Electoral College

Common Core Standards and Mathematical Practices

The following module covers the common core standards and math practices.

7th Grade Number Systems

7.NS.A1 Apply and extend previous understandings of addition and subtraction to add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


7th Grade Ratios and Proportional Relationships

7.RP.1.A Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

7.RP.A.2 Recognize and represent proportional relationships between quantities.

7 .RP.A.3 Use proportional relationships to solve multistep ratio, rate, and percent problems.

Mathematical Practices

MP.4 Modeling with Mathematics

Learning Objectives

Students will be able to...

  • Describe the electoral college process.

  • Explain the Pros and Cons of the Electoral College.

  • Use proportions and ratios to calculate outcome of a US election based on voter turnout and electoral election distribution.



1

HISTORY

2

HOW IT WORKS

3

PROS + CONS

4

EXAMPLES

Please note that all terms in bold are defined at the bottom.

1. HISTORY OF THE ELECTORAL COLLEGE

The Electoral College is a body of electors established by Article II of the United States Constitution. The sole purpose of the Electoral College is to elect the President and the Vice President of the United States every four years.

1787: The Constitutional Convention originally used the Virginia Plan as the basis for electing the President; this plan called for Congress to elect the President. James Wilson, representing Pennsylvania, moved for a body of electors to be created for this purpose.

06 September 1787: The Constitutional Convention approved the creation of the Electoral College. Delegates from more sparsely populated states or those with smaller territories generally favored the Electoral College.

ARTICLE II, SECTION 1, CLAUSE 3

The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves. And they shall make a List of all the Persons voted for, and of the Number of Votes for each; which List they shall sign and certify, and transmit sealed to the Seat of the Government of the United States, directed to the President of the Senate. The President of the Senate shall, in the Presence of the Senate and House of Representatives, open all the Certificates, and the Votes shall then be counted. The Person having the greatest Number of Votes shall be the President, if such Number be a Majority of the whole Number of Electors appointed; and if there be more than one who have such Majority, and have an equal Number of Votes, then the House of Representatives shall immediately chuse [sic] by Ballot one of them for President; and if no Person have a Majority, then from the five highest on the List the said House shall in like Manner chuse [sic] the President. But in chusing [sic] the President, the Votes shall be taken by States, the Representation from each State having one Vote; A quorum for this Purpose shall consist of a Member or Members from two thirds of the States, and a Majority of all the States shall be necessary to a Choice. In every Case, after the Choice of the President, the Person having the greatest Number of Votes of the Electors shall be the Vice President. But if there should remain two or more who have equal Votes, the Senate shall chuse [sic] from them by Ballot the Vice President.

  • Federalist No. 39: James Madison stated that the Constitution combined state-based and population-based government, both of which would elect the President. 

  • Federalist No. 68: Alexander Hamilton argued that electors come expressly from the people, avoiding a party-run legislature. The use of majority rule in the Electoral College was believed to be critical to the doctrines of a Republican government. 

ARTICLE II, SECTION 1, CLAUSE 2


Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.

  • The state legislatures chose the electors in the majority of the states, a practice which changed in the early 19th century.

  • Some states decided that it would be best to choose electors on a "general ticket" to ensure they all voted the same way and pledged their support to a party candidate. James Madison and Alexander Hamilton asserted that this was an unconstitutional approach to the Electoral College.

1789: The "winner-takes-all" method was used in Pennsylvania and Maryland. Massachusetts, Virginia, and Delaware used a district plan organized by popular vote. Connecticut, Georgia, New Hampshire, New Jersey, and South Carolina had their state legislatures choose the electors.

1800: Virginia and Rhode Island used "winner-take-all." Kentucky, Maryland, and North Carolina voted by district, and 11 states used their legislatures.

  • Currently, only Maine and Nebraska use a district plan to choose their electors. All other states use statewide winner-takes-all popular voting.

TWELFTH AMENDMENT

The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President, and they shall make distinct lists of all persons voted for as President, and all persons voted for as Vice-President and of the number of votes for each, which lists they shall sign and certify, and transmit sealed to the seat of the government of the United States, directed to the President of the Senate;The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted;The person having the greatest number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.The person having the greatest number of votes as Vice-President, shall be the Vice-President, if such number be a majority of the whole number of Electors appointed, and if no person have a majority, then from the two highest numbers on the list, the Senate shall choose the Vice-President; a quorum for the purpose shall consist of two-thirds of the whole number of Senators, and a majority of the whole number shall be necessary to a choice. But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.

1804: The Twelfth Amendment to the U.S. Constitution was ratified. The Amendment moved for the President and the Vice President to run and be elected on the same ballot. Initially, the President and the Vice President were elected on different ballots.

1845: The phrase "college of electors" was written into federal law for the first time, in 3 U.S.C. § 4.

02 November 1880: The first Presidential election in which all state electors were chosen based on popular election was held. In effect, the President and the Vice President are chosen through indirect election by the citizens.

2. HOW THE ELECTORAL COLLEGE WORKS

After all citizens of the U.S. cast their individual ballots, their votes enter a statewide tally. With the exception of Maine and Nebraska (where votes are split by congressional district), all jurisdictions operate on a winner-takes-all basis. That is, the candidate receiving most (not majority) votes, receives all the electoral votes allocated to that state.

Electoral votes are allocated to each state based on census results, used to determine the populations of each jurisdiction. Most populous jurisdictions receive the most representation in the electoral college.

It is important to note that votes are not added based on census results, only redistributed. This is because there are a fixed number of electors, and thus, a fixed number of votes. Each state is represented by two senators and a fraction of the total number of representatives in the House proportional to its population. There are a total of 538 electoral votes. A candidate must receive over half of them–270–in order to win the presidency.

Once it is determined that a candidate is the plurality winner of a state or jurisdiction, its electors cast their votes for that candidate. In 32 states, it is required by law that electors vote in accordance with their citizens' choice, but there have been isolated cases of "faithless electors" in history. These are electors who exercise their right to vote against the decision of their state. Ultimately, these electors have failed to ever sway the outcome of an election.

Through the use of the electoral college, the U.S. has implemented a system of indirect election, meaning that its citizens do not have full say over who leads them. Despite its longstanding reign, there is much debate over its utility today.

This begs the question of potential fixes for the Electoral College, as the process for officially abolishing would be long and tedious, requiring an amendment to the Constitution, which is difficult to secure. One plan is called the National Popular Vote Interstate Compact, which is a coalition of states that decide to pledge electoral votes according to the national popular vote. In the event that this compact attracts enough members to account for over 270 electoral votes, the power of the Electoral College would be completely stripped, thus generating a system wherein the popular vote determines the outcome of the election directly, but with the formality of an electoral vote as an in-between.

Potentially, electoral votes could be apportioned such that if a candidate received 60% of the popular vote, she would also receive 60% of the electoral vote. In this circumstance, each state would follow a format closer to Maine and Nebraska's. In any case, it is widely accepted that the terms of the Electoral College are dated and some action is necessary to fix the system. Currently, we do not have a solution without problems, but the National Popular Vote Interstate Compact is actively gaining steam, currently accounting for 196 electoral votes.

HOW DOES THE U.S. PRESIDENT GET ELECTED EVERY FOUR YEARS?

  1. Republican and Democratic parties choose a nominee (by primary and caucus). Other smaller parties (e.g. the Green Party) choose candidates as well.

  2. U.S. citizens (other than disenfranchised convicted felons and the imprisoned population) vote for one candidate on a Tuesday in November.

  3. Each state's electors cast votes for the plurality winner of that state.

  4. A presidential candidate needs 270 electoral votes to win the election. Once they have achieved that quota, they are declared the winner.

3. PROS AND CONS OF THE ELECTORAL COLLEGE

PROS

  1. Guarantees that the concerns of smaller states will be addressed.

  • If an election outcome were strictly dependent on the popular vote, most candidates would focus their energy almost entirely on the needs of major metropolitan areas such as New York and Los Angeles. The interests of less populous states, like agriculture, would fall to the wayside.

  1. In the event that a result is disputed, a national recount is not necessary.

  • With the electoral college, if a candidate disputes a result, the dispute is most commonly centered in a single state. If a count is disputed in an election decided by popular vote, a national recount is required, which is tedious and time-consuming.

  1. Eases the cost of campaigning, making it somewhat more accessible to people across class lines.

  • It is already remarkably expensive to campaign for presidency, but the electoral college eases costs. In the two-party system, the major candidate from the left doesn't have to take several trips to California as they can be reasonably assured it will vote in their favor, regardless. The same is true for a right-leaning candidate in Texas. In an election determined by popular vote, candidates will have to dedicate time to campaigning in each state, as there is no security in any given area.

CONS

  1. Citizens only indirectly elect their leader.

  • The notion that individual votes might not fully count discourages voter participation and instills the mindset that the people don't have any real power in the decisions that are made about their lives.

  1. People's votes are weighted more heavily in smaller states.

    • For example, a person's vote in Wyoming is worth considerably more than a person's vote in California despite each voter representing an equal percentage of the population. Dividing the electoral vote evenly among the residents of each state shows that individual votes from Wyoming residents carry 3.6 more times the weight than votes from California.

  2. The reasons the Electoral College was created in the first place are no longer relevant.

    • Part of the concern with a national popular vote determining the result of a presidential election when the country was founded was that information was difficult to circulate in the absence of technology and most voters did not have access to the information necessary to make a balanced decision. Now, however, regardless of location within the country or even the world, information is spread quickly and, here, openly, so informing voters prior to the election is easy and inevitable.

  3. Allows for the possibility of faithless electors.

    • This would be a completely moot point in the absence of the Electoral College, but adds another layer of disconnectedness between the voters and the election outcome. Given that many states do not legally require their electors to vote in favor of the candidate their citizens prefer, they could choose to go rogue and exercise a power that does not represent the desires of the people.

REAL-LIFE EXAMPLES

2000: The Republican nominee for President was George W. Bush. The Democratic nominee for President was Al Gore. Bush won 217 Electoral College votes, carrying 30 states. Gore won 266 Electoral College votes, winning 20 states and the District of Columbia. HOWEVER, Gore won 50,999,897 popular votes, while Bush only won 50,456,002 popular votes. This is a .5% lead in popular votes. In addition, Bush won Florida by such a close margin that it was not immediately clear who won the presidency, leading to a 5-4 Supreme Court decision that Bush had, in fact, succeeded.

2016: The Republican nominee for President was Donald Trump. The Democratic nominee for President was Hillary Clinton. Trump won 304 Electoral College votes, winning 30 states and Maine's District 02, after a faithless elector broke ties and voted for him. Clinton won 20 states and the District of Columbia. HOWEVER, Clinton won 48.2% of the popular vote with 65,853,514 votes, while Trump only won 46.1% of the popular vote with 62,984,828 votes. This was nearly a 3 million vote loss for Trump, who ultimately succeeded to the presidency.

Populations of States and the Distribution of Electoral College Votes

Populations of States and the Distribution of Electoral College Votes


  • Relative weight is each state's electoral votes divided by the total number of ballots cast and divided again by the fraction of an electoral college vote accorded to the average American voter.
  • Small states are benefitted by the Electoral College due to the +2 effect of the senators.
  • Numbers and computation from electproject.org.

4. EXAMPLES


  1. Suppose there are only four states in the U.S.:

a. Suppose everyone in these states is voting. Create a scenario where one candidate wins the Electoral College but not the popular vote.

b. Now suppose not everyone is necessarily voting. What is the minimum number of votes that could secure a win for a candidate?

2. (a) What is the minimum number of votes needed to win the U.S. presidential election? Explain.

(b) In the scenario from the previous part, what is the maximum number of votes another candidate could have won and still have lost the election? What percentage of the popular votes would the winner have received in this case? For this question, you might want to consult this page.

  • For fun, check out this page to see how a candidate can reasonably win the election with only 23% of the popular vote!

3. In the 2016 presidential election, Clinton was hoping to win the swing states of Wisconsin, Michigan, and Pennsylvania, but did not. Figure out if she would have won the election if she won those three states. By what margin did she lose those states? Namely, figure out the minimum number of votes that would have had to be flipped in her favor in those three states for her to win those states.

4. Assume a country has two states and operates on the same electoral college system as the U.S. (435 Representatives to be distributed according to population and two Senators per state): State A with a population of 1.1 million and State B with a population of 3,000. Determine the number of electoral votes each state receives and the ratio of votes to voters within each state.

  • For the purposes of this exercise, round decimals to the nearest whole number, but note that this is neither the only nor most widely accepted apportionment method. More on that on the Apportionment section of this site.

CHECK OUT THESE SOLUTIONS ONCE COMPLETED!

  1. (a) There are actually many ways to go about this question. One way is to assume that a little over half of Massachusetts' and Wyoming's voters vote for Candidate A (roughly 3,460,000 and 293,000 votes respectively). Candidate A would then win the electoral college with 14 electoral votes. If every other voter voted for B, that candidate would receive 11,182,000 votes, compared to Candidate A's 3,753,000, but still lose the election. (b) Suppose only one voter from Massachusetts and one voter from Wyoming decide to vote. They both vote for Candidate A. That candidate has now secured the same 14 electoral votes as with full voter turnout and wins the election regardless of the number of Candidate B votes from Colorado and Idaho.

  2. (a) The answer is 11. To see this, list the states according to the number of their electoral votes, starting with the highest (California). Add the electoral votes from the top until you get to 270. It turns out that this happens after 11 states. Now suppose only one person in each of those state votes, and they all vote for the same candidate. This candidate then gets 270 electoral votes and wins the election. (b) Add the number of voting age people in each of the remaining 39 states to get 109,332,002. Assume they all voted for the other candidate candidate. This answers the first part. For the second part, the total number of people who voted is 109, 332, 002 + 11 = 109, 332, 013, and so the percentage of popular votes the winner gets is:

(11/109,332,013)*100%=0.00001006109%.

  1. Clinton would have won the election if she won those states, since that would have given her 46 more electoral votes (and would have taken those away from Trump), and she would then have had 278 to Trump’s 260 electoral votes. For the second part of the question, check out, for example, this page. It turns out Clinton lost by a margin of 79,316, or 0.057% of total votes.

  2. To divide the 435 Representatives between the states proportionally, first assess what percentage of the country's population each state's population accounts for. For State A, we assess that (1,100,000/1,103,000)=99.728% of the total population. For State B, we assess that (3,000/1,103,000)=0.272% of the total population. 99.728% of 435 is 433.81, rounded to the nearest whole number is 434 Representatives apportioned to State A, and 1 to state B. Each state receives two extra votes for their Senators, leaving State A with a total of 436 electoral votes and State B with a total of 3. To find the ratio, we divide the state's population by the number of electoral votes it receives. That is, (1,100,000/436) for State A and (3,000/3) for State B. This yields a voters to vote ratio of 2,523:1 for State A and 1,000:1 for State B.

VOCABULARY + FURTHER RESOURCES

Alexander Hamilton: One of the Founding Fathers of the United States and the first U.S. Secretary of the Treasury under Washington.

Article II of the U.S. Constitution: Establishes the executive branch of the federal government and lays out the procedures for electing and removing the President of the United States.

Census: The procedure of acquiring and recording information about the members of a population. The United States census occurs every ten years and helps allot each state the correct number of representatives in Congress.

Congress: The bicameral (two-houses) legislature of the United States government. It consists of the House of Representatives and the Senate and serves to represent both the residents of congressional districts (House) and states (Senate) to the federal government.

Constitutional Convention: A meeting of delegates from different states around the country that created the United States Constitution.

District Plan: A way of choosing Electoral College electors in which one elector is voted in per district.

Electoral College: A body of electors established by the United States Constitution that forms every four years to elect the President and the Vice President of the United States.

Electors: Members of the Electoral College voted in by state residents.

Faithless Electors: Members of the Electoral College who do not vote for the presidential or vice presidential for whom they pledged to vote.

General Ticket: A voting system in which voters select parties, from which representatives select individuals to fill elected positions.

Indirect Election: An election in which voters elect individuals to choose people to fill elected positions.

James Madison: One of the Founding Fathers and the fourth President of the United States. He is known as the "Father of the Constitution" for his role in drafting and promoting the United States Constitution.

James Wilson: One of the Founding Fathers of the United States and a signatory of the United States Constitution. He was one of the first Associate Justices of the Supreme Court.

Majority Rule: A voting method in which the winner of the election must receive over half of the votes cast.

National Popular Vote Interstate Compact: A coalition of states that pledge electoral votes according to the national popular vote.

Plurality: A voting method in which the candidate who gets the most votes wins. This system is only used for more than two candidates.

Popular Election/Popular Vote: Connotes the total number of votes received in the first-phase election. In United States presidential elections, it is the total number or percentage of votes cast by voters in the 50 states and the District of Columbia, as opposed to the Electoral College.

President: The Head of State and Head of Government of the United States; directs the executive branch of the federal government and is the commander-in-chief of the United States Armed Forces.

Same Ballot: An election ticket on which two candidates for the United States President and Vice President may run together.

State Legislature: The legislative body of any of the 50 U.S. states. Depending on the state, known either as the State Legislature, the General Assembly, the General Court, or the Legislative Assembly.

Twelfth Amendment: Provides the procedure for electing the President and Vice President.

Vice President: The second-highest position in the federal branch of the United States government and the president of the Senate.

Virginia Plan: A proposal to the Constitutional Convention for a United States supreme national government with three branches and a bicameral legislation.

Winner-Takes-All Method: Another term for plurality voting in a multi-member district system.

Made by: Lily Forrester and Jules Gabellini