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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.2, Problem 38ES

Textbook Problem

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Film Competition Three films have been selected as finalists in a national student him competition. Seventeen judges have viewed each of the films and have ranked them in order of preference. The results are given in the preference schedule below.

a. Using the plurality with elimination method, which film should win the competition?

b. Suppose the first vote is declared invalid and a revote is taken. All of the judges’ preferences remain the same except for the votes represented by the last column of the table. The judges who cast these votes both decide to switch their first place vote to film C. so their preference now is film C first, then film A. and then film B. Which film now wins using the plurality with elimination method?

c. Has the monotonicity criterion been violated?

To determine

**(a)**

Using the plurality with elimination method, which film should win the competition?

**Given Information:**

Rankings | ||||

Film | | | | |

Film | | | | |

Film | | | | |

Number of votes | | | | |

**Concept used:**

Since three films have been selected, therefore film is selected by plurality elimination method; second choice becomes first, 3^{r}^{d} choice become 2^{n}^{d}

To determine

**(b)**

Suppose the first vote is declared invalid and a revote is taken All of the judges preferences remain me same except for the votes represented by the last column of the table The judges who cast these votes both decide to switch their first place vote to film

To determine

**(c)**

Has the monotonicity criterion been violated?

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