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Chapter 13: Problem 44

What is the pairwise comparison method? Is it possible to use this method without ranking the candidates? Explain.

Short Answer

Expert verified
Pairwise comparison is a process of comparing each candidate against each other to determine the most preferred one. This method inherently involves ranking the comparisons' outcomes. Therefore, it is not possible to use the pairwise comparison method without ranking candidates.

Step by step solution

01

Understanding Pairwise Comparison Method

Pairwise comparison is a method often used in decision making processes. In this method, each option or candidate is compared against each other one-on-one. The one with the most victories is generally considered the winner. The pairwise comparison method can be applied in various situations where decisions need to be made from multiple options, such as in voting systems, product preferences, or hiring choices.
02

Explaining the Role of Ranking in Pairwise Comparison

Ranking plays a critical role in the pairwise comparison method. Since each candidate is compared with all others one on one, a verdict is reached for each pair, and a candidate is ranked higher or lower based on the outcomes of these comparisons. The candidate with the most victories gets the highest rank. If there were no ranking, it would be impossible to determine a clear victor as there is no mechanism to compare the outcome of all the pairwise comparisons. Hence, ranking is an essential part of the pairwise comparison method.

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Most popular questions from this chapter

A school district has 57 new laptop computers to be divided among four schools, according to their respective enrollments. The table shows the number of students enrolled in each school $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { School } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \text { Enrollment } & 5040 & 4560 & 4040 & 610 & 14,250 \\ \hline \end{array} $$a. Apportion the laptop computers using Hamilton鈥檚 method. b. Use Hamilton鈥檚 method to determine if the Alabama paradox occurs if the number of laptop computers is increased from 57 to 58. Explain your answer

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In allocating congressional seats, how does Hamilton's method choose some states over others for preferential treatment? Explain how this is avoided in Jefferson's and Adams's methods.

The winner by the plurality method violates the irrelevant alternatives criterion.

A modified quota of \(46.01\) and a final apportionment of 47 is a violation of the quota rule.
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