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Voting and Apportionment Chapter 15 Voting and Apportionment

WHAT YOU WILL LEARN • Apportionment methods

Apportionment Methods Section 3 Apportionment Methods

Apportionment The goal of apportionment is to determine a method to allocate the total number of items to be apportioned in a fair manner. Four Methods Hamilton’s method Jefferson’s method Webster’s method Adam’s method

Definitions

Example A Graduate school wishes to apportion 15 graduate assistantships among the colleges of education, business and chemistry based on their undergraduate enrollments. Using the table on the next slide, find the standard quotas for the schools.

Example (continued) 14.999 Standard quota 8020 1880 2940 3200 Population Total Chemistry Business Education

Hamilton’s Method 1. Calculate the standard divisor for the set of data. 2. Calculate each group’s standard quota. 3. Round each standard quota down to the nearest integer (the lower quota). Initially, each group receives its lower quota. 4. Distribute any leftover items to the groups with the largest fractional parts until all items are distributed.

Example: Apportion the 15 graduate assistantships 4 5 6 Hamilton’s 13 3 Lower quota 14.999 Standard quota 8020 1880 2940 3200 Population Total Chemistry Business Education

The Quota Rule An apportionment for every group under consideration should always be either the upper quota or the lower quota.

Jefferson’s Method 1. Determine a modified divisor, d, such that when each group’s modified quota is rounded down to the nearest integer, the total of the integers is the exact number of items to be apportioned. We will refer to the modified quotas that are rounded down as modified lower quotas. 2. Apportion to each group its modified lower quota.

Modified divisor = 480 15 3 6 Jefferson 3.9167 6.125 6.67 Modified quota 14.999 Standard quota 8020 1880 2940 3200 Population Total Chemistry Business Education

Webster’s Method 1. Determine a modified divisor, d, such that when each group’s modified quota is rounded to the nearest integer, the total of the integers is the exact number of items to be apportioned. We will refer to the modified quotas that are rounded to the nearest integer as modified rounded quotas. 2. Apportion to each group its modified rounded quota.

Modified divisor = 535 15 4 5 6 Webster 3.51 5.49 5.98 Modified quota 14.999 Standard quota 8020 1880 2940 3200 Population Total Chemistry Business Education

Adams’s Method 1. Determine a modified divisor, d, such that when each group’s modified quota is rounded up to the nearest integer, the total of the integers is the exact number of items to be apportioned. We will refer to the modified quotas that are rounded up as modified upper quotas. 2. Apportion to each group its modified upper quota.

Modified divisor = 590 15 4 5 6 Adams 3.18 4.98 5.42 Modified quota 14.999 Standard quota 8020 1880 2940 3200 Population Total Chemistry Business Education