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MGF 1107 Classroom Ex. Ch9

MGF 1107 Classroom Ex. Ch9 - MGF 1107 Classroom examples...

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MGF 1107/ Classroom examples/ Chapter 9 1. If there are 49 voters, how many are needed to constitute a majority? 2. If there are 50 voters, how many are needed to constitute a majority? 3. Suppose we poll the class to see whether you prefer the pizza at Domino’s, Pizza Hut, Papa John’s, Godfather’s or Little Caesars. Suppose there are 55 students who vote as follows: Domino’s 18 Papa John’s 12 Pizza Hut 10 Little Caesars 9 Godfather’s 6 Who wins the election? 4. In problem 3, we ask each of the 55 voters to rank all 5 chains in order of preference. After gathering all 55 rankings we see that many of the voters turned in the same ranking. In fact, there are only six distinct rankings: 18 votes 12 votes 10 votes 9 votes 4 votes 2 votes st Domino’s Papa John’s Pizza Hut Little Caesars Godfather’s Godfather’s nd Little Caesars Godfather’s Papa John’s Pizza Hut Papa John’s Pizza Hut d Godfather’s Little Caesars Godfather’s Godfather’s Little Caesars Little Caesars h Pizza Hut Pizza Hut Little Caesars Papa John’s Pizza Hut Papa John’s h Papa John’s Domino’s Domino’s Domino’s Domino’s Domino’s Who wins the election? 5. Who wins the election in problem 4 using sequential pairwise voting and the agenda PJ, G, D, PH, LC? 6. Sequential pairwise voting arises naturally in the legislative process. When the U.S. House of Representatives considers a bill, an amendment to the bill can be offered. Two votes are then taken. The first vote is whether to accept the amendment. If accepted, the second vote is between the amended bill and no bill at all. If the amendment is defeated, the second vote is between the original bill and no bill at all. In 1956 the House was considering a bill that would provide federal funding for the construction of schools. An amendment was offered that would only provide the federal funding to states with integrated school systems.

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MGF 1107 Classroom Ex. Ch9 - MGF 1107 Classroom examples...

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