[EM] Defeat strength: WV + margin?

[Hahn, Paul]

In Markus' paper he discusses multiple ways to define defeat strength, in particular ratio, winning votes, and margin.  Each one has instances where intuition would tell us things aren't quite right.  Ratio wouldn't seem to tell the whole story when within an election with 100 ballots, a pairing with 2 for and 1 against is declared equivalent to one with 66 for and 33 against.  Similarly, with winning votes a 50-49 loss being equated to 50-1 defies my intuition, at least.  And finally with margin, 50-49 being equated to 1-0 doesn't fly for me either.



So I wonder about some kind of compromise or combination.  To me, winning votes plus margin appeals.



Markus goes with winning votes because it gives the best results with respect to satisfying most criteria.  My question is, how does the behavior of various strong Condorcet methods such as his and Ranked Pairs change if we use winning votes + margin as the definition of defeat strength?  Would this change cause them to no longer satisfy criteria that they previously did with winning votes alone?



-pH
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