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A Look at the Electoral College through Math and U.S. History Lenses

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This post was written by Peter DeCraene, the 2020-21 Albert Einstein Distinguished Educator Fellow at the Library of Congress. This is the first of a series of posts about using mathematics to develop and analyze data representations found in primary sources.

Exploring Scribner’s Statistical Atlas of the United States with my math-teacher lens, I found charts showing 19th century election results in terms of popular and electoral votes. Discussion of the electoral process has been taking place since Thomas Jefferson’s election in 1800, after which the Twelfth Amendment was passed. As we near the 2020 election, some historical data about the Electoral College seems like a relevant topic for analysis, and the 1876 election had a particularly interesting outcome.

Detail from Political History (Presidential Elections)

The data on these charts showing the election results from 1876 invites interdisciplinary studies between U.S. history and mathematics. Start by asking students to analyze the item using the Library’s Observe-Reflect-Question tool for primary source analysis. Students may ask about the colors representing the Democratic and Republican parties, which  are reversed from what we expect today. Students might look up the history of the current color usage and discover, among other facts, that historically and internationally, the more conservative group was represented by blue.

Students may question why Hayes won the presidency when Tilden won the popular vote, as seen in the bar graph at the bottom. The deal made to decide the electors of this election was controversial at the time and sparked discussions about the purpose and need for the Electoral College.

Understanding of the Electoral College can be deepened mathematically by representing the data from the “Analysis of the Popular Vote, by State” bar chart in a different way: Ask students to calculate Hayes and Tilden’s percentages of the vote in each state. To show the spread of this data, make a box and whisker plot for each candidate using these percentages and compare the results. What do these representations reveal about the distribution of the popular vote? Note that these representations give each state equal weight; how does this compare to the way the Electoral College is structured? (Manipulating this data may also be an opportunity to teach something about spreadsheets.)

Should the present method of electing a president and vice-president of the United States be changed?

In 1879, the Honorable Levi Maish, a Representative from Pennsylvania, gave a speech about changing the electoral process. The published version of his speech included this table showing the number of electoral and popular votes candidates won from 1824 (when the popular vote was first accurately tallied) through 1876.

Maish used the ratios of electoral votes won to the ratios of popular votes won to help make his point. Some of the data on Maish’s table needs clarification. In 1824, no candidate won more than 50% of the electoral vote, so the election was decided by the House of Representatives for John Quincy Adams. In 1872, Horace Greeley died between the election and the casting of electoral votes, so received none of the latter. The data in Maish’s table does not include electors for minor candidates after 1860: In 1864, there were a total of 234 electors; in 1868, 294 (Maish’s total is incorrect), and in 1872, 366.

Apply mathematics to further investigate. Assign students to represent the data on a coordinate system. Show the percentage of the popular vote on the horizontal axis and the percentage of the electoral vote on the vertical axis for the winners of each election, and discuss what inferences you might make based on this representation. Should the 1824 and 1872 elections be included? Calculate a line of best fit, and discuss what points above the line indicate in comparison to points below the line. What does the slope of the line mean? How strong is the correlation between the popular vote ratio and the electoral vote ratio?

The data and history about the electoral versus popular votes can provide good fodder for debate about the purpose of the electors. Share how your students view the data in the comments.


  1. excellent useful document!

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