The Electoral College and Second Terms

Popular vs. Electoral Vote Teaser

The Electoral College is a key aspect of the US presidential elections. Its mechanics and distribution of electors are crucial for presidential campaigns and determine the so-called battleground states – and possibly also distort the will of the people. I was interested this last effect, so I did a little analysis.

A presidential election in the US is essentially 51 separate elections (50 states plus the District of Columbia). All but two states have a winner-takes-all system, with Maine and Nebraska using a slightly more differentiated way of splitting up its delegates between the candidates. There are a number of consequences of this that I don’t want to discuss in detail here, but what I was interested in was the boost this system gives to the strongest candidate.

There are two aspects to this. First, there is the relative majority: which candidate got the most votes? Splitting this up further, there is the popular vote (how many people voted for a particular candidate) and the electoral vote (how many electors voted for that candidate). My hypothesis was that the percentage of electoral votes the winner got would always be higher than the popular vote.

The other aspect is whether the candidate who wins is the candidate the absolute majority of people (i.e., more than 50%) voted for. In recent elections, with only two candidates from the two big parties, this has become almost synonymous with the previous question – any third-party candidate would only get a minuscule fraction of the popular vote and not a single electoral vote.

A Comparison Chart

So I came up with the following graphic to answer my question. The blue bars show the popular vote, the green ones electoral votes. Since I wanted to compare, I tried out a number of different configurations, but none made it easy to see the instances where the electoral vote would be smaller than the popular vote. So I ended up with a kind of stacking where the longer bar would be “behind” the shorter one. The idea was that the instances with electoral < popular would stand out.

Popular vs. Electoral Vote

As you can see, there were only three instances where the electoral percentage was lower than the popular one. The boost from the electoral system is quite astounding in many cases, easily adding 30 points and more to the popular vote.

The other thing the chart shows is where a candidate was elected with less than 50% of the popular vote. The shaded area marks the 50%, and you can see that there were quite a few presidents who where pushed across that mark by the electoral college system. The most recent is George W. Bush, but the list also includes Bill Clinton, Richard Nixon, and others.

This is really only meant to provide a data point for the discussion of the merits of the electoral system – the issue is far too complex to be boiled down to a few numbers. But I think this chart illustrates quite nicely what effect the current system has. For another data-centric discussion of how less than 1% change in popular vote could have changed the outcome of many of the past elections, see Mike Sheppard’s How close were Presidential Elections?

Second Terms

Since I already had the data (which I scraped from Wikipedia), I got interested in looking at the second terms of presidents (or, in the case of FDR, in second, third, and fourth terms). Would a sitting president tend to gain or lose points? And what is the effect of the electoral college here? The following chart shows this data for presidents who got re-elected.

Second Term gains and losses

At first glance, it appears that most re-elected presidents did gain votes, and most of these gains were amplified by the electoral college (the losses, too). There are two notable exceptions, Andrew Jackson and Woodrow Wilson: in these two cases, a gain in one actually translated into a loss in the other. I have no explanation how this was possible, especially in Wilson’s case.

What is missing here is data about sitting presidents who did not get re-elected. But since I was mostly interested in popular vs. electoral, I did not collect this data. I will work on such a comparison for a future posting.

Charting Challenges

What surprised me was how hard it was to produce a good chart for what I considered a simple dataset and question. Putting pairs of bars next to each other was entirely ineffective, there was way too much noise, even with ample spacing between the pairs (which also created a huge chart). Neither Excel nor Numbers would let me specify negative distances between the bars to make them slide behind each other. I’m a bit surprised that this is so difficult, I’m sure I’ve seen charts with overlapping bars.

So I ended up creating stacked bar charts, with a few additional columns of data to generate the needed numbers. While that wasn’t very difficult, it did defeat the point of doing this visually: if I could just look at the sign of the difference between the electoral and popular percentages, why bother with a chart? It still does provide a good way to present the data, especially the amplification of the stronger candidate.

While Numbers doesn’t have nearly the power of Excel, I really like its approach to spreadsheets. It also produces much nicer charts, in my humble opinion. What it does not do, however, is let me change the color of an individual element of a chart – I ended up doing those in PhotoShop. Also, while Numbers lets me draw arbitrary shapes, there is no snapping to chart elements, only their outlines. That makes adding information like the 50% shaded area much more difficult than necessary.

While both Excel and Numbers do provide a large variety of chart types and settings, a lot of manual work is still necessary to make a chart really informative. And many things that should be very simple to do in these programs (including such advanced features as histograms) still require a lot of tweaking and the use of tools like PhotoShop.

See also: Presidential Demographics, Presidential Demographics II

The source data for these charts is available.

A better version of the chart using stacked bar charts is also available.

Published by

Robert Kosara

Robert Kosara is Senior Research Scientist at Tableau Software, and formerly Associate Professor of Computer Science. His research focus is the communication of data using visualization. In addition to blogging, Robert also runs and tweets.

16 thoughts on “The Electoral College and Second Terms”

  1. Here’s another analysis of the sensitivity problem caused by the electoral college:

    To quote Michael Lugo:

    “Let V be the number of voters in a country like the United States which elects its president through an electoral college, and let E be the number of states in that country. Then let n = (log V)/(log E). For the United States at present, V is about 121 million (I’m using the turnout in the 2004 election), E is 51 (the District of Columbia is a “state” for the purposes of this discussion), and so n is about 4.7.

    This quantity n is called the “responsiveness” of the system, and its rough interpretation is that if the party in control receives (1/2 + ?) of the popular vote, then it will receive (1/2 + n?) of the electoral vote, for small ?.”

    In the current case, according to, the popular vote stands at 51.9%-46.5%, so ? is roughly 0.0274. This underestimates the current electoral vote prediction of a fancier model (it predicts 304-234, against’s 345-193), but it’s a good order-of-magnitude approximation.

  2. You can overlap Excel series easily. Select a series, choose Format, Selected Data Series from the menu, click the Options tab in the dialog that pops up, and there is an Overlap setting you can adjust.

  3. I thought the use of larger bars behind smaller bars was a clever, effective approach. It’s actually pretty easy to construct in Excel with regular columns, not stacked, and a single extra column of data. I’ll blog about it today if time permits.

    Aside to db: overlapping is fine, but one series always overlaps in front of the other. You need one more series, formatted like the behind data but plotted in the order that overlaps in front of the other two, and which has the value of the behind series if the behind series is smaller, otherwise zero.

    I actually found the shading behind the bottom 50% distracting. It produces some of the effect where a darker background makes the foreground appear lighter.

  4. Interesting, I don’t think I had seen that (I actually did this a while ago). It’s a bit hidden in those options, I mostly used the (very useful) inspector/toolbar in the Mac version of Excel.

  5. Interesting, thanks! I’ll try that. I agree about the gray being too dark, I’ll lighten that a bit. I just kept all the lines to make it easier to read the numbers from the chart. But just keeping 50% and 100% isn’t a bad idea, either.

  6. You’re right, I really need to get around to doing that. I have it sitting on my computer, but just haven’t gotten around to doing anything with it.

  7. To make every vote in every state politically relevant and equal in presidential elections, support the National Popular Vote bill.

    The National Popular Vote bill would guarantee the Presidency to the candidate who receives the most popular votes in all 50 states (and DC). The bill would take effect only when enacted by states possessing a majority of the electoral votes (270 of 538). When the bill comes into effect, all the electoral votes from those states would be awarded to the presidential candidate who receives the most popular votes in all 50 states (and DC).

    The National Popular Vote bill has been approved by 21 legislative chambers (one house in CO, AR, ME, NC, and WA, and two houses in MD, IL, HI, CA, MA, NJ, RI, and VT). It has been enacted into law in Hawaii, Illinois, New Jersey, and Maryland. These states have 50 (19%) of the 270 electoral votes needed to bring this legislation into effect.


  8. R is very powerful but the learning curve is steep, and to produce clean, elegant graphs takes a lot of work. The defaults are pretty ugly, and simply changing a line colour or thickness takes time & effort to learn how to do. If you’ll be using it all the time, it is worth the investment of effort. If not, finding a flexible GUI system is the way to go.

    Excel can be very useful for wrangling data but is largely rubbish for graphs. Numbers can produce nice, clean output, but is very limited in the type of graphs and the degree to which they can be customised.

    A nice compromise between power and ease of use is Datagraph It has a unique “structured drawing” approach where graphs are created by layering different elements. It takes creating a few graphs to get the hang of: find an example file that is similar to what you want to achieve and work from there.

    It is focussed on 2D, publication quality figures, but has some very nice extra features, like animated output in the form of Quicktime movies. For those who remember the ease and flexibility of CricketGraph, it is a more than worthy successor.

    I’ve been using it for a few months to produce a range of 2D scientific charts and am very happy with it. The developer is also very responsive, releasing fixes overnight on several occasions when I’ve asked for a new feature or found a problem. The demo is functional except I think for printing and exporting. Only $40 for the full version. Versus $0 for R, but what price do you place on time and heartache :)

  9. That is exactly the situation I’m in at the moment. I have R installed, and now I’m wondering when I will ever have time and thinking-space free to break through the learning barrier.

  10. While recreating this overlapped bar view in Tableau with an extra column like Jon Peltier did for Excel, I found that I can improve the view by sorting the bars by the percent of the popular vote because you can clearly see all the presidents that were helped by the Electoral college to get above 50%. You can see the view in my blog.

  11. Having spent several years mastering Excel charts and VBA, I see the R learning as comparable to effective charting with Excel.

    The only difference is that with R, I will have a really powerful tool with 100’s of world class programmers developing new tools.

    I’m documenting my R learning curve here.

    My strategy is to use Excel for all of my data manipulation, transfer data to R through CSV files. This reduces my learning curve to just the graphics aspects.

    I’m using the Lattice package because of my interest in small multiples – trellis -lattice. I’m also using a VBA trick I picked up along the way, I save my code snippets and reuse them extensively so that once I learn something, I can reuse the snippet. Once you have few snippets under your belt, you can be off and running.

  12. Very interesting! I like the trick with the column that’s zero if one is larger, that should also work in Numbers and Excel. I’ll try that and post some results here.

  13. Actually, given the data from October 8, you get that Obama would expect (1/2 + 4.7*.0274)*538 = 338 electoral votes, compared to’s 345 at the time. right now has the popular vote at 52.4-46.0, so ε is about 0.0325; the expected electoral vote is then (1/2 + 4.7*.0325)*538 = 356, while’s prediction is 351. (It should be noted that the more refined model of which mine is a linearization predicts 354 EV for Obama.)

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