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Chapter 13: Problem 14

What is the Alabama paradox?

Short Answer

Expert verified
The Alabama paradox refers to the counter-intuitive situation in apportionment where increasing the total number of items to allocate can decrease the amount apportioned to a certain recipient. It's named after a historical instance when Alabama lost a seat in the U.S. House of Representatives when the size of the House increased. This paradox is attributed to the peculiar characteristics of certain mathematical methods used for apportionment.

Step by step solution

01

Introduction to Apportionment

Apportionment refers to the process of dividing and distributing something, for instance seats in the U.S. House of Representatives among the various states based on their populations.
02

Understanding the Paradox

The Alabama Paradox occurs when increasing the total amount of items to distribute (such as seats) can paradoxically decrease the amount a recipient gets. This is against the usual expectation that an increase in total items would result in an increase, or at least no change, in each recipient鈥檚 allocation.
03

Historical Example

Using the U.S. as an example: In 1880, with a House size of 299, Alabama was allocated 8 seats. However, when the House size was increased to 300 in 1882, Alabama's allocation fell to 7 seats. Hence, the Paradox - Alabama received fewer seats even though the total number of seats increased.
04

Reason Behind the Paradox

The unexpected result is due to the mathematical methods used for apportionment. The most common methods include Hamilton's method and Jefferson's method, among others. Each of these methods has certain peculiar characteristics that can lead to paradoxical results like the Alabama paradox.

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Most popular questions from this chapter

A university is composed of five schools. The enrollment in each school is given in the following table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { School } & \begin{array}{c} \text { Liberal } \\ \text { Arts } \end{array} & \begin{array}{c} \text { Educa- } \\ \text { tion } \end{array} & \text { Business } & \begin{array}{c} \text { Engi- } \\ \text { neering } \end{array} & \text { Sciences } \\ \hline \text { Enrollment } & 1180 & 1290 & 2140 & 2930 & 3320 \\ \hline \end{array} $$ There are 300 new computers to be apportioned among the five schools according to their respective enrollments. Use Hamilton's method to find each school's apportionment of computers.

Research and present a group report on how voting is conducted for the Academy Awards. Describe the single transferable voting method, a variation of the pluralitywith-elimination method, in the nomination stage for best picture. (Members of the Irish Senate are also elected by this method.) Be sure to describe some of the more bizarre occurrences at the Oscar ceremonies.

Describe the difference between how modified quotas are rounded using Jefferson's method and Adams's method.

Members of the Student Activity Committee at a college are considering three film directors to speak at a campus arts festival: Ron Howard (H), Spike Lee (L), and Steven Spielberg \((S)\). Committee members vote for their preferred speaker. The winner is to be selected by the pairwise comparison method. The preference table for the election is shown. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 0} & \mathbf{8} & \mathbf{5} \\ \hline \text { First Choice } & \text { H } & \text { L } & \text { S } \\ \hline \text { Second Choice } & \text { S } & \text { S } & \text { L } \\ \hline \text { Third Choice } & \text { L } & \text { H } & \text { H } \\ \hline \end{array} $$ a. Using the pairwise comparison method, who is selected as the speaker? b. Prior to the announcement of the speaker, Ron Howard informs the committee that he will not be able to participate due to other commitments. Construct a new preference table for the election with H eliminated. Using the new table and the pairwise comparison method, who is selected as the speaker? c. Is the irrelevant alternatives criterion satisfied? Explain your answer.

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