Apportionment: Apply It 1

  • Define apportionment and its importance in political representation in the United States and other representative democracies
  • Identify various methods of apportionment, including Hamilton’s method, Jefferson’s method, Webster’s method, Huntington-Hill method, and Lowndes’ method
  • Understand the apportionment process for legislative districts

Balancing Representation: Exploring Apportionment Methods in Political Systems

Embark on a journey through the complex world of apportionment, a critical process in the realm of political representation. In this ‘Apply It’ section, you will explore various methods of apportionment, including Hamilton’s, Jefferson’s, Webster’s, Huntington-Hill’s, and Lowndes’ methods. You will also delve into the legislative districting process and its implications in representative democracies. This exploration will not only enhance your understanding of the mathematical concepts involved but also their significant impact on political representation and equity.

Scenario 1: Hamilton’s Method in Action

A state needs to apportion [latex]10[/latex] legislative seats among its four regions based on population.

Population Data:

  • Region A: [latex]1,200,000[/latex]
  • Region B: [latex]800,000[/latex]
  • Region C: [latex]600,000[/latex]
  • Region D: [latex]400,000[/latex]

After exploring the allocation of legislative seats through Hamilton’s method, where simplicity in division plays a key role, we now transition to Scenario 2, where Jefferson’s method introduces a different approach. This shift allows us to compare how altering the divisor in apportionment calculations can lead to different outcomes, highlighting the nuances and potential biases inherent in each method.

Scenario 2: Jefferson’s Method of Apportionment

The same state decides to explore Jefferson’s method for the same apportionment.


Having witnessed the impact of Jefferson’s method, which can favor larger regions, we now delve into Scenario 3 to examine Webster’s method. This method offers an alternative perspective on fairness, often striking a balance between the extremes of Hamilton’s and Jefferson’s methods. In this scenario, we explore its application in a municipal council setting, providing a lens to assess its effectiveness in a more localized context.

Scenario 3: Webster’s Method in a Municipal Council

A city is apportioning [latex]15[/latex] seats in its municipal council among five neighborhoods.

Population Data:

  • Neighborhood 1: [latex]45,000[/latex]
  • Neighborhood 2: [latex]30,000[/latex]
  • Neighborhood 3: [latex]25,000[/latex]
  • Neighborhood 4: [latex]20,000[/latex]
  • Neighborhood 5: [latex]10,000[/latex]