Math 131 - presentation notes PDF

Preview

Summary

Professor Nunnally...

Description

Apportionment Definition - to divide and share out according to a plan; to make proportionate division or distribution. ● Apportionment problems - used to determine a method for rounding standard quotas into whole numbers so that the sum of the numbers is the total number of allocated items ● Apportionment is used to determine the size of voting districts and the number of representatives from each state in the house of representatives Terminology ● The seats (M): identical indivisible objects being divided among the N states. ● The states (N): term used to describe parties that have stakes in the apportionment. (broad term, could represent other things like planets, people, districts, etc). ● The populations: individual state populations denoted by PN ○ Total population (P): is the sum of all state populations ● Standard divisor (SD) - the ratio of the total population to the number of seats (how many people are represented by each seat). ○ SD = P (population) / M (seats) ● Standard quota (q): (fair quota) exact fractional number of seats the state would get if fractional seats were allowed. ○ To find: divide each state population by standard divisor (SD) ○ Q = P / SD ● Upper quotas (U): standard quota rounded up ● Lower quotas (L): standard quotas rounded down ○ Both associated with each standard quota ○ In the UNLIKELY event that the standard quota is a whole number, then the upper and lower quotas equal the same number. ●

● ●

Quota rule: every state should be apportioned either its lower quota L or its upper quota U. The basic idea behind this is that the true measure of a fair apportionment is the standard quota, and a fair apportionment method, therefore, it should not differ from the standard quota by more than one seat.

Practice: Finding the Standard Divisor ● Problem: the Richmond transit has 6 bus routes (A, B, C, D, E, F) and 100 buses. Each route has its own populations ○ A - 25,000 ○ B- 31,000 ○ C- 17,000 ○ D- 15,500 ○ E- 11,500 ○ F- 9,000 ● Total population is 109,000 ● What is the standard divisor? ● Formula: q= P/SD

●

109,000 / 100 = 1,090

Answer: Standard Quotas - ?? The Hamilton Method of Apportionment ● Every state gets at least its lower quota ● Step 1: calculate each standard quota ● Step 2: round each standard quota down by stopping at the decimal and give each state its lower quota L. The Webster Method of Apportionment ● Round each standard quota to the nearest whole number ● Find a suitable divisor then calculate each modified quota...