1. 5-2 Election Theory
Flaws of Voting

2. WHAT YOU WILL LEARN
• Flaws of voting methods

3. Fairness Criteria
Mathematicians and political scientists have agreed that a voting method should meet the following four criteria in order for the voting method to be considered fair.
Majority Criterion
Head-to-head Criterion
Monotonicity Criterion
Irrelevant Alternatives Criterion

4. Majority Criterion
If a candidate receives a majority (more than 50%) of the first-place votes, that candidate should be declared the winner.

5. Head-to-Head Criterion
If a candidate is favored when compared head-to-head with every other candidate, that candidate should be declared the winner.

6. Monotonicity Criterion
A candidate who wins a first election and then gains additional support without losing any of the original support should also win a second election.

7. Irrelevant Alternatives Criterion
If a candidate is declared the winner of an election and in a second election one or more of the other candidates is removed, the previous winner should still be declared the winner.

8. Summary of the Voting Methods and Whether They Satisfy the Fairness Criteria
May not satisfy
Irrelevant alternatives
Always satisfies
Monotonicity
Head-to-head
Majority
Pairwise comparison
Plurality with elimination
Borda count
Plurality
Method
Criteria

9. Arrow’s Impossibility Theorem
It is mathematically impossible for any democratic voting method to simultaneously satisfy each of the fairness criteria:
The majority criterion
The head-to-head criterion
The monotonicity criterion
The irrevelant alternative criterion

10. Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the majority criterion using the following election data?
Number of Votes 10 15 20
First A B C
Second
Third
a. Plurality b. Plurality with elimination
c. Borda count d. Pairwise comparison

11. Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the majority criterion using the following election data?
Number of Votes 10 15 20
First A B C
Second
Third
a. Plurality b. Plurality with elimination
c. Borda count d. Pairwise comparison

12. The high school band is voting on a new mascot
The high school band is voting on a new mascot. Their choices are a bulldog (B), an eagle (E), and a wildcat (W). The 75 committee members rank their choices according to the following preference table. Does the plurality with elimination method violate the head- to-head criterion?
Number of Votes 23 20 17 15
First B E W
Second
Third
a. Yes b. No c. Can’t determine

13. The high school band is voting on a new mascot
The high school band is voting on a new mascot. Their choices are a bulldog (B), an eagle (E), and a wildcat (W). The 75 committee members rank their choices according to the following preference table. Does the plurality with elimination method violate the head- to-head criterion?
Number of Votes 23 20 17 15
First B E W
Second
Third
a. Yes b. No c. Can’t determine

14. Practice Problems