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Study Guides > Mathematics for the Liberal Arts

Assignment: Electoral College Trouble

Do you believe that the US presidency can be won with less than half of the popular vote?  It's true, it has been done 4 times now. With a little math you can prove how it is done, your friends will be so impressed!  In this assignment, you will use the minimum criterion for winning electoral college votes to show that a candidate with less than half of the popular vote could become president. This is how it works. The Electoral College consists of 538 votes.  Each state is assigned a certain number of votes that make up a part of the 538. If these votes were divided up equally across the population of the US, which was approximately 308,745,538 in 2010 [footnote]We used data from 2010 because it is more complete than current data. https://en.wikipedia.org/wiki/Demography_of_the_United_States[/footnote] each vote would represent

[latex]\frac{308,745,538}{538}\approx{573,877}[/latex] people

But, the electoral college votes are not distributed that way.  For example, from the map below we find that Georgia gets 15 electoral college votes.

Map of the 50 states of the US with the number of electoral college votes for each state. Follow this link for a list of the number of votes each state gets. http://state.1keydata.com/state-electoral-votes.php

The population of Georgia in 2010 was 9,919,945[footnote]https://en.wikipedia.org/wiki/Demography_of_the_United_States[/footnote], which means that if the electoral college votes were distributed evenly, they would get

[latex]\frac{9,919,945}{573,877}\approx{17}[/latex] votes.

This happens because the distribution of electoral college votes starts by assigning each state 3 votes, even though, based on population, each state may not "need" three votes to represent it's population.  Remember that each vote in the electoral college would represent 573,877 if they were distributed evenly amongst the population. For example, Rhode Island's population was 1,050,292 in 2010. This means that they would get

[latex]\frac{1,050,292}{573,877}\approx{2}[/latex] votes.

But since every state starts off with three, some states with larger populations, like Georgia have to give up some of their electoral votes. A citizen's vote in Rhode Island is weighted more heavily in the electoral college than one in Georgia. :(

Now, this isn't the full story. There's more. We use a winner-take-all approach so you only need one more vote than half of all the votes to win all of the votes for the electoral college. This is why you see candidates only polling in states where the race will be really close.

The outcome of this imbalance is that the bid for the presidency in the US can be won by someone who does not win the popular vote. Hopefully you will see how by doing this activity.

Wyoming had a population of 576,412 in 2010, they also get 3 electoral college votes.

Your first questions:
  1. What percent of the US population did Wyoming have in 2010?
  2. What percent of the total votes of the electoral college did Wyoming have?
  3. What is the minimum number of citizen's votes needed from Wyoming to take all the electoral college votes for the state?
  4. What percent of the total population of the US is this?

Answer:

Percent of US population Percent of total votes of the electoral college Minimum number of citizen's votes needed to take all the electoral college votes for Wyoming Percent of total US population representing Wyoming's Electoral Votes
Wyoming [latex]\frac{576,412}{308,745,538}\approx{0.0019}[/latex] = 0.19%  [latex]\frac{3}{538}\approx{0.0056}[/latex] = 0.56%  half + 1 = [latex]\frac{576,412}{2}+1=288,206+1=288,207[/latex]  [latex]\frac{288,207}{308,745,538}\approx{0.0009}[/latex]=0.09%

Continue to do these calculations using this chart (  OR Excel spreadsheet format). If you use the google spreadsheet, you will need to make a copy for yourself by clicking on "File" then "Make a Copy" Click on Warning! It may be a bit tedious, but the results tell an interesting story. Use census data from 2010, found here, and the map above to make your calculations. Your next questions:
  1. From the spreadsheet you filled in, what was the total percent of the population when the total percent of electoral votes reached 50%?
  2. Are you surprised by the outcome? Why or why not?
  3. Do you think our presidential election process is fair?  Write a paragraph or two to defend your opinion.
  What you turn in: Your spreadsheet, either as an Excel attachment, or provide the link to the Google Spreadsheet. Make sure to set permissions on your spreadsheet so your instructor can see it. The answers to both question sets in a separate document. Please cite any resources you used other than what was provided here.

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