Chapter 13: Problem 16
What is the new-states paradox?
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Chapter 13: Problem 16
What is the new-states paradox?
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In Exercises 27-30, 72 voters are asked to rank four brands of soup: \(A, B, C\), and \(D\). The votes are summarized in the following preference table. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & 34 & 30 & 6 & 2 \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { D } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { D } & \text { B } & \text { C } \\ \hline \text { Fourth Choice } & \text { D } & \text { A } & \text { A } & \text { A } \\ \hline \end{array} $$ Determine the winner using the Borda count method.
Describe the plurality method. Why is ranking not necessary when using this method?
A country has 200 seats in the congress, divided among the five states according to their respective populations. The table shows each state’s population, in thousands, before and after the country’s population increase. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \\ \text { (in thousands) } \end{array} & 2224 & 2236 & 2640 & 3030 & 9870 & 20,000 \\ \hline \begin{array}{l} \text { New Population } \\ \text { (in thousands) } \end{array} & 2424 & 2436 & 2740 & 3130 & 10,070 & 20,800 \\ \hline \end{array} $$ n thousands) 2424 2436 2740 3130 10,070 20,800 a. Use Hamilton’s method to apportion the 200 congressional seats using the original population. b. Find the percent increase, to the nearest tenth of a percent, in the population of each state. c. Use Hamilton’s method to apportion the 200 congressional seats using the new population. What do you observe about the percent increases for states A and B and their respective changes in apportioned seats? Is this the population paradox?
What is the population paradox?
Describe the difference between how modified quotas are rounded using Jefferson's method and Adams's method.
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