Use Plurality Runoff to determine the winner of the following election: Number of Voters (13) 3 2 C First Second Third Fourth Fifth 4 A B C D E 3 B A CDE ABDE B C A E 1 -EDCB с A Now, use this election to show that Plurality Runoff FAILS to satisfy Monotonicity. By this, we mean to move the winning candidate to a higher position on one of the preference lists so that the candidate no longer wins.
Use Plurality Runoff to determine the winner of the following election: Number of Voters (13) 3 2 C First Second Third Fourth Fifth 4 A B C D E 3 B A CDE ABDE B C A E 1 -EDCB с A Now, use this election to show that Plurality Runoff FAILS to satisfy Monotonicity. By this, we mean to move the winning candidate to a higher position on one of the preference lists so that the candidate no longer wins.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:**Title: Understanding Plurality Runoff and Monotonicity in Elections**
Use Plurality Runoff to determine the winner of the following election:
**Preference Table:**
| Number of Voters (13) | 4 | 3 | 3 | 2 | 1 |
|-----------------------|------|------|------|------|------|
| **First** | A | B | C | D | E |
| **Second** | B | A | A | B | D |
| **Third** | C | C | B | C | C |
| **Fourth** | D | D | D | A | B |
| **Fifth** | E | E | E | E | A |
**Explanation of the Table:**
- The table displays the preference order of candidates (A, B, C, D, E) by groups of voters.
- The number at the top of each column indicates the number of voters who have that preference order.
**Objective:**
- Determine the winner using Plurality Runoff.
- Discuss how this example shows that Plurality Runoff can fail to satisfy Monotonicity.
**Explanation of Concepts:**
- **Plurality Runoff**: In this voting system, if no candidate wins a majority of first-place votes, a runoff is held between the two candidates with the most first-place votes.
- **Monotonicity**: This property states that if a candidate wins an election, and then in a recount all changes to ballots are favorable to the winning candidate, they should still win.
**Instruction:**
- Now, use this election to demonstrate that Plurality Runoff fails to uphold the principle of Monotonicity. This can be done by moving the winning candidate to a higher position on one of the preference lists, causing them to no longer win the election.
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