1. Suppose that the Chess Club must vote on a restaurant to celebrate its championship in the World College Chess Tournament. Being a logical group it first sets a particular voting agenda. According to the agenda, the members first vote on Restaurant A vs Restaurant B. The winner of that vote it then pitted against Restaurant C in a majority vote. Finally, that second round winner is pitted against Restaurant D. The winner of that last vote is the chosen celebration venue.(a) Show that if the same venue results from all possible agendas, then there is no voting cycle involving the chosen venue.(b) Suppose there is no voting cycle at all. Will the same venue result from all possible agendas? Prove or provide a counterexample.
1. Suppose that the Chess Club must vote on a restaurant to celebrate its championship in the World College Chess Tournament. Being a logical group it first sets a particular voting agenda. According to the agenda, the members first vote on Restaurant A vs Restaurant B. The winner of that vote it then pitted against Restaurant C in a majority vote. Finally, that second round winner is pitted against Restaurant D. The winner of that last vote is the chosen celebration venue.(a) Show that if the same venue results from all possible agendas, then there is no voting cycle involving the chosen venue.(b) Suppose there is no voting cycle at all. Will the same venue result from all possible agendas? Prove or provide a counterexample.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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1. Suppose that the Chess Club must vote on a restaurant to celebrate its championship in the World College Chess Tournament. Being a logical group it first sets a particular voting agenda. According to the agenda, the members first vote on Restaurant A vs Restaurant B. The winner of that vote it then pitted against Restaurant C in a majority vote. Finally, that second round winner is pitted against Restaurant D. The winner of that last vote is the chosen celebration venue.(a) Show that if the same venue results from all possible agendas, then there is no voting cycle involving the chosen venue.(b) Suppose there is no voting cycle at all. Will the same venue result from all possible agendas? Prove or provide a counterexample.
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