[EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?

robert bristow-johnson rbj at audioimagination.com
Wed May 22 17:18:55 PDT 2019

i'm posting this to the list.  i hope it's okay.
i had been asked:

> This "plausible example" you can think of, why don't you show it to us?
i'm not as good as you guys in dreaming up the number of ballots ranked however:
  ex. A>B>C>D
but could you have a defeat matrix where
but   C>A by a smaller defeat strength than A>B or B>C.  But D>A by an even smaller defeat strength, however D<B and D>C?  
i dunno how to dream up ballot combinations to do that.

> Without it all I can say that is that the River winner may or may not be

> a "better choice" than the

> RP winner.


> River's main practical point is that it easier than Schulze and RP to use.
i think it's more complicated than RP.  it's RP with an additional exception.
i have to say i am still not convinced of WV.  probably Schulze-Margins is still the best, but RP-Margins
good enough and possibly easier to sell to policy makers and the public.
i like Margins in principle:  The percentage Margin is (WV-LV)/(WV+LV) and is a measure of the decisiveness of defeat, without respect to the size of the election.  So 5% defeat is a more decisive defeat than a
4% defeat.
But if you consider every Condorcet pair as it's own little election, then the salience of the election would be the number of voters that weigh in on it, which is WV+LV.
So if the net defeat strength (the index to rank the pairs) is the product of how important the election
is with the decisiveness of defeat you get:
   (WV+LV) x (WV-LV)/(WV+LV)  =  WV - LV 
it just seems to me that Margins is better than WV.
but say, WV, is a good idea for defeat strength.  is LV a better idea?

r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."

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