Exam 12: Voting Methods

A club voted on whether to meet on Monday (M), Wednesday (W), Friday (F), or Saturday (S). The Results of the election are summarized in the preference table below. (a)Using the pairwise comparison voting method, determine the winner. (b)If candidate S is eliminated and the votes are recounted, does this election violate the irrelevant alternative Criterion?

If there are 4 candidates in an election, how many pairwise comparisons need to be made in order to determine a winner?

The results of an election are summarized in the following preference table. If the plurality method Is used to determine the winner, decide whether the head-to-head comparison criterion has been Violated and explain your answer.

The math department is voting for a new department chairperson. The candidates are Jenkins (J), Peterson (P), and Thomas (T). The results of the election are summarized in the preference table Below. Using the plurality-with-elimination method of voting, determine the winner.

Suppose the election is declared invalid, and a reelection is held in which the people who originally voted XWYZ change their vote to ZWYX. Is the monotonicity criterion violated? Explain your answer.

The results of an election are summarized in the preference table below. (a)Using the pairwise comparison voting method, determine the winner. (b)If candidate Z drops out, does this election violate the irrelevant alternative criterion?

Use a preference table for the following preference ballots to determine the winner of the election Using the plurality method.

The results of an election are summarized in the preference table below. Using the plurality-with-elimination method of voting, determine the winner.

Use a preference table for the following preference ballots to answer the questions. (a)How many people voted? (b)How many people voted for the candidates in the order of preference BCA? (c)How many people voted for candidate B for their first choice?

The preference table below summarizes the results of an election. (a)Using the Borda count method of voting, determine the winner. (b)Does the election violate the majority criterion?

A committee must select one of its members to serve as president. They vote using the approval Method. The results are shown. Who was selected to be president of the committee?

Use a preference table for the following preference ballots to determine the winner using the plurality method.

The results of an election are summarized in the following preference table. (a)Determine the winner using the Borda method of voting. (b)Is the winner the same as the one determined by the plurality method?

A large chain store needs to assign 11 buyers to its five stores. The standard divisor is 29.7 and the Number of employees and standard quota for each store are shown below. (a)Determine how many Buyers each store should receive using Jefferson's method and (b)indicate the modified divisor used (answers may vary). Round the divisor to the nearest tenth, if necessary.

The results of an election are summarized in the following preference table. Determine the winner Using the plurality method.

A county has three clinics; the weekly number of patients seen by a nurse practitioner in each clinic Is shown below. The director hires eight new nurse practitioners; find the geometric mean of the Upper and lower quotas for each clinic. Round to three decimal places, if necessary.

The table shows the enrollment at two campuses of a community college. (a)Apportion 55 new media podiums to the two campuses according to Hamilton's method. (b)Suppose the college adds a third campus with enrollment of 1,143 and correspondingly adds seven Podiums. Reapportion the 62 podiums using Hamilton's method. (c)Determine if the new states paradox occurs.

Make a preference table for the following preference ballots.

Use a preference table for the following preference ballots to answer the questions. (a)How many people voted? (b)How many people voted for the candidates in the order of preference XYZ? (c)How many people voted for candidate Y for their first choice?

A department store is hiring 13 new sales associates and needs to assign them to four departments According to the volume of sales in dollars. The daily sales in dollars are given below. (a)Use the Huntington-Hill method to decide how many associates each department should receive and (b)write the (standard or modified)divisor used (answers may vary). Round divisor to the nearest Whole number.