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.

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.

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