A weighted voting system is when one individual’s vote is worth more than other individual(s) vote.
It is sometimes agreed that a person’s vote should be worth more than another person’s vote. If one person owns 30% of a company and another person owns 0.3%, we might want the person who owns 30% of a company to have a bigger voice in a decision for the company.
The United States uses a weighted voting system when selecting a president by using the Electoral College voting system. California’s choice in president is worth more than Maine’s choice in president as California reflects the opinion of many more citizens of the United States than Maine.
The electoral college has 538 "electors" (similar to having 538 votes). If a presidential candidate wins 270 of the votes, they have won a majority.
Each state gets as many electors as they have representatives to congress. Each state has two Senate representatives. These represent 100 of the 538 available electors, so there are \(538 - 10 = 438\) electors left to be distributed. 3 of the electors are given to the District of Columbia. That leaves 435 U.S. House of Representatives, so there are 435 electors to be distributed among the states based on population.
The U.S. uses the Huntington-Hill method to split up the 435 house representatives based on population, but for simplicity of calculation, we will use a simpler weighted voting calculation.
1.
Assume a school board uses a weighted voting system for their
school board. The major towns that they represent have the following
populations:
Town A’s population: 1,837
Town B’s population: 445
Town C’s population: 397
Town D’s population: 1,604
There is one representative per town. When the school board votes, there are 1,001 votes. Each representative votes proportionately to their town’s size. How many votes does each town representative get?
The total population of the three towns is
\[1,837 + 445 + 397 + 1,604 = 4,283\]
Town A represents \(\frac{1,837}{4,283} \cdot 100\% \approx 42.89\%\) of the population represented by the school board. Town B represents \(\frac{445}{4,283} \cdot 100\% \approx 10.39\%\) of the population represented by the school board. Town C represents \(\frac{397}{4,283} \cdot 100\% \approx 9.27\%\) of the population represented by the school board. Town D represents \(\frac{1,604}{4,283} \cdot 100\% \approx 37.45\%\) of the population represented by the school board.
Town A gets \(1,000 \cdot 0.4289 = 428.9\) votes. We round up to 429 votes.
Town B gets \(1,000 \cdot 0.1039 = 103.9\) votes. We round up to 104 votes.
Town C gets \(1,000 \cdot 0.0927 = 92.7\) votes. We round up to 93 votes.
Town D gets \(1,000 \cdot 0.3745 = 374.5\) votes. We round up to 375 votes.
If a vote requires 50% or more of the available votes, then town A needs just one other town to vote with them. If town B, C, and D want to outvote town A, they all have to work together!
2.
In the electoral college, 435 of the votes are based on
population. Assume the population of the United States is 333 million.
Assume the election is waiting on results from Arizona, Georgia, and
Pennsylvania. Assume Arizona’s population is 7 million, Georgia’s
population is 11 million, and Pennsylvania’s population is 13 million.
How many electors should each of these three states get if we use a
weighted average?
We will divide each state population by the total population of the United States. That calculates the fraction of the country that lives in this state. We then multiply this fraction by the total number of electors, 435.
\[\text{Arizona: }\frac{7}{333} \cdot 435 \approx 9 \text{ electors}\]
\[\text{Georgia: }\frac{11}{333} \cdot 435 \approx 14 \text{ electors}\]
\[\text{Pennsylvania: }\frac{13}{333} \cdot 435 \approx 17 \text{ electors}\]
1. Assume a school district uses a weighted voting system for their school board. The major towns that they represent have the following populations:
Town A population: 966
Town B population: 1,156
Town C population: 1,028
Town D population: 461
There is one representative per town. When the school board votes, there are 1,000 votes. Each representative votes proportionately to their town’s size. How many votes does each town representative get?
2. In the electoral college, 435 of the votes are based on population. Assume the population of the United States is 333 million. Assume the election is waiting on results from Florida, Michigan, and Wisconsin. Assume Florida’s population is 22 million, Michigan’s population is 10 million, and Wisconsin’s population is 6 million. How many electors should each of these three states get if we use a weighted average?
1. Do you think the above town voting system is a fair way of voting? Or should each town just get one vote? Why or why not?
2. Do you think the electoral college system is a fair voting system? Why or why not?