Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 6.1, Problem 12E
Four candidates, Harrison (H), Lennon (L), McCartney (M), and Starr (S), are running for region-al manager. After the polls close, ranked ballots are tallied, and the results are summarized in Figure 6.32.
| Number of Ballots Cast | |||||||
| 23 | 98 | 45 | 82 | 32 | 17 | 21 | |
| 1st choice | H | L | L | M | M | S | S |
| 2nd choice | L | M | S | L | L | H | M |
| 3rd choice | S | H | M | H | S | L | H |
| 4th choice | M | S | H | S | H | M | L |
a. How many votes were cast?
b. Use the plurality method of voting to determine the winner.
c. What percent of the votes did the winner in part (b) receive?
d. Use the instant runoff method to determine the winner.
e. What percent of the votes did the winner in part (d) receive?
f. Use the Borda count method to determine the winner.
g. How many points did the winner in part (f) receive?
h. Use the pairwise comparison method to determine the winner.
i. How many points did the winner in part (h) receive?
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Chapter 6 Solutions
Mathematics: A Practical Odyssey
Ch. 6.1 - Four candidates, Alliotti, Baker, Cruz, and Daud,...Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Number of Ballots Cast 6 8 7 10 15 1st choice C C...Ch. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Four candidates, Harrison H, Lennon L, McCartney...Ch. 6.1 - Prob. 13ECh. 6.1 - Five candidates, Fino F, Gempler G, Holloway H,...Ch. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - In an election, there are seven candidates. a....Ch. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - What is Arrows Impossibility Theorem?Ch. 6.2 - A small country consists of three states, A, B and...Ch. 6.2 - A small country consists of three states, A, B and...Ch. 6.2 - Suppose that the governors of three Middle...Ch. 6.2 - Suppose that the governors of three midwestern...Ch. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - A local school district contains four middle...Ch. 6.2 - A local school district contains four elementary...Ch. 6.2 - Prob. 11ECh. 6.2 - In J.R.R. Tolkiens Middle Earth, the regions in...Ch. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Use the Hill-Huntington Method to determine how...Ch. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - What is apportionment?Ch. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Since the founding of the United States, what...Ch. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.3 - A small country consists of three states: A, B,...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - A small country consists of four states: A, B, C,...Ch. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - A small country consists of three states:A, B, and...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - What is the Alabama Paradox? Explain its meaning.Ch. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.CR - Prob. 1CRCh. 6.CR - Prob. 2CRCh. 6.CR - Prob. 3CRCh. 6.CR - Prob. 4CRCh. 6.CR - Prob. 5CRCh. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - Prob. 9CRCh. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - Prob. 12CRCh. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 17CRCh. 6.CR - A small country consists of three states: A, B,...Ch. 6.CR - Prob. 19CRCh. 6.CR - Prob. 20CRCh. 6.CR - Prob. 21CRCh. 6.CR - Prob. 22CRCh. 6.CR - Prob. 23CRCh. 6.CR - Prob. 24CRCh. 6.CR - Prob. 25CRCh. 6.CR - Prob. 26CRCh. 6.CR - Prob. 27CRCh. 6.CR - Prob. 28CRCh. 6.CR - What is the New States Paradox? Explain its...Ch. 6.CR - Prob. 30CRCh. 6.CR - Prob. 31CRCh. 6.CR - Prob. 32CRCh. 6.CR - Prob. 33CRCh. 6.CR - Prob. 34CRCh. 6.CR - What method of appointment for the House of...
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