Understanding the Hare Method

Oct 13, 2025 by wbrum.org 19 views

Introduction

In voting systems, the Hare method is a proportional representation voting system that is used to elect a single winner from a list of candidates. This method is also known as the single transferable vote (STV) system. In this article, we will use the Hare method to determine the winner among three candidates based on the given voting outcomes.

Voting Outcomes

The voting outcomes are reported as follows:

(ABC) = 3
(ACB) = 2
(BAC) = 2
(BCA) = 0
(CAB) = 1
(CBA) = 4

Understanding the Hare Method

The Hare method is a voting system that is used to elect a single winner from a list of candidates. The method works as follows:

The candidate with the lowest number of votes is eliminated.
The votes of the eliminated candidate are transferred to the other candidates in proportion to the number of votes they received.
The process is repeated until a candidate has more than half of the total votes.

Applying the Hare Method

Let's apply the Hare method to the given voting outcomes.

Step 1: Eliminate the Candidate with the Lowest Number of Votes

The candidate with the lowest number of votes is (BCA) with 0 votes. Therefore, we eliminate (BCA).

Step 2: Transfer the Votes of the Eliminated Candidate

Since (BCA) has 0 votes, we do not need to transfer any votes.

Step 3: Eliminate the Candidate with the Lowest Number of Votes

The candidate with the lowest number of votes is now (CAB) with 1 vote. Therefore, we eliminate (CAB).

Step 4: Transfer the Votes of the Eliminated Candidate

We transfer the 1 vote of (CAB) to the other candidates in proportion to the number of votes they received. Since (CAB) has 1 vote, we transfer 1/6 of the total votes to each of the other candidates.

(ABC) receives 1/6 of 3 votes = 0.5 votes
(ACB) receives 1/6 of 2 votes = 0.33 votes
(BAC) receives 1/6 of 2 votes = 0.33 votes
(CBA) receives 1/6 of 4 votes = 0.67 votes

Step 5: Eliminate the Candidate with the Lowest Number of Votes

The candidate with the lowest number of votes is now (ACB) with 0.33 votes. Therefore, we eliminate (ACB).

Step 6: Transfer the Votes of the Eliminated Candidate

We transfer the 0.33 votes of (ACB) to the other candidates in proportion to the number of votes they received. Since (ACB) has 0.33 votes, we transfer 0.33/6 of the total votes to each of the other candidates.

(ABC) receives 0.33/6 of 3.5 votes = 0.17 votes
(BAC) receives 0.33/6 of 2.67 votes = 0.14 votes
(CBA) receives 0.33/6 of 4.33 votes = 0.19 votes

Step 7: Eliminate the Candidate with the Lowest Number of Votes

The candidate with the lowest number of votes is now (BAC) with 0.14 votes. Therefore, we eliminate (BAC).

Step 8: Transfer the Votes of the Eliminated Candidate

We transfer the 0.14 votes of (BAC) to the other candidates in proportion to the number of votes they received. Since (BAC) has 0.14 votes, we transfer 0.14/6 of the total votes to each of the other candidates.

(ABC) receives 0.14/6 of 3.72 votes = 0.07 votes
(CBA) receives 0.14/6 of 4.19 votes = 0.06 votes

Step 9: Eliminate the Candidate with the Lowest Number of Votes

The candidate with the lowest number of votes is now (ABC) with 0.07 votes. Therefore, we eliminate (ABC).

Step 10: Transfer the Votes of the Eliminated Candidate

We transfer the 0.07 votes of (ABC) to the other candidates in proportion to the number of votes they received. Since (ABC) has 0.07 votes, we transfer 0.07/6 of the total votes to each of the other candidates.

(CBA) receives 0.07/6 of 4.25 votes = 0.01 votes

Step 11: Determine the Winner

The candidate with the most votes is (CBA) with 4.25 votes. Therefore, (CBA) is the winner.

Conclusion

In this article, we used the Hare method to determine the winner among three candidates based on the given voting outcomes. The winner is (CBA) with 4.25 votes. The Hare method is a proportional representation voting system that is used to elect a single winner from a list of candidates. It works by eliminating the candidate with the lowest number of votes and transferring their votes to the other candidates in proportion to the number of votes they received. The process is repeated until a candidate has more than half of the total votes.

References

Hare, T. (1857). The Election of Representatives, Utilitarian.
Hare, T. (1861). The Election of Representatives, Utilitarian.
Hare, T. (1865). The Election of Representatives, Utilitarian.

Q: What is the Hare method?

A: The Hare method is a proportional representation voting system that is used to elect a single winner from a list of candidates. It is also known as the single transferable vote (STV) system.

Q: How does the Hare method work?

A: The Hare method works by eliminating the candidate with the lowest number of votes and transferring their votes to the other candidates in proportion to the number of votes they received. The process is repeated until a candidate has more than half of the total votes.

Q: What are the advantages of the Hare method?

A: The advantages of the Hare method include:

Proportional representation: The Hare method ensures that the winner represents the proportion of votes they received.
Fairness: The Hare method is a fair voting system that gives each candidate an equal chance of winning.
Transparency: The Hare method is a transparent voting system that allows voters to see how their votes are being counted.

Q: What are the disadvantages of the Hare method?

A: The disadvantages of the Hare method include:

Complexity: The Hare method can be complex to understand and implement.
Time-consuming: The Hare method can be time-consuming to count the votes.
Voter fatigue: The Hare method can lead to voter fatigue, as voters may need to rank multiple candidates.

Q: When is the Hare method used?

A: The Hare method is used in various elections, including:

Local elections: The Hare method is used in local elections, such as city council elections.
National elections: The Hare method is used in national elections, such as parliamentary elections.
International elections: The Hare method is used in international elections, such as European Parliament elections.

Q: How is the Hare method different from other voting systems?

A: The Hare method is different from other voting systems in that it uses a proportional representation system, where the winner represents the proportion of votes they received. Other voting systems, such as first-past-the-post, use a winner-takes-all system, where the winner is the candidate with the most votes.

Q: Can the Hare method be used in conjunction with other voting systems?

A: Yes, the Hare method can be used in conjunction with other voting systems. For example, the Hare method can be used in conjunction with a runoff election, where the top two candidates compete in a runoff election.

Q: How can the Hare method be improved?

A: The Hare method can be improved by:

Simplifying the voting process: The voting process can be simplified by using a ranked-choice voting system, where voters rank candidates in order of preference.
Increasing transparency: The voting process can be made more transparent by using electronic voting systems, where voters can see how their votes are being counted.
Reducing voter fatigue: The voting process can be made less time-consuming by using a single transferable vote system, where voters only need to rank one candidate.

Conclusion

The Hare method is a proportional representation voting system that is used to elect a single winner from a list of candidates. It has several advantages, including proportional representation, fairness, and transparency. However, it also has some disadvantages, including complexity, time-consuming, and voter fatigue. The Hare method can be improved by simplifying the voting process, increasing transparency, and reducing voter fatigue.