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Copyright 2013, 2010, 2007, Pearson, Education, Inc. 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
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 15.2
Flaws of Voting
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
Fairness CriteriaMajority CriterionHead-to-Head CriterionMonotonicity CriterionIrrelevant Alternative Criterion
15.2-2
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Fairness CriteriaMathematicians 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 CriterionHead-to-head CriterionMonotonicity CriterionIrrelevant Alternatives Criterion
15.2-3
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Majority Criterion
If a candidate receives a majority (more than 50%) of the first-place votes, that candidate should be declared the winner.
15.2-4
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
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.
15.2-5
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
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.
15.2-6
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Irrelevant Alternatives CriterionIf 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.
15.2-7
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Summary of the Voting Methods and Whether They Satisfy the Fairness Criteria
May not satisfy
May not satisfy
May not satisfy
May not satisfy
Irrelevant alternatives
May not satisfy
May not satisfy
May not satisfy
Always satisfies
Monotonicity
Always satisfies
May not satisfy
May not satisfy
May not satisfy
Head-to-head
Always satisfies
Always satisfies
May not satisfy
Always satisfies
Majority
Pairwise comparison
Plurality with elimination
Borda count
Plurality
Method
Criteria
15.2-8
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Arrow’s Impossibility TheoremIt 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
15.2-9
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