Getting Started
In this discussion, you will use the voting methods you're learning in this workshop to practice your knowledge and understanding of voting based on the first letter of your last name. You will investigate methods for choosing a winner and why different methods can lead to different winners.
Upon successful completion of the course material, you will be able to:
· Utilize critical thinking skills to evaluate quantitative information in everyday life.
· Formulate a plan based on the mathematical concepts that apply to a problem.
· Describe the relationships among quantitative information in real world applications.
· Analyze the mathematical relationships and patterns that confront the modern world.
· Recognize connections between mathematics and voting theory.
Resources
Voting Theory:
· Watch: Introduction to Voting Theory and Preference Tables
· Watch: Voting Theory: Fairness Criterion
· Watch: Voting Theory: Plurality Method and Condorcet Criterion
· Watch: Voting Theory: Borda count
· Watch: Voting Theory: Instant Runoff Voting
· Read: Examples of Voting Methods (Zalta)
Background Information
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First letter of your Last name
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Solve the problem
Show and explain the steps you take to solve the problem; post your work and the solution.
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A - D
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Consider a three-way race between candidates called A, B, and C with a preference table shown here.
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First Choice
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C
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A
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B
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A
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Second Choice
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A
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B
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A
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C
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Third Choice
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B
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C
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C
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B
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21
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17
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9
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4
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1. Find the winner by plurality.
2. Find the winner by instant runoff.
3. Find the winner by point system (Borda count).
4. Find the winner by pairwise comparisons (Condorcet method).
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E - K
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A club of 50 people hold an election among five candidates. Each ballot asks the voter to rank these candidates in order of preference. The results are summarized in the following preference table. If Candidate E withdrew from the election (and votes for the other candidates were moved up in the table), how many votes would the other four candidates receive?
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First
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B
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C
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C
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A
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D
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E
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Second
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A
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E
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A
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D
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B
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C
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Third
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D
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A
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D
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E
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C
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A
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Fourth
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E
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B
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E
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C
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A
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D
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Fifth
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C
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D
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B
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B
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E
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B
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Voters
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13
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12
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10
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8
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4
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3
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1. Who won a plurality?
2. Once Candidate E withdraws from the election, who won by plurality?
a. How many first-place votes did Candidate A receive?
b. How many first-place votes did Candidate B receive?
c. How many first-place votes did Candidate C receive?
d. How many first-place votes did Candidate D receive?
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L - R
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Consider an election in which the votes were cast according to the table.
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Number of Votes
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Candidate A
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43%
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Candidate B
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38%
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Candidate C
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19%
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1. Who won a plurality?
2. Does any candidate have a majority?
3. What percentage of Candidate C's votes would Candidate B need to win a runoff election?
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S - Z
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Suppose that Candidates A and B have moderate political positions, while Candidate C is quite liberal. Voter opinions about the candidates are as follows. 35% want A as their first choice, but would also approve of B. 31% want B as their first choice, but would also approve of A. 20% want B as their first choice, and approve of neither A nor C. 10% want C as their first choice, and approve of neither A nor B.
1. If all voters could vote only for their first choice, which candidate would win by plurality?
2. Which candidate wins by an approval vote?
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Instructions
1. Review the rubric to make sure you understand the criteria for earning your grade.
2. In the 5.3 Discussion forum respond by solving one of the problems above based upon the First letter of your Last name. You must show your work, not just give the answers.
3. Your initial posting needs to thoroughly answer the discussion question, using critical thinking and thoughtful reasoning.
lanny.wilson
5.3Discussion.docx
