Graphics that Lie

This week in an election aftermath edition, Occupy Math wants to look at the very tricky business of visually displaying data. Below is an example of an extremely bad election-related graphic that got over two million views. This graphic manages to:

  • Display the information it has in a deceptive fashion,
  • Ignore hidden assumptions that are wrong,
  • Ignore important data from the election,
  • Choose a set of comparison elections that are probably inappropriate, and
  • Get the information it displays wrong.

The overall effect is to propose an unsupported and probably false hypothesis about why the election came out the way it did. This graphic is an incredible example of how not to inform people.


Let’s go though the defects in detail. Look at the vertical scale on the left side of the graphic. It starts at 52,000,000 votes — which means that the difference of about ten million votes it shows for the blue between 2008 and 2016 is magnified about five-fold. This creates a false impression of the collapse of Democratic turnout – which we will see is not what happened. In fact, the graph does not measure partisan turnout at all.

Next up, the hidden assumption: that Democrats voted for Clinton and Republicans voted for Trump. The information about party is not present in the graph — it is just assumed. While the graph just says red and blue, it is widely discussed as showing Democratic and Republican turnout. We know that there were substantial Republican crossover votes for Obama in 2008 and 2012 and a story from NPR notes that there were Democrats voting for Trump in droves in the 2016 election. In fact, more Americans identify as independents than as Democrats or Republicans.

Moving on, we come to the ignored data. Trump’s margin of victory is small (in the Electoral College) or negative (in the popular vote). According to the United States election project and (unfinished) tallies — if you crunch some numbers — there were 4,274,975 votes cast for Gary Johnson, 2,820,080 voters who cast a ballot without voting for president, and 1,316,086 people that voted for Jill Stein. That is 8,411,141 votes (by persons of unknown party), that don’t appear in the graphic. That is enough votes to flip every battleground state in the election. In the interests of honesty, these figures are still changing — but almost certainly not enough to modify Occupy Math’s conclusions.

Continuing through the list, the two elections that the 2016 election are being compared to feature a black guy as the candidate. We now have incontrovertible evidence that there is a lot of racism left in America — because it is now less hidden than it was a year ago. This means that there is a potentially large confounding factor in the comparison. Going back three more elections might give a much better picture of what happened.

Saving the best for last: the information in the graphic for 2016 is just wrong. The vote totals for 2008 and 2012 are complete. The graphic Occupy Math is deservedly mocking was made long before we finished counting the votes. Turning again to the United States election project, the more nearly correct totals are:


Reading the graphic, it has 118 million votes displayed in 2016 when 135 million plus votes were cast (still counting!). While we will be sorting out the 2016 election for a long time — absolutely an event for the history books — this graphic about the election both lacks critical information and displays its incorrect information in a very misleading fashion.

Wrapping up the discussion of the very bad graphic, this picture has been used to support a number of ideas about the outcome of the election that it does not support and, in fact, that it has no information about. The issue (discussed in last week’s blog) about knowing what your assumptions are is relevant, but also there is a deep problem with assuming everything is simple when it is not.


Occupy Math is, by nature, an optimist and so includes a beautiful example of a data graphic. This shows it is possible to do a good job of displaying data and above is a classic of the discipline. Charles Joseph Minard’s graphic of Napoleon’s Russian campaign. It displays six types of data in two dimensions: the number of Napoleon’s troops; the distance traveled; temperature; latitude and longitude; direction of travel; and location relative to specific dates.

Minard’s graphic probably took weeks to compose and doubtless went through several versions. The election graphic at the top of the post was created much more quickly — before the 2016 votes were counted — and this emphasized the need for much better math education in this age of instant news. Citizens trained in mathematics, in critical thinking, and who are aware of their assumptions, make fewer mistakes. They are less likely to accidentally mislead others. They are harder to deceive and are more resistant to con artists and fanatics.

Occupy Math hopes that you benefited to some degree from this deconstruction of a very bad graphic. While the current President-Elect is qualified by the vital factor of having won the election, by almost any other measure he is not prepared for the role he will assume in January. The situation that permitted his election was fraught with muddy thinking, disinformation, and easy-to-spot falsehoods. Occupy Math will keep plugging away in the hope that the next American election will have voters with a clearer understanding of the issues, the assumptions, and the possibilities before them. As always, other takes on today’s post are welcome, please comment or tweet!

I hope to see you here again
Daniel Ashlock
University of Guelph
Department of Mathematics and Statistics


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