5-2 Election Theory Flaws of Voting

WHAT YOU WILL LEARN • Flaws of voting methods

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

Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the majority criterion using the following election data? Number of Votes 10 15 20 First A B C Second Third a. Plurality b. Plurality with elimination c. Borda count d. Pairwise comparison

Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the majority criterion using the following election data? Number of Votes 10 15 20 First A B C Second Third a. Plurality b. Plurality with elimination c. Borda count d. Pairwise comparison

The high school band is voting on a new mascot The high school band is voting on a new mascot. Their choices are a bulldog (B), an eagle (E), and a wildcat (W). The 75 committee members rank their choices according to the following preference table. Does the plurality with elimination method violate the head- to-head criterion? Number of Votes 23 20 17 15 First B E W Second Third a. Yes b. No c. Can’t determine

The high school band is voting on a new mascot The high school band is voting on a new mascot. Their choices are a bulldog (B), an eagle (E), and a wildcat (W). The 75 committee members rank their choices according to the following preference table. Does the plurality with elimination method violate the head- to-head criterion? Number of Votes 23 20 17 15 First B E W Second Third a. Yes b. No c. Can’t determine

Practice Problems