[EM] Re: RAV/DMC

[Araucaria Araucana]

Hi Kevin,

Interesting post, see inserted comments below.

On 10 Apr 2005 at 22:42 UTC-0700, Kevin Venzke wrote:
> Dear Jobst,
>
> --- Jobst Heitzig <heitzig-j at web.de> wrote:
>> You also wrote:
>> > Of course RAV just substitutes an approval measure for WV or
>> > Margins.  It's unchanged, that increasing the strength of one
>> > candidate's wins can cancel another candidate's wins.
>> 
>> That is also a strange interpretation. Of course, as some of us
>> including me realized or proved, DMC/RAV is *logically equivalent*
>> to a number of well-known defeat dropping methods when defeat
>> strength is defined in a certain way. But defeat strengths are not
>> at all the idea of neither RAV or DMC, and those methods don't
>> "cancel" any wins.
>
> I don't agree that this is a strange interpretation, or that defeat
> strength is not the idea of RAV. When I (re)proposed this method in
> November, you and I spoke primarily in terms of defeat strength, and
> already in my initial message I noted the method was the same as
> electing the least-approved candidate who beats everyone with
> greater approval:
>
> http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-November/014115.html

Excellent! Yes, that appears to be the first observation.  I should
add a link to this post into the DMC page when I get the time, or you
can do so if you like.

I'm interested in other parts of the message though -- you stated
there that you had a special technique for avoiding having to fill in
25 votes in the

        A>>BCDEFGHIJKLMNOPQRSTUVWXYZ

case, but I didn't see how your 2004-11-04 message explained that.
Maybe I'm just dense or preoccupied.

>
> It seems to me that you were quite critical of RAV/DMC and I still don't know
> why you changed your mind:
>
> http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-November/014127.html
> http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-November/014148.html
>
> You wrote:
> "Then you came up with the topic of how to measure defeat strength
> best without having to count all winning votes, and suggested to use
> approval scores. I pointed out that when using approval of A to
> measure the strength of A>B, you count some people towards that
> strength who actually prefer B to A, and that this possibility will
> be counter-productive when trying to convince people to go voting."
>
> I guess you and Russ think that if we "interpret away" defeat
> strengths, then this problem disappears??
>
> Kevin Venzke

My interpretation of why Jobst 'changed his mind' was that Forest's
reinterpretation of RAV was much more persuasive than any other
previous explanation, including your one-line summary.  And since
Jobst is more interested in counter-strategy measures using random
ballots, he is looking not only for a winner but a set of near
winners.  Forest's P (aka Definite Majority) set is simple to define
and calculate and satisfies Jobst's criteria of including the Approval
Winner and some set of highly-approved candidates.

And yes, interpreting away defeat strengths (and the resulting
simplicity of the explanation) is what makes the method attractive as
an initial public proposal.  But the reinterpretation is also what
exposes the P set.  Possibly the "Sieve of Eratosthenes"-like nature
of the P set is what appeals to mathematically-minded folks like us.

(for non-math-geeks:  http://ccins.camosun.bc.ca/~jbritton/jberatosthenes.htm)

Note that Forest's Approval Seeded Bubble Sort proposal (in my
terminology, Pairwise Sorted Approval) from early 2001 also finds the
same winner as RAV, and also has some set of candidates, Q, that are
ranked higher than the AW.  But Q may contain a cycle, and P does not.

Ted
-- 
araucaria dot araucana at gmail dot com