairfax County to Maryland.

That would have given President Trump 61% of the electoral vote, putting him in 36th place for the electoral vote share historically, one spot behind Barack Obama in 2012. Again, the electoral vote changes significantly without any change in voter preferences, just some slight changes in state boundaries. Just to make things even sillier, let's combine all three scenarios.

While we are now moving some fairly significant numbers of votes in total, it is hard to argue that these changes in state borders would have led to changes in campaigning strategy from either candidate, since they all involve small changes to states that were already contested. The table below summarizes the information from these four scenarios, compared to the actual 2016 result.

Wasted Dem. Votes* Wasted Rep. Votes* Efficiency Gap Votes Moved* (% of total) Electoral Votes Flipped (% of total)
2016 Actual 41.34 29.43 R 9.15% - -
FL, MI 34.72 36.05 D 1.02% 0.41 (0.32%) 45 (8.36%)
MI, PA, WI 34.79 35.89 D 0.85% 0.59 (0.45%) 46 (8.55%)
NV, NH, VA 43.40 27.51 R 12.21% 1.36 (1.05%) 23 (4.28%)
All 32.47 38.36 D 4.53% 2.29 (1.76%) 98 (18.22%)
* All vote counts are in millions

Small changes to state boundaries, which are small in terms of vote percentages, lead to substantial changes in the electoral result. The total votes stay the same, but the counts of wasted and electoral votes vary significantly. How is it possible for a voting system that is so sensitive to arbitrarily drawn state boundaries to truly reflect the preferences of voters? It should not be a surprise that pundits have wildly different interpretations of the election results given that the Electoral College obscures voter preferences so thoroughly. It is difficult to make much sense of the popular vote results in our elections as well. The concept of a wasted vote is not lost on the electorate, and turnout tends to be lower in non-swing states. The realization that one's vote doesn't matter is among the likely causes of depressed turnout in those states. We can't be sure how turnout and campaigning would have been different in an election where every vote counted, and the only thing we can say for sure is that the electoral winner fulfilled the legal requirements for taking the office of the president.

As I mentioned in the beginning of this post, a voting system should be designed so that it elects winners who reflect voters' preferences. The Electoral College is such an ill-conceived system that it is a struggle to even determine what voters' preferences truly are. As a result, any attempt to evaluate whether or not the results reflect those preferences becomes all but impossible.

A de facto implementation of a popular vote system is possible through the National Popular Vote Interstate Compact. The National Popular Vote Interstate Compact is an agreement among several states to cast their electoral votes for the winner of the national popular vote, regardless of the state level vote. For a state to adopt the compact, it must be passed by the state legislature and signed into law by the governor. Check here to see the status of your state. If you live in a state that is not part of the compact, writing to your state representatives is a simple action you can take immediately. If you have never written your representative before, or you do not know who your representatives are, a site called writetocongress.org has simplified the whole process. Here is what to do:

1. Go to writetocongress.org and enter your address. This will take you a page with a drop down menu listing your state and federal representatives.

2. Under pick an issue, choose "write your own". Writetocongress has form letters for a number of issues, but at the time of posting, they did not have anything for this topic.

3. Choose your state official from the second drop down. Since you have multiple state officials you can write multiple letters, and writetocongress will take care of generating the letter head for you.

4. Click the letter template to edit the body of the letter, and urge your representative to support the national popular vote interstate compact. I've taken a crack at writing a template which you can use or modify as you see fit.

5. Print the letter and send it via snail mail.

That's all it takes to help move us toward a more sensible voting system. 

All source code for the analysis and visualizations in this post can be found on GitHub. The election data was compiled by Tony McGovern using the guardian and townhall.com as sources, and may be found here.