Week 14 (apportionment and voting essay exam)

Question 1

What is apportionment and why is it important?

Answer 1

Apportionment is the process of fairly dividing or distributing something, like representatives, among different groups based on their population or size. It is important because it ensures equal and proportional representation, especially in government, where each area or district should have a fair voice in decision-making. Beyond politics, apportionment is also used in schools, hospitals, competitions, and other fields to allocate resources or responsibilities in a just way.

Question 2

Explain and compare the Hamilton, Jefferson, and Webster methods.

Answer 2

The Hamilton, Jefferson, and Webster methods are three different ways to perform apportionment, each with its own rule for handling decimal results. The Hamilton method uses a standard divisor and gives each group a whole number of seats based on its quota, then gives the leftover seats to those with the biggest decimal remainders. The Jefferson method adjusts the divisor downward and always rounds down the quotas until the total number of representatives is reached, favoring larger groups. The Webster method uses regular rounding rules—rounding up if the decimal is 0.5 or higher, and down if it is lower. While all three aim to distribute fairly, they can give different results depending on the method used.

Method | How It Works | Special Rule |

Question 3

Explain Hamilton Method

Answer 3

The Hamilton method uses a standard divisor and gives each group a whole number of seats based on its quota, then gives the leftover seats to those with the biggest decimal remainders.

Question 4

Explain Jefferson Method

Answer 4

The Jefferson method adjusts the divisor downward and always rounds down the quotas until the total number of representatives is reached, favoring larger groups.

Question 5

Explain Webster Method

Answer 5

The Webster method uses regular rounding rules—rounding up if the decimal is 0.5 or higher, and down if it is lower.

Question 6

Why are different voting systems used? Explain three methods.

Answer 6

Different voting systems are used to give fairer results in elections and decision-making, depending on how people rank their choices. The plurality method is the simplest—it chooses the candidate with the most first-place votes, but it can be unfair if the winner doesn’t have a true majority. Plurality with elimination is more detailed, removing the lowest-ranked choices and recounting until someone wins with over 50% of the votes. The Borda count method gives points based on how candidates are ranked, so it considers everyone’s full preferences. These systems are important because each one can give different outcomes, and the best system depends on what kind of fairness or decision is needed.

Question 7

Explain Plurality Method

Answer 7

The plurality method is the simplest—it chooses the candidate with the most first-place votes, but it can be unfair if the winner doesn’t have a true majority.

Question 8

Explain Plurality with Elimination Method

Answer 8

Plurality with elimination is more detailed, removing the lowest-ranked choices and recounting until someone wins with over 50% of the votes

Question 9

Explain Borda Count Method

Answer 9

The Borda count method gives points based on how candidates are ranked, so it considers everyone’s full preferences.

Question 10

Explain Pairwise Comparison

Answer 10

Pairwise comparison is fair in one-on-one matchups but can be confusing if there are cycles or ties.