Week 11 Math QZ 1. Twelve people serve on a board and are considering three alternatives: A, B, and C. The choices followed by vote is shown in following table. Determine the winner, if any, using the pairwise comparison method. The winner is 1 (ABC)(ACB)(BAC)(BCA)(CAB)(CBA)242121Viewing Saved Work Revert to Last Response 2. In 1993 the 101st International Olympic Committee met in Monaco to select the 2000 Winter Olympics site. The cities in the running were Beijing (B), Berlin (L), Istanbul (I), Manchester (M), and Sydney (S). Suppose we look at their voting preferences. (BLIMS) (LBSIM) (IBLSM) (MSBLI) 32 3 5 8 (LSBIM) (SBLMI) (IMSBL) (MBSLI) 6 30 2 3 (a) Is there a majority winner? yes no (b) If not, which city wins the plurality vote? B L I M S (c) Find the results of the election using the Hare method. Just after the third vote, one of the committee members voting for Manchester was accused of cheating and was disqualified. Because of that scandal, one member admitted she was voting insincerely, and changed her vote from Manchester to Sydney. What is the result of using the Hare method? B L I M S (d) Do the results of parts (a) and (b) violate any of the fairness criteria? yes no (e) If the last answer positive, which fairness criterion is being violated? None Majority Criterion Condorcet Criterion Irrelevant Alternatives Criterion Monotonicity Criterion 3. Use Hamilton's plan to apportion the new seats to the existing states. Which state illustrates the Alabama paradox? Assume that the populations are in thousands. 1 State A B C D E Population 300 301 340 630 505 Number of seats 50 4. Find the standard divisor for the given population and number of representative seats. Assume the population is equal to 170,000 and the number of seats is 16. d = 1 5. Twelve board members are voting on after-meeting activities, and they are asked to check any that they might like....
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