Guest Post: Election Math

Girl Future VoterOur elections have math at their core, and we want children — our future leaders — to understand these fundamentals. ”Election math” is also a great illustration of how you may find math in places you might not think to look … like politics!

This quick review will help you and your children understand the basics of the math involved with national elections and our U.S. government. If you come across words or ideas that you’d like to learn more about, Congress for Kids is great resource.

Basics of the U.S. Government and Elections

We hold elections for two branches of the U.S. federal government: the executive and the legislative. The executive branch includes the president and vice president. These two offices are considered to represent every person in the United States.

The legislative branch, known as Congress, includes the House of Representatives and the Senate. Members of Congress represent only the residents of their state.

Federal elections happen every two years. The president is elected in years whose last two digits are divisible by four. The last digits of the years 2016 and 2020, for example, are 16 and 20. Since 16 and 20 are both divisible by 4, 2016 and 2020 are presidential election years. Congressional elections (also called midterm elections because they occur near the middle of the president’s term) happen on even years that aren’t divisible by four (2018, 2022 etc.).

States’ Representation in Congress

The U.S. is a “representative democracy,” in which citizens vote for representatives to make laws and rule the country on their behalf. The Founding Fathers used math to create our democracy so that its people would get fair representation.

Let’s start with the House of Representatives, which has a fixed number of 435 “seats,” each seat filled by a “member” of the House.

Every 10 years, the federal government counts the number of U.S. residents; this is called the U.S. Census. Using a mathematical formula, the federal government “apportions” a number of representatives to each state based on the Census’ population data. “Apportion” is a mathematical term meaning, “to divide and distribute according to a plan.”

The more people who live in a state, the more representatives the state has.

For example, in the 2010 Census, California had an estimated 37,253,956 residents. The government apportioned 53 representatives for the state. By contrast, Wyoming, with a population of 563,626, has only one representative.

Ratios Make a Difference, Too

To obtain the ratio of representatives to residents, use division. (A ratio is “a comparison of two numbers by division.”)

Since, in 2010, California had 53 representatives and a population of 37,253,956, the ratio of California representatives to residents is one for every 702,905 people, expressed as 1: 702,905. The ratio of Wyoming representatives to residents is 1: 563,626.

Since, in 2010, California had 53 representatives and a population of 37,253,956, the ratio of California representatives to residents is 53: 37,253,956. When you divide both numbers by 53, this reduces to 1: 702,905. So, the ratio of representatives to residents in California in 2010 was one representative for every 702,905 residents. The ratio of Wyoming representatives to residents was 1: 563,626.

The Senate, which has 100 seats, was designed differently, to have equal representation for every state, regardless of the state’s population. The U.S. has 50 states. Fifty goes into 100 two times, so each state gets two senators.

As you can see, Americans living in states with small populations have far fewer representatives in Congress; however, they actually enjoy a lower ratio of representatives to residents. A lower ratio enables the state’s residents to have their voices “heard” more easily. (If representatives from smaller states pay insufficient attention to the demands of comparatively small groups of voters, those residents can more easily vote them out of office.)

Electing a President

We don’t vote directly for president. We vote for “electors,” and they vote for the president. The 538 electors in the Electoral College represent the voters in their home states.

In order to become president, a candidate must win a majority of the Electoral College votes. In order to become president, a candidate must win a majority (more than half) of the Electoral College votes. Since half of 538 = 269, the person with 270 votes wins the majority of votes and becomes the next president.

Use this math formula to determine the number of electors in your state:

The number state representatives in the House
+ 2 (the number of senators)
= the number of electors

Using Wyoming and California as examples again, Wyoming gets three electors (1 representative + 2 senators) and California gets 55 electors (53 representatives + 2 senators).

Looking at the formula above, you may wonder why the number of Congressional members (435 representatives + 100 senators = 535 Congressional members) doesn’t equal the number of electors (538). It’s because Washington D.C., which is not a state, does not have Congressional representation, but it does have three electors.

“Power” Math

The U.S. has two major political parties: The Republican Party and the Democratic Party. Members of Congress who belong to the same party often vote the same way. The party with at least 218 House seats has a majority ( 1/2 of 435 = 217 1/2 ), giving it more power in the House. The party with at least 51 senators in office will have the majority in the Senate ( 1/2 of 100 = 50 ).

A party with the majority in both chambers of Congress will have even more power. But even when the president and the majority of both chambers of Congress belong to the same party, that party does not have absolute power.

Why? Major changes in government require a “supermajority,” a mathematical term used in Congressional votes. A supermajority requires at least 2/3 of the members of Congress or states to vote the same way. This rarely occurs, because getting that many politicians to agree is a challenge!

The requirement of a supermajority thus acts as a “check” on the power of the majority party’s power to make sweeping changes.

Here are some examples of when a supermajority is required:

  • Recommending an amendment to the Constitution requires 2/3 of the states (34 out of 50 states) or 2/3 of Congress (357 out of 535 members).
  • Ratifying a recommended amendment to the Constitution takes 3/4 of Congress (402 out of 535 members) or state conventions (38 out of 50 states).
  • Convicting a president, after an impeachment, requires a 2/3 vote of the Senate (67 out of 100 senators).
  • Overriding a presidential veto requires 2/3 vote in both the House and the Senate (290 out of 435 House votes and 67 out of 100 Senate votes).

We hope you take a few moments to discuss with your child how math lies at heart of a functioning democracy and the importance of everyone’s vote in shaping our nation.


Thanks to Mathnasium for this fun election-prep post!