Defeat strength: Difference between revisions
Content added Content deleted
No edit summary |
(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.) |
||
| Line 6: | Line 6: | ||
=== Standard === |
=== Standard === |
||
* '''winning votes (wv)''' = |
* '''winning votes (wv)''' = number of votes for W>L if greater than the number of votes for L>W, otherwise zero. |
||
** Example method: the [[Schulze method]] is usually taken to use winning votes.{{cn|date=May 2024}} |
|||
* '''margins''' = ( |
* '''margins''' = (number of votes for W>L) - (number of votes for L>W) |
||
** Gives more strategic incentive than wv |
** Gives more strategic incentive than wv but may be easier to understand. |
||
| ⚫ | |||
** 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: [[MMPO]]. |
|||
* '''Relative margins''': Defeat strength = margin ÷ (votes for W≠L) |
* '''Relative margins''': Defeat strength = margin ÷ (votes for W≠L) |
||
| Line 23: | Line 26: | ||
* (Pairwise) '''defeat''' <=> ''more voters expressed to prefer A over B than expressed to prefer B over A'' |
* (Pairwise) '''defeat''' <=> ''more voters expressed to prefer A over B than expressed to prefer B over A'' |
||
* '''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. |
||
== References == |
|||
<references /> |
|||
[[Category:Voting theory metrics]] |
[[Category:Voting theory metrics]] |
||