HW 16a Section 16.1 – The Possibilities of Voting Name Show all

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.
`