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'''.
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[[Condorcet methods]] require the resolution of [[Condorcet cycle|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'''.
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Most election experts agree that either winning votes or margins (see below) are the best ways to measure defeat strength, with the consensus generally leaning in favor of winning votes.
   
 
The most common measures of defeat strength for a pairwise winner W over a pairwise loser L include:
 
The most common measures of defeat strength for a pairwise winner W over a pairwise loser L include:
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====== Approval opposition ======
 
====== Approval opposition ======
 
'''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]].
 
'''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]].
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See [[Techniques of method design#Defeats and defeat strength]] for more information.
 
[[Category:Voting theory metrics]]
 
[[Category:Voting theory metrics]]
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[[Category:Condorcet-related concepts]]

Latest revision as of 14:29, 25 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.

Most election experts agree that either winning votes or margins (see below) are the best ways to measure defeat strength, with the consensus generally leaning in favor of winning votes.

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[edit | edit source]

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

See Techniques of method design#Defeats and defeat strength for more information.