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

[Toby Pereira]

I think the problem with Schulze versus Ranked Pairs or River is that Schulze is more complicated to understand/explain, and also it's not even obviously a method. Also, realistically you'll probably never encounter an election where any of these three would give a different result. I've often heard people say that these methods can give different results, but I don't think I've ever seen an example, and this suggests to me that it would have to be pretty contrived and complex.
But about Schulze not obviously being a method - have a look at the Wikipedia article under "Computation" - https://en.wikipedia.org/wiki/Schulze_method#Computation
And it's that last bit that sticks out:
"It can be proven that  and  together imply .[1]:§4.1 Therefore, it is guaranteed (1) that the above definition of "better" really defines a transitive relation and (2) that there is always at least one candidate  with  for every other candidate ."
"It can be proven..." I don't necessarily mind if it takes a complex proof to show that a method obeys certain criterion like monotonicity etc. But this is just about it being a method that can elect a winner. How complex is this proof? I'm just taking it on trust that it works as a method. With Ranked Pairs or River, it's pretty trivial.
And on Warren Smith's rangevoting.org, https://rangevoting.org/SchulzeComplic.html
"(4) If the strongest path from L to W, is stronger than, or at least as strong as, the strongest path from W to L, and if this is simultaneously true for every L, then W is a "Schulze winner." Schulze proved the theorem that such a W always exists (at least using "margins"; I am confused re the "winning-votes" enhancement)."
So even Warren is confused about the proof for winning votes. And bear in mind, this isn't a proof about some property of the method, but that it is even a method.
Toby

      From: robert bristow-johnson <rbj at audioimagination.com>
 To: election-methods at lists.electorama.com 
 Sent: Wednesday, 22 May 2019, 23:14
 Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?
   


---------------------------- Original Message ----------------------------
Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot?
From: "Chris Benham" <cbenhamau at yahoo.com.au>
Date: Wed, May 22, 2019 2:35 pm
To: election-methods at lists.electorama.com
--------------------------------------------------------------------------


> Another Condorcet-compliant method that might interest you, from a Kevin
> Venzke webpage:
>
>> *Jobst Heitzig's River method* is identical to Tideman's method,
>> except that one additionally ignores (without locking) defeats against
>> candidates against whom some defeat has already been locked. This is
>> possibly the easiest of the three to work out by hand.maybe someone needs to explain this more to me.  i can think of a plausible example where it may differ from RP, but i can't think of what the motivating principle is.  if River and RP disagree, why is the River winner abetter choice?
> The other two he is referring to are Schulze and Tideman RP. Nearly all
> the time it will elect the same candidate and as far as I know is at
> least as good.well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner.  dunno about this River method, though.
> I strongly suggest that the measure of defeat strength should be Losing
> Votes and that ballots that equal-rank A and B above bottom should
> contribute a whole vote
> to each in the A-B pairwise comparison. Ballots that rank A and B
> equal-bottom (or truncate both A and B) should contribute nothing to the
> A-B pairwise comparison.that's an interesting proposal i hadn't heard before.  i'll be interested in hearing the motivation of it.  i presume you mean that the defeat strength should be a strictly decreasing function of the losing votes, perhaps -LV (and the greatestdefeat strength is the least negative -LV).  in principle, why is this better than Winning Votes or Margins?  (seems like Margins is the midpoint compromise between WV and LV since it is WV-LV.) > I'll be posting more on this soonish, but since you asked the questionI
> thought I'd just give you some food for thought to be going along with.i am digesting.Thank you, Chris.
--

r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."
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