# exam1 - 12 Rank the candidates using extended Borda count...

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MA 103 QUIZ 1 Consider the preference schedule given by # of voters 3 4 9 9 2 5 8 3 12 A A A B B B C C D B B C C A C D A C C D B D C A B D A D C D A D D A B B 1. How many voters are there? 2. How many first place votes are needed for a majority? 3. Which candidate has the most first place votes? 4. Which candidate has the least first place votes? 5. Which candidate has the least last place votes? 6. Which candidate has the most last place votes? 7. Which candidate would win using the plurality method? 8. Which candidate would win using pairwise comparison method? Consider the preference schedule given by # of voters 153 102 55 202 108 20 110 160 175 155 A A A B B B C C D D C B D D C C A B A B B D C A D A D A C C D C B C A D B D B A 9. Which candidate wins using Borda count method? 10. Which candidate wins using plurality-with-elimination method? Consider the preference schedule given by # of voters 14 10 8 4 1 A C D B C B B C D D C D B C B D A A A A 11. Rank the candidates using extended plurality method

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Unformatted text preview: 12. Rank the candidates using extended Borda count method 13. Rank the candidates using extended plurality-with-elimination method 14. Rank the candidates using extended pairwise comparison method. (OVER) Consider the weighted voting system [ 5; 3, 2, 1, 1 ]. 1. What is the weight of the coalition formed by P 1 and P 3 ? 2. Which players are critical in the coalition { P 1 , P 2 , P 3 } ? 3. Which players are critical in the coalition { P 1 , P 3 , P 4 } ? 4. Write down all winning coalitions. 5. Find the Banzhaf power distribution of this weighted voting system. Consider the weighted voting system [ 8; 7, 6, 2 ] 6. Write down all sequential coalitions involving all three players. 7. In each of these coalitions, underling the pivotal player. 8. Find the Shapley-Shubik power distribution of this weighted voting system. Consider the weighted voting system [ 6; 4, 3, 2, 1 ]. 9. Find the Shapley-Shubik power distribution of this weighted voting system....
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## This note was uploaded on 03/27/2009 for the course MA 103 taught by Professor Solfiell during the Spring '08 term at N.C. State.

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exam1 - 12 Rank the candidates using extended Borda count...

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