It’s. Essay related to math needed by tomorrow,please do it rightly. Thank you
Math 103 Optional Project Over the course of the semester, you have and will continue to see math applied to a variety of topics related to finance, voting, power, apportionment, and fair division. In a semester, we can only show you specific highlights. However, there are many interesting topics that we could explore further. The goal of this project is to give you an opportunity to either analyze topics we studied in more depth or give you an opportunity to learn more about topics in the various chapters that are not currently in the course but are interesting follow-up topics to study. As the title states, this project is OPTIONAL. It will give you an opportunity to demonstrate your knowledge of a topic of your choosing in an alternate way that is not an exam. If completed well, it can raise up to two of your scores to Mastered, from something below Mastered. In other words, if you are borderline between two course grades, a strong performance on this project can push you over the border for that next course grade. Deadline and Grading: The project is due March 30 10 pm. You are welcome to submit it sooner. Please note that we are giving you a long time so you have time to submit a well-done project. A Rubric is given on the last page. Project Options: Pick one project topic from the list below. Option 1 (Voting) This project doing some research into contexts outside the course in which people/organizations /governments use different voting methods. You will write a 5-page paper discussing real life examples of voting methods. Be sure to cite your sources. (Must include all 3 topics below.) · Discuss real-life examples in which the Borda Count method, or some variation on it, is used. · Discuss real-life examples in which the Instant Runoff Voting method is used. · Describe how Approval Voting works and discuss real-life examples in which it is actually used. Option 2 (Voting) This project involves constructing your own examples of elections in the context of the Monotonicity and I.I.A. fairness criteria, i.e., involving “the election before and the election after.” a. Construct your own example of the election before and the election after, where the Monotonicity Criterion does not apply, and explain why it does not apply. Give a specific story that makes clear which voters are changing their ballots. b. Construct your own example of the election before and the election after, where the Monotonicity Criterion does apply, and is violated. Explain why it does apply and why what occurs counts as a violation. c. Construct your own example of the election before and the election after, where the I.I.A. Criterion does not apply, and explain why it does not apply. Give a specific story that makes clear which candidate is disqualified or drops out. d. Construct your own example of the election before and the election after, where the I.I.A. Criterion does apply and is violated. Explain why it does apply and why what occurs counts as a violation. (This project will be about 4 pages of examples with explanations.) Option 3 (Power) Write a 5-page paper discussing the history of applying Banzhaf’s approach to measuring power in actual court cases. You can also discuss how other approaches to measuring power have actually been used. Some examples of court cases worth looking at are Graham v Board, Bechtle v Board, League of Women Voters v Board. There are many others you can research as well. Option 4 (Power) In the U.S., the Electoral College is used in presidential elections. Each state is awarded a number of electors equal to the number of representatives (based on population) and senators (2 per state) they have in congress. Since most states award the winner of the popular vote in their state all their state’s electoral votes, the Electoral College acts as a weighted voting system. To explore how the Electoral College works, we’ll look at a mini-country with only 4 states. Here is the outcome of a hypothetical election: State Cook-Douglass Livingston Busch College Ave Population 50,000 70,000 100,000 240,000 Votes for A 40,000 50,000 80,000 50,000 Votes for B 10,000 20,000 20,000 190,000 Complete all parts a-f: a. If this country did not use an Electoral College, which candidate would win the election? b. Suppose that each state gets 1 electoral vote for every 10,000 people. i. Set up a weighted voting system for this scenario, calculate the Banzhaf power index for each state, then calculate the winner if each state awards all their electoral votes to the winner of the election in their state. ii. Also find each state's percentage of total population, and say which states have a smaller or larger share of the actual power than their share of total population. c. Suppose that each state gets 1 electoral vote for every 10,000 people, plus an additional 2 votes. i. Set up a weighted voting system for this scenario, calculate the Banzhaf power index for each state, then calculate the winner if each state awards all their electoral votes to the winner of the election in their state. ii. Also find each state's percentage of total population, and say which states have a smaller or larger share of the actual power than their share of total population. d. Suppose that each state gets 1 electoral vote for every 10,000 people, and awards them based on the number of people who voted for each candidate. Additionally, they get 2 votes that are awarded to the majority winner in the state. Calculate the winner under these conditions. Say which states have a smaller or larger share of the actual power than their share of total population. e. Based on what you found in parts b, c, and d, are there any examples of an individual state having more power in the Electoral College under one vote distribution (b, c, or d) than under a different one? Can you make an argument for one of the three vote distributions (b, c, or d) being fairer than the others? f. Research the history behind the Electoral College to explore why the system was introduced instead of using a popular vote. Based on your research and experiences, in a 3-page paper state and defend your opinion on whether the Electoral College system is or is not fair. Your discussion should make some reference to what you found in parts b, c, d, and e above. Option 5 (Apportionment) William Lowndes (1782-1822) was a Congressman from South Carolina (a small state) who proposed a method of apportionment that was more favorable to smaller states. Unlike the methods of Hamilton, Jefferson, and Webster, Lowndes’s method has never been used to apportion Congress. Lowndes believed that an additional representative was much more valuable to a small state than to a large one. a. Research Lowndes’s method and write a 3-page paper about the method and how to apply it. b. Then, apply it to the nurses problem from the homework and compare the results to both Hamilton’s and Jefferson’s Methods. Option 6 (Apportionment) Write a 5-page paper discussing the history of implementing methods in the USA for apportioning the House of Representatives. Include a discussion of some of the controversies that have arisen, including the 1880 apportionment and the Alabama paradox. Option 7 (Fair Division) This project involves investigating other notions of fairness than the one we used for fair division and fair distribution. In a 3-page paper, explain the meaning of envy-free and equitable divisions. Then, for two different problems on fair division/distribution that appear in this course, explain whether they are envy-free, and whether they are equitable. Option 8 (Fair Division) This project also involves investigating other notions of fairness than the one we used for fair division and fair distribution. In a 4-page paper, explain how the Adjusted Winner Method works. Then, apply it to a particular example (not from this course). Option 9 (Growth/Finance) In this project, you will investigate the process of buying a house. For the purposes of this project, we will assume that you are going to graduate at the end of the spring semester, get a job, and begin saving for your first home. You will plan to buy your house five years after graduation. At that time, you will use the money you saved as a down payment and take out a loan for the rest of the cost of the house. (You must complete all of parts a-c.) 0. Figure out your anticipated salary for the first five years after you graduate. The, write a 1-page paper describe what kind of job you expect to have and what starting monthly salary is realistic for that job type. Also project your salary over five years. Support your salary assumptions with data. 0. Assume for the purposes of this project that 10% of your monthly salary you projected in part (a) will be invested in an annuity. 1. Research the types of annuities available to you and describe the terms, APR, and fees. Write a 1-2 page paper on your findings. 1. Use this information to compute the amount of money you will have in 5 years. 0. How much can you afford to spend on a home and how much will your monthly mortgage expenses be? 2. To do this, determine how much you can afford to spend on a home, use your estimate of how much you saved for a down payment, and assume your down payment is 15% of the cost of the home. 2. Research the types of home loans currently available to someone with your credit rating and income for the 5-year period. Determine the terms of a loan you might be able to take out, including interest rate type and length of