# Section 17.2: Voting Dilemmas

## 17.2 Outline

1. Fair voting principles
2. Majority criterion
3. Condorcet criterion
1. Condorcet candidate
2. definition
4. Monotonicity criterion
1. straw vote
2. definition
5. Irrelevant alternative criterion
6. Arrow’s impossibility theorem
1. fairness criterion
2. comparison of voting methods
3. insincere voting
4. transitive law
6. 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:

1. Unrestricted domain; Any set of rankings is possible.
2. Decisiveness; Given any set of individual rankings, the method produces a winner.
3. Symmetry and transitive; The voting system should be symmetric and transitive over the set of all outcomes.
4. 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.
5. Pareto principle; If each voter prefers A over B, then the group chooses A over B.
6. There should be no dictator.