Probability / Statistics
- Thread starter RAK
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Hello, and welcome to FMH! 
You'll be much more likely to get a reply if you post the question directly so that people don't have to download a file, and include any work you have
to go along with it so we can see where you need help.
You'll be much more likely to get a reply if you post the question directly so that people don't have to download a file, and include any work you have
to go along with it so we can see where you need help.
When you vote for president, you are actually voting for a list of electors to represent your state. The number of electors for a state is roughly determined by the state's population. More specifically, the number of electors for a state equals the number of representatives and senators that the state has in Congress. If a candidate wins the plurality of votes in a state, this typically means that every elector selected in the state will vote for this candidate.
To get a better idea of the oddities of this Electoral College Method, we will model the situation with a smaller imaginary country. This country only has four states. Just like in the United States, the individual state populations vary greatly. To elect their president, each state first holds an election using the Plurality Method. The winner in a state receives all of the electoral votes for that state.
Each state in our imaginary country is given one electoral vote for every 10,000 people and an extra two electoral votes to represent the state's senators. To win the election, a candidate must win a majority of the 54 total electoral votes. The table below gives the population and number of electoral votes for each state.
Here is an example election.
Candidate A earned a total of 11 + 13 = 24 electoral votes while candidate B earned a total of 8 + 22 = 30 electoral votes. Candidate C earned zero electoral votes. Thus, candidate B is elected.
One common objection to the Electoral College Method is that it violates the Majority Criterion. It is possible for a presidential candidate to get a majority of individual votes yet still lose the election. This has actually happened. In 1876, Tilden earned 50.9% of the individual votes, yet he lost the election to Hayes.
Problem 1: (5 points) In the example election given above, Candidate A received a total of 210,000 individual votes while Candidate B only received 190,000 individual votes and Candidate C received 60,000 individual votes. Even though Candidate A received the most individual votes, they lost the election to Candidate B. However, this does NOT demonstrate a violation of the Majority Criterion. Explain why not.
Problem 2: (18 points) Construct an example election with 3 candidates for our imaginary 4-state country that demonstrates a violation of the Majority Criterion. Use the populations that were provided and assume that every member of every state votes. Fill appropriate numbers in the following table, and then explain in detail why the Majority Criterion has been violated.
Include detailed work and explanations with your answer.
Another common objection to the Electoral College Method is that it violates the principle of one-person-one-vote.
Problem 3: In our imaginary 4-state country, 60,000 people are represented by 8 electoral votes in Alaskigan. Divide to determine how many people are represented by just one electoral vote in Alaskigan. Also determine how many people are represented by each electoral vote in D'ohio.
Problem 4: Based on your results from Problem 3, whose vote holds more individual power, a voter from a smaller state or a voter from a larger state? Justify your answer with a brief explanation.
Use of the Electoral College Method has been debated essentially since the time that it was created in 1787. Included next are two articles that give different perspectives on the method.
To get a better idea of the oddities of this Electoral College Method, we will model the situation with a smaller imaginary country. This country only has four states. Just like in the United States, the individual state populations vary greatly. To elect their president, each state first holds an election using the Plurality Method. The winner in a state receives all of the electoral votes for that state.
Each state in our imaginary country is given one electoral vote for every 10,000 people and an extra two electoral votes to represent the state's senators. To win the election, a candidate must win a majority of the 54 total electoral votes. The table below gives the population and number of electoral votes for each state.
| State | Alaskigan | Barkansas | Colorida | D'ohio |
| Population | 60,000 | 90,000 | 110,000 | 200,000 |
| Electoral Votes | 8 | 11 | 13 | 22 |
| State | Alaskigan | Barkansas | Colorida | D'ohio |
| Individual votes for Candidate A | 20,000 | 60,000 | 60,000 | 70,000 |
| Individual votes for Candidate B | 30,000 | 20,000 | 30,000 | 110,000 |
| Individual votes for Candidate C | 10,000 | 10,000 | 20,000 | 20,000 |
| Electoral votes go to Candidate. . . | B | A | A | B |
One common objection to the Electoral College Method is that it violates the Majority Criterion. It is possible for a presidential candidate to get a majority of individual votes yet still lose the election. This has actually happened. In 1876, Tilden earned 50.9% of the individual votes, yet he lost the election to Hayes.
Problem 1: (5 points) In the example election given above, Candidate A received a total of 210,000 individual votes while Candidate B only received 190,000 individual votes and Candidate C received 60,000 individual votes. Even though Candidate A received the most individual votes, they lost the election to Candidate B. However, this does NOT demonstrate a violation of the Majority Criterion. Explain why not.
Problem 2: (18 points) Construct an example election with 3 candidates for our imaginary 4-state country that demonstrates a violation of the Majority Criterion. Use the populations that were provided and assume that every member of every state votes. Fill appropriate numbers in the following table, and then explain in detail why the Majority Criterion has been violated.
Include detailed work and explanations with your answer.
| State | Alaskigan | Barkansas | Colorida | D'ohio |
| Individual votes for Candidate A | ||||
| Individual votes for Candidate B | ||||
| Individual votes for Candidate C | ||||
| Electoral votes go to Candidate. . . |
Problem 3: In our imaginary 4-state country, 60,000 people are represented by 8 electoral votes in Alaskigan. Divide to determine how many people are represented by just one electoral vote in Alaskigan. Also determine how many people are represented by each electoral vote in D'ohio.
Problem 4: Based on your results from Problem 3, whose vote holds more individual power, a voter from a smaller state or a voter from a larger state? Justify your answer with a brief explanation.
Use of the Electoral College Method has been debated essentially since the time that it was created in 1787. Included next are two articles that give different perspectives on the method.
Dr.Peterson
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Where do you need help?
I hope you aren't expecting someone to do the whole problem for you.
I hope you aren't expecting someone to do the whole problem for you.