Difference between revisions of "Defeat strength"

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[[Condorcet methods]] require the resolution of [[cycles]]. Typically, this is done by ignoring "weak" pairwise defeats in favor of "strong" ones. The metric used to distinguish these is called '''defeat strength'''.
 
[[Condorcet methods]] require the resolution of [[cycles]]. Typically, this is done by ignoring "weak" pairwise defeats in favor of "strong" ones. The metric used to distinguish these is called '''defeat strength'''.
   
Measures of defeat strength for a pairwise winner W over a pairwise loser L include:
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The most common measures of defeat strength for a pairwise winner W over a pairwise loser L include:
   
 
* '''winning votes''': Defeat strength = votes for W>L
 
* '''winning votes''': Defeat strength = votes for W>L
 
* '''margins''': Defeat strength = (votes for W>L) - (votes for L>W)
 
* '''margins''': Defeat strength = (votes for W>L) - (votes for L>W)
 
* '''relative margins''': Defeat strength = margin ÷ (votes for W≠L)
 
* '''relative margins''': Defeat strength = margin ÷ (votes for W≠L)
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Less common measures:
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====== Approval opposition ======
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'''Approval opposition''' or '''AO''' is a measure of defeat strength for [[Condorcet method|Condorcet methods]]. It is equivalent to using [[Cardinal pairwise|approval-weighted pairwise]].
 
[[Category:Voting theory metrics]]
 
[[Category:Voting theory metrics]]

Revision as of 18:34, 20 March 2020

Condorcet methods require the resolution of cycles. Typically, this is done by ignoring "weak" pairwise defeats in favor of "strong" ones. The metric used to distinguish these is called defeat strength.

The most common measures of defeat strength for a pairwise winner W over a pairwise loser L include:

  • winning votes: Defeat strength = votes for W>L
  • margins: Defeat strength = (votes for W>L) - (votes for L>W)
  • relative margins: Defeat strength = margin ÷ (votes for W≠L)

Less common measures:

Approval opposition

Approval opposition or AO is a measure of defeat strength for Condorcet methods. It is equivalent to using approval-weighted pairwise.