Webster\'s Method PDF

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Explanation and Practice Examples about Webster's Method....

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MATH 11008:

Webster’s Method Section 4.6 Webster’s Method:

1. Find a “suitable” divisor D. 2. Using D as the divisor, compute each state’s modified quota. modified quota =

state’s population D

3. Find the apportionments by rounding each modified quota the traditional way. (Round the quotas down when the fractional part is less than 0.5 and round the quotas up when the fractional part is greater or equal to 0.5.) • For Webster’s Method, we always start with D = SD. The following flow chart can be used to find a suitable divisor.

• Webster’s Method does not suffer from any paradoxes and it shows no bias between small and large states. • Webster’s Method can violate the quota rule, but such violations are rare in real-life apportionments. In fact, if Webster’s Method had been used for every apportionment between 1790 and 2000, not a single violation of the quota rule would have shown up.

MATH 11008: WEBSTER’S METHOD SECTION 4.6

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• Webster’s Method has a short tenure in the U.S. House of Representatives. It was used for the apportionment in 1842, then replaced by Hamilton’s Method, the reintroduced for the apportionments of 1901, 1911, and 1931, and then replaced again by the Huntington-Hill Method, the apportionment method we currently use.

Example 1: Use the Webster Method to apportion the 109 computers for the Highwood School District. School Enrollment Applegate 335 Bayshore 456 Claypool 298 Delmar 567 Edgewater 607 Totals 2263

Modified Quota

Traditionally rounded

School Enrollment Applegate 335 Bayshore 456 Claypool 298 Delmar 567 Edgewater 607 Totals 2263

Modified Quota

Traditionally rounded

School Enrollment Applegate 335 Bayshore 456 Claypool 298 Delmar 567 Edgewater 607 Totals 2263

Modified Quota

Traditionally rounded

MATH 11008: WEBSTER’S METHOD SECTION 4.6

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Example 2: Forty nurses from North Carolina have volunteered to help at 5 hospitals treating the victims of an earthquake in a remote mountainous region of Mexico. The Mexican government decides to apportion the nurses based on the number of beds at each of the hospitals. Hospital Number of beds

A 137

B 237

C 337

D 455

E 555

Use Webster’s Method to apportion the 40 volunteer nurses to the five hospitals in Mexico....