Added Fair Electoral Tally for 2012

I created a notebook to compute what the Electoral College tally would have been in 2012, had my fair and efficient method been used. As one might expect, Barack Obama would still have won, but at 276-261 (Gary Johnson managing to win 1 vote in CA) instead of the apparent blowout 332-206 he received under the winner-take-all (WTA) system. This is also much more in line with the 51.1%-47.2% national popular vote result, also as might be expected. Both candidates got a bump over the popular percentage: Obama got 51.3% of the Electoral College votes, while Romney got 48.5%. This makes sense, since even under my system, the party more popular in the less populous states gets a representation boost. It’s a fundamental design feature of the Electoral College, and I don’t attempt to diminish the states’ role, like a national popular vote hack would. See the full details in the current commit.

These fantasy tallies make one wonder how different presidential campaigns would be conducted without WTA. I imagine candidates would focus on anywhere they could bump the electoral college count in their favor, and the concept of key “swing” states would fade away. I counted the number of states/districts in 2012 where, under my method, the candidate would have at least 2 more votes than their opponent. It was 19. Only 7 states/districts had a differential of 3 or more.  In 2016, those numbers were 20 and 8. That tells me that much fewer of the states/districts lean heavily partisan than typically thought. Our concept of “red” and “blue” states has been heavily influenced by the WTA system.


Updated Fair Electoral College Tally

I have created a project on GitHub at dwvisser/electoral-fair that scrapes the state results compiled at the Wikipedia page for the 2016 U.S. Presidential Election, and computes a fair electoral college tally according to the methodology I laid out in my blog post, Fair, Efficient State-wise Electoral College Vote Allocation. As you can see for yourself in the Jupyter notebook, the results are as follows:

Party Presidential Candidate Electoral College Voters “Wasted” Popular Votes
Democratic Hillary Clinton 261 1,014,221
Republican Donald Trump 261 443,583
Libertarian Gary Johnson 14 2,089,659
Green Jill Stein 1 1,188,700
Independent Evan McMullin 1 513,253
Other various 0 955,577
Total 538 6,204,993

The “Wasted” column tallies all votes that didn’t manage to count towards securing an Electoral College member. Remember that this number is closer to half of the ~137 million total popular votes under the current “winner-take-all” system. I interpret this as an over 90% reduction (~68M -> ~6M) in “unfairness”. Due to the Wikipedia article’s lumping of all candidates below the top 5 into the “Other” column, I forced the calculations to never assign an electoral vote to “Other”, which would be meaningless. It should be clear that this makes no material difference in the results. California has the largest “Other” count at 147,244. It appears that the largest of these was write-ins for Bernie Sanders, so it is possible that one electoral vote may have gone to him in my allocation method.

In my fantasy ideal implementation of the Electoral College, these electors would be selected by the states, and sent to the U.S. Capitol as an actual deliberative body. Normally, their “moral obligation” is to vote as shown in the table, meaning no winner with the needed 270 votes, which would throw the choice to the House. In my fantasy version, they could have a chance to deliberate when there is no clear immediate winner. This would often be the case in my allocation method, judging by the national popular vote results in 4 of the last 7 elections.

In this year’s election, the Libertarian electors are the ones which could swing the electoral victory. They come from all kinds of states: red, blue, and purple. I see it more likely than not that they would break for the Republican, given the philosophical similarities. Lessig has made the case that the College should break from obligation, and instead give the needed votes to national popular vote victor, Hillary Clinton. He argues this based on the information that has come to light since election day about the  compromised position that Donald Trump is in vis-a-vis Russian hacking. In my scenario, they would be free to do that, too.

Fair, Efficient State-wise Electoral College Vote Allocation

Twice now in recent memory, in the U.S. presidential election system, we have had the popular vote loser still win in the Electoral College. As laid out brilliantly in Lawrence Lessig’s recent blog post, The Equal Protection argument against “winner take all” in the Electoral College, the blame for this can be laid at the feet of the “winner take all” system of allocating electors used by the vast majority of states.

Within that post, a spreadsheet from Atlanta attorney Jerry L. Sims is shared that shows how the electors would have been allocated if each state had allocated them proportional to the popular vote. I was not happy with the methodology, though. They apply an arbitrary requirement of candidates needing a de minimus 5% of the vote in order to get allocated any electors. Looking at California, which has 55 electors, a de minimus 1.8% (~1/55), would have been a more appropriate choice. A 1.8% de minimus should have produced one elector for the Libertarian candidate (who received 2.6%). I suspect it is no accident that a 5% de minimus results in Clinton/Kaine receiving the requisite 270 electoral votes to win. I feel Lessig and Sims went against their own fairness arguments by pressing a thumb on the scales in favor of the two major parties.

In my recent blog post, Presidential Elections Efficiency Gap, I was inspired by the notion of the efficiency gap. The efficiency gap, as nicely explained and illustrated in the Washington Post, is a comparison measure of how fairly voters are represented in legislatures, based purely on votes cast in actual elections. The deeper notion in efficiency gap is that the representatives in an elected body should ideally be selected proportionally to how the populace votes.

Put in the language of the efficiency gap, the most fair representation result is one that minimizes the number of wasted votes, i.e, votes that didn’t ultimately get representation. To that end, I will attempt to lay out a scheme here that, like in the spreadsheet above, attempts to fairly and efficiently allocate electoral votes. In my scheme, I strive to not unnecessarily disenfranchise voters for third parties or independent candidates. I attempt to adhere to the following principles in my scheme:

  1. The number of people voting for electors in each state whose votes are “wasted” should be minimized, within reason.
  2. States independently select their electors, just once. That is, there can be no automatic run-offs or reallocations in the case that no candidate garners 270 electors. That would be adjusting the individual states’ results based on the national result.

Here is the scheme: For each state, define V as the total popular votes cast. Define Vi as the votes cast for electors for the i’th party/candidate, such that ∑Vi=V. E is the number of electoral votes allocated to that state. Bi=⌊E×Vi/V⌋ is the baseline number of electors allocated to the i’th candidate. Ri=Vi-⌈V×Bi/E⌉ is the remaining “unused” popular votes for the i’th candidate. The Ri all have the property that they are less than V/E. We now allocate the remaining electoral votes, E-∑Bi,one at a time by sorting the Ri from largest to smallest. The end result is the Ei, the actual allocation of electors to the college. Taking my earlier California example, using data from the current Wikipedia page for the 2016 election:

Candidate Popular Votes Percentage Bi Ri Ei
Hillary Clinton – DEM 8,696,374 62.28% 34 63,827 34
Donald Trump – GOP 4,452,094 31.88% 17 135,820 18
Gary Johnson – LIB 474,615 3.40% 1 220,715 2
Jill Stein – GRN

275,823 1.98% 1 21,924 1
Others 65,507 0.47% 0 65,507 0
Total 13,964,413 53 (out of 55) 55

How fair is this allocation? At one extreme, Jill Stein gets 1 elector for 1.98% votes cast. At the opposite extreme, Gary Johnson gets approximately one elector per 1.70% votes cast. The two major party candidates fall in the middle. Only “Other”, with just 0.47% of the cast votes, is unrepresented. This seems right, given that 1/E is about 1.8%. Contrast this with the earlier-cited spreadsheet, which with the above vote counts would have still allocated 35 electors to Clinton and 20 to Trump. That’s 1 elector per 1.77% of the popular vote for Clinton, and 1 elector per 1.62% of the popular vote for Trump. However, ~4.7% of the popular votes went unrepresented. I see this as 10 times more unfair than the 0.47% lack of representation in my scheme.

Using the same “townhall” dataset as I considered in my efficiency gap post, here’s the electoral vote tally I come up with:

Candidate Ei
Hillary Clinton – DEM 262
Donald Trump – GOP 261
Gary Johnson – LIB 13
Jill Stein – GRN 2
Others 0
Total 538

The California result was identical to that given here considering the latest data, giving me confidence in the result’s robustness. The earlier dataset showed only a 47.0% of the national popular vote for Trump, while the latest Wikipedia data set shows only 46.1% Trump, with Clinton’s percentage holding essentially constant at 48%. It’s possible that might alter this result by switching as many as 4 electoral votes away from Trump to other candidates, but it doesn’t even come close to affecting the outcome. There are 2 major observations to make about this outcome:

  1. Most importantly, the almost 5.9 million (at latest count) votes cast for the Green and Libertarian candidates get some representation. Admittedly, Jill Stein got over 1% of the popular votes, which one would hope would have translated into about 5 electors, rather than 2. However, as I stated above, the idea in the Constitution that the states pick the electors should be respected. Also, 2 electors is infinitely more representative than zero.
  2. Both the major party candidates are denied the 270 electors needed for a win under the rules of the Electoral College. This outcome shouldn’t be surprising that when the popular vote is close and there’s a big desire for change, pushing many people to third party candidates. Having no Electoral College winner throws the election to the state delegations in the House. The vote would be among the top three Electoral College candidates (Clinton, Trump and Johnson). where it is likely that the Republican candidate would be selected by a vote of 27-24.

It could be argued that a Trump win in the House is itself disproportional, and due to gerrymandering distortion. However, it would still be a valid, legal result, ultimately determined by state representatives. It is up to the courts to solve the gerrymandering issue.

An Interesting Alternate Analysis

If you liked my post, “On the Fairness of the 2000 and 2016 Presidential Elections“, go check out “Fixing a Presidential Election“. They start with a similar analysis discounting the Electoral College votes “not based on population”. They go much deeper, including looking at the other instance of electoral-popular mismatch, 1888, which was a mess of vote buying corruption. I’ll withhold from commenting on their arguments about rigging in 2016. I prefer to let them make those for themselves.

Presidental Elections Efficiency Gap


In the recent New York Times article, “Judges Find Wisconsin Redistricting Unfairly Favored Republicans” (, a panel of judges rejected Wisconsin’s state 2010 redrawing of State Assembly districts as an unconstitutional partisan gerrymander. What caught my eye in this story was the acceptance of a metric called the “efficiency gap” for measuring the fairness of voting districts directly from election data. Just consider the two major parties. In each district, each party will have a winner and loser. All of the loser’s votes are considered “wasted”, in that they didn’t result in a seat. Similarly, the winners votes beyond one more than the loser’s are all “wasted” as well, since they would have still won without those extra votes. If you subtract the total wasted votes for one party in all districts from the total wasted votes for the other party, and divide by the total cast votes, you obtain the efficiency gap. The ideal efficiency gap for fairly drawn districts would be very close to zero. i.e., each party ends up almost the same number of wasted votes in a set of closely contested races.

I wondered about applying this idea as a measure of fairness in the U.S. presidential election. Substitute states for districts. When I run the numbers (ignoring for simplicity the fact that Nebraska and Maine don’t follow the same winner-takes-all-electors rule as the other states). I found that for the 2016 election, for ~130.2M total votes, Red had ~21M wasted votes and Blue had ~41.5M wasted votes, giving an efficiency gap of 15.8%. (A Jupyter notebook with the actual calculations is available at What about the previous election, where Blue won the popular vote and the electoral college? One would intuitively expect a lower efficiency gap when popular votes and the electoral college winner align. Well, in 2012, for 123.7M total votes, Red had 41.1M wasted votes and blue had 28.2M wasted votes. The magnitude of wasted votes was indeed closer, and the efficiency gap works out to be 10.4%.

However, the article talks about the unfairness threshold for the efficiency gap as applied to legislative districting. Studying 4 decades worth of state redistricting plans and election data, they determined that any gap in excess of 7% led to a situation where the party in power maintained that power. In 2012, even when the Electoral College result was matched by a popular majority, the efficiency gap was a quite large value of 10.4%. The 2016 gap of 15.8% is interesting: In Wisconsin, the State Assembly 2011 districting that was rejected partly based on an increase in the efficiency gap from 11.69% to 13%, both of which are lower than 15.8%.

I admit the comparison is a bit apples and oranges. The interpretation of the gap is not as straightforward in presidential races, since the “districts” don’t ever get redrawn. The conclusion I would draw, though, is that the two-party dominated system we’ve had since the 1880s where winner-takes-all-the-electors, is fundamentally serving only stability of the two major parties. I would personally prefer a system closer to what is actually described in the Constitution, where the states nominate electors to the college every 4 years, and those electors deliberate in a convention-like process to elect a president and vice-president. I would be happier if we, the citizens, elected representatives at the state and federal level, and the President was selected indirectly by our state legislatures via the Electoral College. I really don’t enjoy the quadrennial circus of U.S. Presidential elections as they currently are run.

On the Fairness of the 2000 and 2016 Presidential Elections

What follows is an interesting thought experiment I thought I’d share. The two major candidates had roughly equal shares of the popular vote. (Red=47.3%, Blue=47.8%). What if the system was modified to take away the 2 bonus “senatorial” electoral votes from each state (and DC)? Well: Red votes => 306-2*30=246; Blue votes => 232-2*21=190. Red still gets the same disproportional amount of electoral votes! (Source:

Here’s what I mean by same: Define D, the “distortion factor” in favor of the winner, as the ratio of received electoral votes to the number they would have had if electoral votes were perfectly proportional to popular vote. So D[Red, actual]=306/(.473*538)≈1.20 and D[Blue, actual]≈0.90. D[Red, modified]=246/(0.473*436)≈1.19, and D[Blue, modified]=190/(.478*436)≈0.91, which are essentially the same as before. You can also define G, the unfairness gap, as |D[red]-D[blue]|. G[actual]≈0.30, and G[modified]≈0.28, so we did manage to design a slightly more fair electoral tally.

I think that assigning electoral votes by congressional district would probably barely budge this result. The current House has a 247-188 Red majority, despite the fact that in 2014, Blue had a greater number of popular votes for House seats.

By contrast, in 2000, (the most recent other example of electoral college-popular vote mismatch) Red and Blue had similar proportions of the popular vote (47.9% Red, 48.4% Blue), but with Red only winning 271-266 in the electoral college (one elector abstained, Source: D[Red, actual]=277/(0.479*538)≈1.07 and D[Blue, actual]=266/(0.484*538)≈1.02. G[actual, 2000]=0.05, a lot less unfair than this year, where G is approximately 0.30. In addition, it was still the case that Red had 30 states, giving 60 “senatorial” electoral votes; likewise Blue had 20 states and DC, just like in 2016. Run the same math as above and you get a Blue 211-222 electoral victory. D[red, modified]=211/(0.479*436)≈1.01 and D[blue, modified]=222/(.484*436)≈1.05. G[modified]≈0.04…so we only slightly reduced unfairness, however by making it unfair in Blue’s favor, and just happening to match up with the popular result.

The difference, of course, is that Red picked up some of the bigger states (by population) in 2016 that belonged to Blue in 2000, while Blue picked up fewer of Red’s big states. While it is clear 2016 was more unfair, as measured by D (distortion) and G (distortion gap, a.k.a., unfairness gap), the electoral college result is completely robust due to Red’s capturing of majority of the right states. Notwithstanding any concerns you may have about the particular Red candidate this year, if you accept the electoral college at all, I would say that Red’s victory this year is robust and legitimate.