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6: Apportionment Method and Paradox

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    • 6.1: Hamilton’s Method
      This section covers the apportionment process of distributing fixed resources among groups, focusing on political contexts like representative allocation. It introduces key concepts such as standard divisor and quota, and details Hamilton's method through five implementation steps. Examples illustrate the method's application, including assigning representatives to counties, adhering to the Quota Rule, and distributing resources like vaccine packs and scheduling volunteers based on averages.
    • 6.2: Jefferson’s Method
      This section examines Thomas Jefferson's apportionment method, utilized from 1791 to 1842, which favors larger states like Virginia. It involves adjusting a standard divisor to meet a quota for representatives, illustrated through examples that show how to allocate seats based on population. The text also compares Jefferson's method to Hamilton's, emphasizing the different outcomes and the importance of divisor adjustments for fair representation.
    • 6.3: Adam’s Methods
      This section explains Adam's method for solving apportionment problems using a modified divisor based on upper quotas. It outlines the steps of finding a standard divisor, selecting a slightly larger modified divisor, and adjusting it iteratively to align upper quotas with a total. An example illustrates its application in allocating firefighters in Adamstown, highlighting its versatility for distributing legislative seats among counties as well.
    • 6.4: Webster’s Methods
      This section discusses Webster's Method of apportionment, which employs a modified divisor for seat distribution through rounding quotas. The process begins with determining a standard divisor and then selecting a modified one. Quotas are rounded, and the divisor is adjusted iteratively until the total of rounded quotas matches the available seats.
    • 6.5: Apportionment Paradoxes
      This section explores apportionment paradoxes, including the Alabama, Population, and New-States Paradoxes, emphasizing the flaws in representation methods such as Hamilton's method. It illustrates how states or groups can lose representation even with population growth or increases in total seats.

    Thumbnail: Breakdown of US House of Representatives as of January 1, 2022. Blue circles are Democratic Representatives, red are Republican Representatives and white are vacant (Public Domain; AlSmith28 via Wikipedia)

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