Political Science /Voting Methods and Fairness Criteria
Voting Methods and Fairness Criteria
This deck covers various voting methods and the fairness criteria associated with them, including the plurality, Borda count, plurality-with-elimination, and pairwise comparison methods. It also addresses Arrow's Impossibility Theorem and the criteria these methods may or may not satisfy.
Plurality method
The candidate with the most first place votes wins. (Does not have to be majority)
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Key Terms
Term
Definition
Plurality method
The candidate with the most first place votes wins. (Does not have to be majority)
Borda count method
Voters rank all candidates from most favorable to least. Each last place vote receives 1 pt, each next to last vote receives 2 pts and so on. Candidat...
Plurality-with-elimination method
Candidate with majority (over 50%) of 1st place votes wins. If no candidate receives majority, eliminate the candidate with fewest 1st place votes. Ei...
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Pairwise comparison method
Voters rank all candidates. Series of comparisons is made and each of the candidates is compared to each of the other candidates. Preferred candidate ...
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Fairness Criteria (4)
1-Majority criterion
2-Head to head criterion
3-Monotonicity criterion
4- Irrelevant Alternatives criterion
Majority criterion
If a candidate receives a majority of 1st place votes, then that candidate should win.
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| Term | Definition |
|---|---|
Plurality method | The candidate with the most first place votes wins. (Does not have to be majority) |
Borda count method | Voters rank all candidates from most favorable to least. Each last place vote receives 1 pt, each next to last vote receives 2 pts and so on. Candidate with most points wins. |
Plurality-with-elimination method | Candidate with majority (over 50%) of 1st place votes wins. If no candidate receives majority, eliminate the candidate with fewest 1st place votes. Either hold another election or adjust preference table. Continue process until a candidate receives a majority of 1st place votes. That person wins. |
Pairwise comparison method | Voters rank all candidates. Series of comparisons is made and each of the candidates is compared to each of the other candidates. Preferred candidate in each comparison receives 1 point. In case of a tie, each receives a half point. Candidate with most points wins. |
Fairness Criteria (4) | 1-Majority criterion
2-Head to head criterion
3-Monotonicity criterion
4- Irrelevant Alternatives criterion |
Majority criterion | If a candidate receives a majority of 1st place votes, then that candidate should win. |
Head to head criterion (Condorcet) | If a candidate is favored when compared head to head with every other candidate, then that candidate should win. |
Monotonicity criteria | If a candidate wins an election, in a reelection, the only changes are changes that favor candidate, then that candidate should win reelection. |
Irrelevant Alternatives criterion | If a candidate wins election, and in recount, the only changes are that one or more of other candidates are removed from ballot, then that candidate should still win election. |
Arrow’s Impossibility theorem | It is mathematically impossible for any democratic voting system to satisfy each of the four fairness criteria. |
Preference ballots | Ballots that rank candidates in order of preference |
What voting method may not satisfy majority criterion? | Borda count method |
Which voting methods may not satisfy Head-to-head criterion? (3) | Plurality method Plurality with elimination method |
Which voting methods may not satisfy monotonicity criterion? (3) | Borda count method |
Which voting methods may not satisfy irrelevant alternatives criterion? | All: Plurality |