MATH 1010                                                   …

MATH 1010                                                                                                  Test 1 NAME: ……………………………………………………………DATE ……………………. ANSWER ALL THE QUESTIONS. SHOW EVERY STEP! Questions. 1.Students in Math 1010 class are choosing a class representative. Five students; Benjamin, Angie, Cindy, Dan and Eliot have declared interest in the position. The instructor has asked the other students to rank the five candidates using the labels A, B, C, D, and E. The individual ballots are shown below. (35 points) CAEDB, BCADE, DCAEB, BDCAE, CAEDB, DCAEB, CDBEA, DCAEB, BCADE, BDCAE, DCAEB, CAEDB, AEBCD, BCADE, EDBAC, CDBEA, CAEDB, DCAEB, BDCAE, EDBAC, CAEDB, DCAEB, BDCAE, AEBCD, BDCAE, AEBCD, EDBAC, DCAEB, DCAEB, DCAEB, AEBCD, DCAEB. a) Create a preference Schedule from the individual ballots. b) How many students voted in this election? c) How many students are needed for a majority vote? d) Find the winner under the plurality method? e) Find the winner under the standard runoff method? f) Find the winner under the Borda count method? g? Find the winner under the Pairwise Comparison method? h) How many total pairwise comparisons must be made? i) How many different preference lists could there be with the five candidates?