1. Flaws of the Voting Methods
Section 14.2
Flaws of the Voting Methods

2. What You Will Learn
Upon completion of this section, you will be able to:
Determine if the results of an election violate the majority criterion.
Determine if the results of an election violate the head-to-head criterion.
Determine if the results of an election violate the monotonicity criterion.
Determine if the results of an election violate the irrelevant alternatives criterion.

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
Plurality
Borda count
Plurality with elimination
Pairwise comparison
Majority
Always satisfies
May not satisfy
Head-to-head
Monotonicity
Irrelevant alternatives
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 irrelevant alternatives criterion