Flaws of the Voting Methods Section 14.2 Flaws of the Voting Methods

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.

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

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

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.

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.

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.

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

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