# John Quincy Adams, the sixth president of the United States, proposed an apportionment method. Research this method, which is known as the Adams method of apportionment. Describe how this method works. Also indicate whether ii satisties the quota rule and whether it is susceptible to any paradoxes.

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

Chapter
Section

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.1, Problem 33ES
Textbook Problem
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## John Quincy Adams, the sixth president of the United States, proposed an apportionment method. Research this method, which is known as the Adams method of apportionment. Describe how this method works. Also indicate whether ii satisties the quota rule and whether it is susceptible to any paradoxes.

To determine

Create an apportionment problem in which the Hamilton, Jefferson, and Webster methods produce the same apportionment.

### Explanation of Solution

Given Information:

Hamilton, Jefferson and webster method.

Concept used:

Hamilton method:

Under the Hamilton plan, divide the enrollments of each division by the standard divisor and round the quotient down to a whole number.

Jefferson method

In Jefferson we need to select modified standard divisor by trial and error this is 87.5 and get the number of Computers in each divisions

Webster method

In Webster we need to select modified standard divisor by trial and error this is 87.5 and get the number of Computers in each divisions

Calculation:

Hamilton method

Under the Hamilton plan, divide the enrollments of each division by the standard divisor and

round the quotient down to a whole number

 Divisions Enrollments Quotient Standard Quota Liberal arts 3455 345588≈39.261 39 Business 5780 578088≈65.681 65 Humanities 1896 189688≈21.545 21 Science 4678 467888≈53.159 53 Total 178

From the calculation in the above table, the total number of representatives is 178, not 180 as

required by college divisions. When this happen the Hamilton plan calls for revisiting the

calculation of the quotients and assigning an additional representative to the college with the

largest decimal remainder. This process is continued until the number of representatives equals

The number required by college divisions. For school we have

 Divisions Enrollments Quotient Standard Quota Number of Representatives Liberal arts 3455 345588≈39.261 39 39 Business 5780 578088≈65.681 65 66 Humanities 1896 189688≈21.545 21 22 Science 4678 467888≈53.159 53 53 Total 178 180

Jefferson method

In Jefferson we need to select modified standard divisor by trial and error this is 87.5 and get the number of Computers in each divisions

 Divisions Enrollments Quotient Number of computers to be apportioned Liberal arts 3455 345587.5≈39.485 39 Business 5780 578087

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