Consider the preference schedule below: 10 15 8 14 5 13 1st Choice Emma Emma Dan Dan Rupert Rupert 2nd Choice Dan Rupert Emma Rupert Emma Dan 3rd Choice Rupert Dan Rupert Emma Dan Emma Suppose the election is held using the Borda Count Method. Determine each of the following: a. How many points will be awarded to Emma? Answer: Work/Explain: b. How many points will be awarded to Dan? Answer: Work/Explain: c. How many points will be awarded to Rupert? Answer: Work/Explain: d. Who wins this election? QUESTION 2 Consider the preference schedule below: 35 21 37 18 38 26 15 10 1st Choice Blanche Rose Rose Rose Dorothy Dorothy Sophia Sophia 2nd Choice Sophia Sophia Dorothy Dorothy Rose Rose Dorothy Blanche 3rd Choice Dorothy Dorothy Sophia Blanche Blanche Sophia Rose Rose 4th Choice Rose Blanche Blanche Sophia Sophia Blanche Blanche Dorothy Which candidate would win under the Borda Count Method? State your answer below and give your work explaining how you found your answer. QUESTION 3 Consider the preference schedule below: 10 15 8 14 5 13 1st Choice Emma Emma Dan Dan Rupert Rupert 2nd Choice Dan Rupert Emma Rupert Emma Dan 3rd Choice Rupert Dan Rupert Emma Dan Emma Suppose the election is held using Copeland’s Method. Determine each of the following: a. Who wins in a head-to-head match between Emma and Dan? Answer: Work/Explain: b. Who wins in a head-to-head match between Emma and Rupert? Answer: Work/Explain: c. Who wins in a head-to-head match between Dan and Rupert? Answer: Work/Explain: d. Who wins this election? QUESTION 4 There are five books in the Percy Jackson & the Olympians series by Rick Riordan. For ease, let’s just refer to them as Book 1, Book 2, Book 3, Book 4, and Book 5 instead of their titles. Fans of the books are asked to rank them based on which books they like best. The results are presented in the preference schedule below. 9 7 20 6 10 12 8 10 3 1st Choice Book 1 Book 1 Book 2 Book 3 Book 4 Book 4 Book 4 Book 5 Book 5 2nd Choice Book 4 Book 5 Book 1 Book 2 Book 5 Book 1 Book 1 Book 4 Book 4 3rd Choice Book 5 Book 4 Book 4 Book 1 Book 1 Book 5 Book 2 Book 1 Book 3 4th Choice Book 2 Book 2 Book 3 Book 5 Book 2 Book 2 Book 5 Book 2 Book 1 5th Choice Book 3 Book 3 Book 5 Book 4 Book 3 Book 3 Book 3 Book 3 Book 2 If the “best book in the series” is selected using Copeland’s Method, which book is the best book? State your answer below and give your work explaining how you found your answer. QUESTION 5 The 9 members of an anime club are trying to decide what show to watch next. They vote on whether or not they would watch each of several shows as indicated below. Anna Elizabeth Heather Jen Jess Kristin Natalie Tina Yuko Aggretsuko X X X X X Chihayafuru X X X X X Demon Slayer X X X X X X X Fruits Basket X X X X X X X X Kakuriyo X X X X Mushi-shi X X X X X Using Approval Voting, which show should the anime club watch next? State your answer below and give your work explaining how you found your answer. QUESTION 6 The time has come for the Dunder Mifflin Office BBQ (Scranton Branch). Michael is making chicken, cheeseburgers, and hotdogs. He takes orders from each of the employees and records them below: Andy: chicken, cheeseburger, hotdog Angela: chicken Creed: hotdog, chicken Dwight: chicken Jim: cheeseburger Kelly: chicken Kevin: chicken, cheeseburger, hotdog Meredith: chicken, hotdog Michael: chicken, cheeseburger, hotdog Oscar: hotdog Pam: chicken Phyllis: chicken, cheeseburger Ryan: cheeseburger, hotdog Stanley: hotdog, cheeseburger Toby: cheeseburger, chicken Tally the orders into the table below. The first total has been done for you as an example. 3 Cheeseburger X X X X Chicken X X X X Hotdog X X X X How many cheeseburgers are ordered? How many orders of chicken are there? How many hotdogs have been ordered? Using the Approval Voting Method, which protein order is the most popular? ] QUESTION 7 There have been several actors who have played the titular character in the British sci-fi series Doctor Who since the show began in the early 1960s. In 2005 the series was rebooted and Christopher Eccleston, David Tennant, Matt Smith, Peter Capaldi, and Jodie Whittaker have all played the Doctor since. Several Whovians (fans of the show) were asked to rank the actors of the Doctor from their favorite to their least favorite. The results are in the preference schedule below using the initials of each actor (so CE = Christopher Eccleston; DT = David Tennant; etc.). 6 8 12 16 17 18 23 20 1st Choice CE DT DT DT MS MS PC JW 2nd Choice MS CE PC PC JW CE JW CE 3rd Choice DT JW CE JW CE DT DT PC 4th Choice PC MS JW MS PC PC CE DT 5th Choice JW PC MS CE DT JW MS MS Using this preference schedule and the Plurality Method, which actor had the most favored portrayal of the Doctor? State your answer below and give your work explaining how you found your answer. QUESTION 8 Using the preference schedule from #7 and the Instant Runoff Voting Method, which actor had the most favored portrayal of the Doctor? State your answer below and give your work explaining how you found your answer. QUESTION 9 Using the preference schedule from #7 and the Borda Count Method, which actor had the most favored portrayal of the Doctor? State your answer below and give your work explaining how you found your answer. QUESTION 10 Using the preference schedule from #7 and Copeland’s Method, which actor had the most favored portrayal of the Doctor? State your answer below and give your work explaining how you found your answer. QUESTION 11 Review the preference schedule from #7. a. Is there a Condorcet winner? Answer: Explain: b. Do any of the voting methods from #7–10 violate the Majority Criterion? Answer: Explain: QUESTION 12 An election resulted in Smith winning, with Jones coming in a close second, and Williams being a distant third. If for some reason the election had to be held again and Williams decided to drop out of the election, which caused Jones to become the winner, which is the primary fairness criterion violated in this election? Condorcet Criterion Independence of Irrelevant Alternatives (IIA) Criterion No fairness criteria are violated Majority Criterion Monotonicity Criterion QUESTION 13 An election resulted in Smith winning, with Jones coming in a close second, and Williams being a distant third. If for some reason the election had to be held again and many people who had voted for Williams switched their preferences to favor Smith, which caused Jones to become the winner, which is the primary fairness criterion violated in this election? Independence of Irrelevant Alternatives (IIA) Criterion Monotonicity Criterion Condorcet Criterion Majority Criterion No fairness criteria are violated QUESTION 14 An election resulted in Brown winning, with Kelly coming in a close second, and candidate Whitmore being a distant third. If in a head-to-head comparison a majority of people prefer Kelly to Brown or Whitmore, which is the primary fairness criterion violated in this election? Condorcet Criterion Independence of Irrelevant Alternatives (IIA) Criterion Majority Criterion No fairness criteria are violated Monotonicity Criterion QUESTION 15 An election resulted in Brown winning, with Kelly coming in a close second, and Whitmore being a distant third. If Kelly had received a majority of first place votes, which is the primary fairness criterion violated in this election? Independence of Irrelevant Alternatives (IIA) Criterion Condorcet Criterion No fairness criteria are violated Majority Criterion QUESTION 16 1. A retail store would like to hire three new sales reps. A hiring committee made up of 8 current employees reviews the 6 candidates who applied for the position and rank the candidates (named U, V, W, X, Y, and Z) as indicated below. Committee Member Alice Bhanvi Carlos Doris Eiichiro Frieda Gigi Haakim 1st Choice W Y Y W Y W Y Z 2nd Choice Y W Z U X Y W X 3rd Choice Z X W Z W V U Y 4th Choice X U X X V U X W 5th Choice V Z U Y Z V 6th Choice U V V V X Who should the hiring committee select? Justify your answer by including the following information: o Which of the voting methods discussed in this chapter do you think the committee should use? o Why did you choose that method? o Show your work of using your chosen method to determine the three candidates the retail store will hire. Please note that there are multiple correct answers and methods for this problem. In particular, I’m not necessarily looking for any one specific voting method to be used here, so don’t think about this problem as “looking for the one perfect right answer.” Instead, think about the methods that have been discussed and determine which one you think will be most helpful in selecting three candidates for the position, and why you think that method will work best. Then explain your thought process with your answer. Also notice that some members of the hiring committee did not include some of the candidates in their rankings. Once you have decided on the method you want to use, how do you use that method to use the missing rankigns.