1. Section 15.2 Flaws of Voting

2. What You Will Learn Fairness Criteria Majority Criterion
Head-to-Head Criterion
Monotonicity Criterion
Irrelevant Alternative 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
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