HW 16a Section 16.1 – The Possibilities of Voting Name ________________________________________ Show all necessary work. 1) A local animal shelter is choosing a poster dog. The choices are an Australian shepherd (a), a boxer (b), a cocker spaniel (c), or a Dalmatian (d). Thirteen staff members completely rank the four dogs on the ballots. The thirteen individual ballots are the columns in the table. Use the plurality method to determine the shelter’s poster dog. 3) If there are n = 5 candidates, then how many rankings of the candidates are possible? 15) A senator invited one person from each of the 21 counties in her state to a weekend workshop. The senator asked the attendees to rank the issues of job creation (j), education (e), health care (h), and gun control (g) in order of importance to themselves and their counties. The 21 members each gave a complete ranking of the issues on a separate ballot. For each voter profile, determine which issue workshop members felt was the highest priority using the a. plurality method b. pairwise comparison method c. Borda method d. Hare method 19) Members of the Adventure Club are selecting an activity for their yearly vacation. Choices are hiking (h), rock climbing (c), white-water kayaking (k), bungee jumping (b), or just sitting by a mountain lake and tanning (t). For each voter profile of the 55 members, determine the selected activity using the a. plurality method b. pairwise comparison method c. Borda method d. Hare method 25) Use the Hare method to select a winner for the following voter profile. 29) Find the missing number of pairwise comparisons. 35) Find the missing number of Borda points. 37) The Coombs method of voting is a variation of the Hare method. Voting takes place in rounds, but instead of eliminating the candidate with the fewest first-place votes, the candidate with the most last-place votes is eliminated. Use the Coombs method to determine which issue the senator’s workshop members felt was the highest priority.
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