## 17.2 Outline

- Fair voting principles
- Majority criterion
- Condorcet criterion
- Condorcet candidate
- definition

- Monotonicity criterion
- straw vote
- definition

- Irrelevant alternative criterion
- Arrow’s impossibility theorem
- fairness criterion
- comparison of voting methods
- insincere voting
- transitive law
- Codorcet’s paradox
- impossibility theorem

## 17.2 Essential Ideas

**Majority Criterion**

If a candidate receives a majority of the first-place votes, then that candidate should be declared the winner.

**Condorcent Criterion
**

If a candidate is favored when compared one-one-one with every other candidate, then that candidate should be declared the winner.

**Monotonicity Criterion
**

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

**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, then the previous winner should still be declared the winner.

**Fairness Criterion
**

The four criteria listed above: majority criterion, Condorcet criterion, Monotonicity criterion, and irrelevant alternatives criterion are referred to as the **fairness criterion.**

**Arrow’s Impossibility Theorem
**

No social choice rule satisfies all six of the following conditions:

**Unrestricted domain**; Any set of rankings is possible.- Decisiveness; Given any set of individual rankings, the method produces a winner.
**Symmetry and transitive**; The voting system should be symmetric and transitive over the set of all outcomes.**Independence of irrelevant alternatives**; If a voter prefers*A*to*B*with*C*as a possible choice, then the voter still prefers*A*to*B*when*C*is not a possible choice.**Pareto principle**; If each voter prefers*A*over*B*, then the group chooses*A*over*B*.- There should be
**no dictator.**