Chapter 13: Problem 16
What is the new-states paradox?
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These are the key concepts you need to understand to accurately answer the question.
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Chapter 13: Problem 16
What is the new-states paradox?
These are the key concepts you need to understand to accurately answer the question.
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What is the Alabama paradox?
The following preference table gives the results of a straw vote among three candidates, \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 0} & \mathbf{8} & \mathbf{7} & \mathbf{4} \\ \hline \text { First Choice } & \text { C } & \text { B } & \text { A } & \text { A } \\ \hline \text { Second Choice } & \text { A } & \text { C } & \text { B } & \text { C } \\ \hline \text { Third Choice } & \text { B } & \text { A } & \text { C } & \text { B } \\ \hline \end{array} $$ a. Using the plurality-with-elimination method, which candidate wins the straw vote? b. In the actual election, the four voters in the last column who voted \(A, C, B\), in that order, change their votes to \(\mathrm{C}, \mathrm{A}, \mathrm{B}\). Using the plurality-with-elimination method, which candidate wins the actual election? c. Is the monotonicity criterion satisfied? Explain your answer.
A town has five districts in which mail is distributed and 50 mail trucks. The trucks are to be apportioned according to each district's population. The table shows these populations before and after the town's population increase. Use Hamilton's method to show that the population paradox occurs. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \end{array} & 780 & 1500 & 1730 & 2040 & 2950 & 9000 \\ \hline \text { New Population } & 780 & 1500 & 1810 & 2040 & 2960 & 9090 \\ \hline \end{array} $$
In Exercises 19-22, suppose that the pairwise comparison method is used to determine the winner in an election. If there are five candidates, how many comparisons must be made?
In Exercises 28–31, determine whether each statement makes sense or does not make sense, and explain your reasoning. My candidate received a majority of first-place votes and lost the election.
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