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 Criteria Majority Criterion Head-to-Head Criterion Monotonicity Criterion Irrelevant Alternative Criterion

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

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

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

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

Copyright 2013, 2010, 2007, Pearson, Education, Inc. 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

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Summary of the Voting Methods and Whether They Satisfy the Fairness Criteria May not satisfy Irrelevant alternatives May not satisfy Always satisfies Monotonicity Always satisfies May not satisfy Head-to- head Always satisfies May not satisfy Always satisfies Majority Pairwise comparison Plurality with elimination Borda count PluralityMethod Criteria

Copyright 2013, 2010, 2007, Pearson, Education, Inc. 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