CRLS Electoral College Worksheet

Electoral College Assignment

This assignment was used in a junior-senior level applied physics classroom at Cambridge Rindge and Latin high school in the fall semester of 2004. During the lesson, students are divided into groups which act as “states” in a classroom-electoral college system. The questions lead the students through a step-by-step calculation of the probability that their individual vote can determine the outcome of the election. This is used to show that large states have a disproportionate amount of power relative to their population. An attached spreadsheet contains the power ratings calculated for each of the 50 states.

CRLS Electoral College Worksheet

Tuesday, October 26, 2004

Answer the following questions:

1. If your class were to decide on issues based on popular vote, what would be the drawbacks?

2. On the chart on the next page, fill in the population and number of electoral votes in each “region” of your classroom.

3. List the different ways that coalitions could form to win a vote. In each coalition, circle the group that could make the coalition lose by changing their vote.

4. For each region, count the number of times in question 3 when it has an opportunity to make a coalition lose. Add this to your chart.

5. If there are n regions in your classroom, the number of different coalitions that can form is 2n-1. Calculate this number for your classroom.

6. The probability that a region will make a difference in an election is equal to the number of opportunities it has divided by the number of possible coalitions. Add these numbers to your chart.

7. Now we will consider how voting takes place inside a region. Assume there are 3 people in a region and they must vote Yes/No on some issue. Here are all of the possibilities for the vote:

A B C Winner

N N N No

N N Y No

N Y N No

N Y Y Yes

Y N N No

Y N Y Yes

Y Y N Yes

Y Y Y Yes

Circle the votes above where person A could change the outcome by switching his vote. How many circles are there? What is the probability of this happening?

8. On your chart on the next page, add the probability that someone will change the outcome of the election in each region.

9. As a final step, we will calculate the probability that someone can change the result of the entire election. In order for this to happen, a person would have to both change the election in their region, and then have their region change the result of the election. So, to calculate this, multiply columns 5 and 6 in your chart on the next page and put the result in column 7.