"Votes over" (Re: [EM] Why Margins isn't as democratic or ethical as)
Norman Petry
npetry at cableregina.com
Tue Feb 8 22:44:18 PST 2000
Hi Rob,
Since you're suggesting new terminology, and I sort-of introduced some bad
terminology this morning, I thought I'd reply quickly in the hope that we
can settle on something reasonable before becoming bogged down in
discussion. It would be great if we were all talking about the same thing!
Anyway, as an alternative to your idea, I would propose that we use
terminology that was sent to me by Blake in a private response to my earlier
message. His suggestion is that we use the following terms:
1) Winning-Votes (WV) -- This is equivalent to the "Votes-Against" methods
which only consider the majority side of each pairwise win. I had referred
to it as "VA" in my earlier post.
2) Both-Votes (BV) -- This is equivalent to what I called "Absolute Votes",
or AV in my post this morning. Blake pointed out that "Absolute Votes" is
probably a poor term, since it could equally apply to Winning Votes or
Losing Votes, since these are also absolute. The idea here is that we use
simple vote totals, but do not arbitrarily eliminate minority vote totals
before applying the method.
3) Margins (M) -- This is the same as always. Pairwise victories are
measured as differences between majority and minority vote totals.
4) Losing-Votes (LV) -- only included for completeness, in case some lunatic
decides to add to the confusion by proposing a method which ignores
majorities and considers only the minority vote totals (please don't!).
*****
Using these designations, it will be easy to distinguish between different
variants of each method. For example, what Blake calls "Path Voting" on his
website is equivalent to Schulze(m) -- or was, last time I looked, and
Markus' original definition of his method is equivalent to Schulze(wv).
Of course, the method I was arguing for this morning is Schulze(bv). As I
pointed out, I had always thought that Markus' method was Schulze(bv), until
he gave this example a couple of days ago which exposed my error:
> A:B=51:49
> A:C=45:48
> A:D=58:42
> B:C=35:65
> B:D=75:25
> C:D=40:60
>
[...]
>
>Schulze:
>
> A has 58 votes against B via the beat path A > D > C > B.
> A has 58 votes against C via the beat path A > D > C.
> A has 58 votes against D via the beat path A > D.
>
> B has 48 votes against A via the beat path B > D > C > A.
> B has 60 votes against C via the beat path B > D > C.
> B has 75 votes against D via the beat path B > D.
>
> C has 48 votes against A via the beat path C > A.
> C has 65 votes against B via the beat path C > B.
> C has 65 votes against D via the beat path C > B > D.
>
> D has 48 votes against A via the beat path D > C > A.
> D has 60 votes against B via the beat path D > C > B.
> D has 60 votes against C via the beat path D > C.
>
> Candidate A is the Schulze winner because candidate A defeats
> every other candidate via beat paths.
In this case, Schulze(bv) gives:
A has 58 votes against B via the beat path A > D > C > B.
A has 58 votes against C via the beat path A > D > C.
A has 58 votes against D via the beat path A > D.
B has 48 votes against A via the beat path B > D > C > A.
B has 60 votes against C via the beat path B > D > C.
B has 75 votes against D via the beat path B > D.
C has 48 votes against A via the beat path C > A.
C has 65 votes against B via the beat path C > B.
C has 65 votes against D via the beat path C > B > D.
--> D has 49 votes against A via the beat path D > C > B > A <--
difference here.
D has 60 votes against B via the beat path D > C > B.
D has 60 votes against C via the beat path D > C.
It was this one-vote difference that caused me to notice the problem (of
course, it doesn't affect the result in this case). Note that I should
probably not be using the term "beat-paths" when talking about Schulze(bv),
since the paths do not necessarily follow pairwise wins, exclusively. My
definition for Schulze(bv) looks like this:
*****
Schulze(bv) Method:
Candidate A "links" to candidate B if some voters rank A over B. The
"strength" of that link is the number of voters who ranked A over B.
There's a "path" from A to B if either A links to B, or if A links to a
candidate that has a path to B. The strength of a path is equal to the
strength of its weakest link.
Candidate A "defeats" candidate B if A has a stronger path to B than B has
to A.
The winners are those candidates who are undefeated. If there is more than
one winner, exclude all the defeated candidates from the election and
reapply the method until a single winner is found.
*****
The above definition differs a bit from the one I posted a long time ago
for the Schulze method, which by the proposed terminology is Schulze(wv):
Schulze(wv) Method:
Candidate A "beats" candidate B if more voters rank A over B than
vice-versa. The strength of that victory is the number of voters who ranked
A over B.
There's a "beat-path" from A to B if either A beats B, or if A beats
something that has a beat-path to B. The strength of a beat-path is
measured by its weakest victory.
Candidate A "defeats" candidate B if A has a stronger beat-path to B than B
has to A.
The winners are those candidates who are undefeated. If there is more than
one winner, exclude all the defeated candidates from the election and
reapply the method until a single winner is found.
*****
Norm
-----Original Message-----
From: Rob Lanphier <robla at eskimo.com>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Date: February 8, 2000 11:40 PM
Subject: "Votes over" (Re: [EM] Why Margins isn't as democratic or ethical
as)
>I feel guilty making such a trivial reply to such a substantive post,
>but...
>
>On Tue, 8 Feb 2000, Norman Petry wrote:
>> First -- A Rant about "Votes Against" terminology
>
>How does "Votes Over" sound?
>
>I'll be replying to your other post later. I think you make some
>excellent pints that deserve highlighting.
>
>Rob
>----
>Rob Lanphier
>robla at eskimo.com
>http://www.eskimo.com/~robla
>
>
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