2. Consider a society with three people (Aretha, Melanie, and Salvador) who use majority rule to decide between three levels of defense spending, A, B, and C. Level A is small, level B is moderate, and level C is large. The voters' preferences are depicted in the table below. Each column shows how the voters rank the choices. Choice First Second Third Aretha A B с Choice First Second Third Voter Melanie с B A a. Consider all possible pairwise elections: A versus B, B versus C, and C versus A. What is the outcome of each election? Does it appear, in this case, that majority rule would lead to a stable outcome on defense spending? If so, what is that choice? b. Now suppose that Melanie's preference ordering changes as depicted in the table below: Aretha A B с Voter Melanie с A B Salvador B C A Would majority rule lead to a stable outcome in this case? Why or why not? Salvador B с A

Practical Management Science
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Author:WINSTON, Wayne L.
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2. Consider a society with three people (Aretha, Melanie, and Salvador) who use majority rule to decide
between three levels of defense spending, A, B, and C. Level A is small, level B is moderate, and level C
is large. The voters' preferences are depicted in the table below. Each column shows how the voters rank
the choices.
Choice
First
Second
Third
Aretha
A
B
C
Choice
First
Second
Third
Voter
Melanie
с
B
A
a. Consider all possible pairwise elections: A versus B, B versus C, and C versus A. What is the
outcome of each election? Does it appear, in this case, that majority rule would lead to a stable
outcome on defense spending? If so, what is that choice?
b. Now suppose that Melanie's preference ordering changes as depicted in the table below:
Aretha
A
B
с
Voter
Melanie
с
A
B
Salvador
B
C
A
Would majority rule lead to a stable outcome in this case? Why or why not?
Salvador
B
с
A
Transcribed Image Text:2. Consider a society with three people (Aretha, Melanie, and Salvador) who use majority rule to decide between three levels of defense spending, A, B, and C. Level A is small, level B is moderate, and level C is large. The voters' preferences are depicted in the table below. Each column shows how the voters rank the choices. Choice First Second Third Aretha A B C Choice First Second Third Voter Melanie с B A a. Consider all possible pairwise elections: A versus B, B versus C, and C versus A. What is the outcome of each election? Does it appear, in this case, that majority rule would lead to a stable outcome on defense spending? If so, what is that choice? b. Now suppose that Melanie's preference ordering changes as depicted in the table below: Aretha A B с Voter Melanie с A B Salvador B C A Would majority rule lead to a stable outcome in this case? Why or why not? Salvador B с A
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