Chapter 13: Problem 40
Describe what is contained in a preference table. What does the table show?
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Chapter 13: Problem 40
Describe what is contained in a preference table. What does the table show?
These are the key concepts you need to understand to accurately answer the question.
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How are modified quotas rounded using Webster's method?
The preference table shows the results of an election among three candidates, A, B, and C. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{7} & \mathbf{3} & \mathbf{2} \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { A } & \text { A } \\ \hline \end{array} $$ a. Using the plurality method, who is the winner? b. Is the majority criterion satisfied? Explain your answer. c. Is the head-to-head criterion satisfied? Explain your answer. d. The two voters on the right both move candidate A from last place on their preference lists to first place on their preference lists. Construct a new preference table for the election. Using the table and the plurality method, who is the winner? e. Suppose that candidate \(\mathrm{C}\) drops out, but the winner is still chosen by the plurality method. Is the irrelevant alternatives criterion satisfied? Explain your answer. f. Do your results from parts (b) through (e) contradict Arrow's Impossibility Theorem? Explain your answer.
The preference table for an election is given. Use the table to answer the questions that follow it. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 4} & \mathbf{1 2} & \mathbf{1 0} & \mathbf{6} \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { Second Choice } & \text { B } & \text { A } & \text { B } & \text { C } \\ \hline \text { Third Choice } & \text { C } & \text { C } & \text { A } & \text { B } \\ \hline \text { Fourth Choice } & \text { D } & \text { D } & \text { D } & \text { A } \\ \hline \end{array} $$ a. Using the plurality-with-elimination method, who is the winner? b. The six voters on the right all move candidate A from last place on their preference lists to first place on their preference lists. Construct a new preference table for the election. Using this table and the plurality-with- elimination method, who is the winner? Is the monotonicity criterion satisfied? Explain your answer.
Describe the apportionment problem.
a. A country has three states, state A, with a population of 99,000 , state B, with a population of 214,000 , and state C, with a population of 487,000 . The congress has 50 seats, divided among the three states according to their respective populations. Use Hamilton's method to apportion the congressional seats to the states. b. Suppose that a fourth state, state D, with a population of 116,000 , is added to the country. The country adds seven new congressional seats for state D. Use Hamilton's method to show that the new-states paradox occurs when the congressional seats are reapportioned.
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