Defeat strength: Difference between revisions
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(Fixed definitions and added citation needed to pairwise opposition Plurality failure. MMPO fails Plurality, but to say that PO as such does needs more evidence. Added cn to Schulze being wv - would be good to get a ref from Markus.) |
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** Gives more strategic incentive than wv but may be easier to understand. |
** Gives more strategic incentive than wv but may be easier to understand. |
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** Example method: Tideman originally defined [[Ranked Pairs]] as a margins method.<ref name="Tideman2">{{Cite journal |last=Tideman |first=T. N. |date=1987-09-01 |title=Independence of clones as a criterion for voting rules |url=https://doi.org/10.1007/BF00433944 |journal=Social Choice and Welfare |language=en |volume=4 |issue=3 |pages=185–206 |doi=10.1007/BF00433944 |issn=1432-217X}}</ref> |
** Example method: Tideman originally defined [[Ranked Pairs]] as a margins method.<ref name="Tideman2">{{Cite journal |last=Tideman |first=T. N. |date=1987-09-01 |title=Independence of clones as a criterion for voting rules |url=https://doi.org/10.1007/BF00433944 |journal=Social Choice and Welfare |language=en |volume=4 |issue=3 |pages=185–206 |doi=10.1007/BF00433944 |issn=1432-217X}}</ref> |
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* '''pairwise opposition''': number of votes for |
* '''pairwise (non)opposition''': number of votes for W≥L, or equivalently 1 - votes for L > W |
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** Gives even less strategic incentive than wv, and has a strong theoretical appeal (pick the candidate opposed by the fewest voters) |
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** Violates [[plurality criterion]]. |
** Violates [[plurality criterion]]. |
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*** A complete unknown can win with no real support, just because everyone forgot to rank them on their ballot. |
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** Very little strategic incentive |
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** Example method: [[MMPO]]. |
** Example method: [[MMPO]]. |
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* '''Relative margins''': Defeat strength = margin ÷ (votes for W≠L) |
* '''Relative margins''': Defeat strength = margin ÷ (votes for W≠L) |
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== Kinds of defeats == |
== Kinds of defeats == |
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* (Pairwise) '''defeat''' |
* '''(Pairwise)''' '''defeat''' = ''more voters prefer A over B than B over A'' |
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* '''Majority-strength defeat''' = ''pairwise defeat which has a wv-strength of more than half the no. of voters.'' Using only such defeats can reduce incentive to truncate by reducing the likelihood that additional preferences will harm earlier ones. Voters adding a preference can create a majority-strength win, but they can't reverse the direction of one. |
* '''Majority-strength defeat''' = ''pairwise defeat which has a wv-strength of more than half the no. of voters.'' Using only such defeats can reduce incentive to truncate by reducing the likelihood that additional preferences will harm earlier ones. Voters adding a preference can create a majority-strength win, but they can't reverse the direction of one. |
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