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MATH 1010 – 01 & 01E EXAM 1 NAME…………………………………………………………………………… INSTRUCTIONS ANSWER аll questiоns in the spаces prоvided аnd shоw all your workings to earn all points. SECTION A (30 points) You are provided with a list of concepts discussed in class in the box below. Select the best match and fill the corresponding concept in the blank space at the end of each question. [Borda Method, Cracking, Plurality Method, Condorcet Criterion, Monotonicity Criterion, Unfavorable Majority Criterion, Arrow’s Impossibility Theorem, Agenda Effect, Insincere Voting, Independence of Irrelevant Alternatives Criterion, Gerrymandering, Pareto Criterion, Runoff Method, Elimination Method, Sequential Pairwise Method, Method of Pairwise Comparisons, Wasted Votes, Condorcet Candidate, Satisfies, Majority Criterion, Majority Candidate, Majority, Packing, Violates.] 1. Process of manipulating the boundaries of an electoral district using the political affiliation of the constituents to the advantage of those drawing the boundary……………….. 2. Which term refers to voting against your true preferences in order to alter the outcome of the election? ………………………………………….. 3. Which voting method decides the winner based on which candidate receives the most first place votes? ……………………………………… 4. Which fairness criterion would be violated by a situation in which a candidate that beats every other candidate in pairwise competition does not win the election? …………………………… 5. Which voting method consists of a plurality round, followed by a one-on-one competition between the top two candidates? …………………………………………… 6. Which fairness criterion states: “If every voter prefers candidate X over candidate Y, then candidate Y should not win the election?” ………………………………… 7. Any voting method that uses voters’ ranked choices to decide an election with a single winner will violate at least one of the four criteria we’ve discussed: majority, monotonicity, Condorcet, or IIA. What important idea from voting theory does this statement represent?..................................................................... 8. If two elections are held, and the only difference is that the winner of the first election is ranked higher by some voters in the second election, then that candidate should still win the second election. Which fairness criterion is described by this statement?................................. 9. If a party wins the district, any votes for that party past the number necessary to win are………………….. 10. What is the term used to describe more than half of the total? ………………………….. 11. Grouping as many members as possible of the opposing party into the smallest number of districts so they win fewer representatives……………….. 12. Method of voting that assigns points to candidates…………………… 13. What is the term used to refer to a candidate who would defeat any other candidate in a one-on-one contest? ……………………………….. 14. If a voting method does not satisfy a given fairness criterion, even if it fails in only one election, then we say that the method …………………the given criterion. 15. Which voting method compares all pairs of candidates, and determines the winner by whoever wins the most comparisons? ………………………… SECTION B 11. A group of students plans to watch a movie together over the weekend. To decide on a movie to watch, a group of friends all vote for one of the choices (labeled A, B, and C). The individual ballots are shown below. Create a preference table. (5 points) CAB, CBA, BAC, BCA, CBA, ABC, ABC, CBA, BCA, CAB, CAB, BAC 12. Find the winner of the following election using IRV (Instant Runoff Voting). (5 Points) Election 1 Number of voters Rankings 37 22 12 29 1st choice Adams Brown Brown Carter 2nd choice Brown Carter Adams Adams 3rd choice Carter Adams Carter Brown 13. Use the results of Election 2 as shown in the table to answer the questions below. Preference Table for Election 2 Number of votes 26 25 15 34 1st A B B C 2nd C A C A 3rd B C A B How many total voters were there? (2 points) True or False: a total of 26 voters preferred Candidate A over Candidate B. (2 points) Who is the plurality winner? Does that candidate have a majority? (5 points) Calculate the winner under Borda Count Voting Method. (6 points) 14. The Oregon State governor’s race has five candidates, F, G, H, I, J. The votes are: Number of voters 16 12 9 21 17 11 6 1st choice F F H I G G J 2nd choice I G I F H J F 3rd choice G H G J I F H 4th choice J J J H F I G 5th choice H I F G J H I Find the winner under the standard runoff voting method. (5 points) Based on this election, Does standard runoff voting method satisfy or violate the majority criterion? (3 points) 15. Calculate the efficiency gap EG for districting Method shown in the figure below. Let A be the red voters and B be the blue voters. Each square box represent one voter. (5 points) 15. Use the following election to show that the method of pairwise comparisons violates Independence of Irrelevant Alternatives Criterion. (6 points) 16. Using the preference schedule below, apply Sequential Pairwise voting to determine the winner, using the agenda: A, B, C, D. (6 points) Borda points Rankings 10 15 12 4 1st choice C A B 3 2nd choice A B D 2 3rd choice B D C 1 4th choice D C A