# Sum-up for Ranked Pairs; wv & margins comments

Rob LeGrand honky1998 at yahoo.com
Fri Apr 27 17:51:30 PDT 2001

```Richard wrote:
> One idea I'm thinking about is to define a minimum cost dropping algorithm.
> Let's say you could make A the winner by dropping C's defeat of A, but that
> defeat has a margin of 5 votes. And let's say you could make D the winner by
> dropping A's, B's, and C's defeates of D, and each of those defeats is by
only
> 1 vote. In the minimum cost algorithm, the total cost of declaring a winner
> would be the sum of the margins of the dropped defeats, so the cost of
> declaring D the winner (3) would be lower than that of A (5). If the B and C
> defeats also have margins of 4 or higher, then D would be the winner. If two
> candidates tie for the lowest cost then of course you can take the pairwise
> contest results between just those candidates.
>
> I like this method intuitively, but don't have any ideas about what criteria
> (other than Condorcet and I believe monotonicity) it may or may not satisfy.
> It seems to me that it is somewhat similar to path voting. Any comments?

That exact method is implemented in my simulation as Dodgson(m).  My "Dodgson"
isn't exactly Dodgson's method; it simply takes whatever pairwise matrix is
calculated (whether margins, winning-votes, etc.) and sums each candidate's
column.  The one with the lowest sum is elected.  (Mike's "Minimize Overruling"
in http://groups.yahoo.com/group/election-methods-list/message/6433 is the same
as Dodgson(wv).)  The "Dodgson" methods do very well in my SU simulations; in
fact, Dodgson(av) almost rivals Borda in SU.  Unfortunately, Dodgson methods do
poorly in criterion compliances.  I believe all four of them fail independence
of clones and Smith, both of which are important to me.  And Dodgson(av), the
best in SU, even fails Condorcet, just like most other "all-votes" methods.

Craig wrote:
> I do believe that there is a certain intuitive appeal for Ranked Pairs.  A
> basic idea in Path Voting (and by extension SSD) is that if there is a
> majority path from A to B (A>C>F>B), the assumption is that this is a reason
> not to elect B.  I belive that this assumption is warranted, but it does not
> necessarily follow that there is a reason not to elect B over A.  The only
> assumptions I would make from that infomation is that there is a reason to
> elect A over C, a reason to elect C over F, and a reason to elect F over B.
> Each of these majorities is quite likely made up of different people, some
> of whom might not appreciate their vote for C over F being used to elect A
> over B.

That's true, and I don't use that kind of reasoning to justify Path Voting.  I
just see it as the most natural way to resolve Condorcet paradoxes while
keeping clone independence.  For what it's worth, I don't even think of the
presence or absence of majority beatpaths so much as I think of comparing the
strengths of beatpaths.  Of course, I also appreciate the intuitive appeal for
Ranked Pairs.

And, finally, Mike wrote:
> Richard has written about how one thing he likes about margins is
> that it looks nice on a certain diagram. Rob L.G. likes it because
> it has pleasing symmetry.

I don't remember using the word "symmetry", but anyway that's not the whole
story.  I just don't see Mike's majority defensive strategy criteria as
meaningful enough to favor winning-votes over margins, as I've explained.

> The wv methods were designed to get rid of those
> problems, including the well-known and politically disastrous
> lesser-of-2-evils problem--to the extent possible.

I don't think winning-votes gets rid of the lesser-of-two-evils problem to any
meaningful extent.  Mike does, and given that, he should certainly keep
supporting wv methods.  But I think winning-votes's guarantees are just too
easy for voters to get around.  Generally, I think you have to be pretty darn
clever to gain by voting insincerely under margins, but under winning-votes,
it's very very frequently to your advantage to vote lots of ties near the top
of the ballot and none near the bottom.  Just my opinion; I'll post later if I
can back that up with specifics.

I wouldn't be surprised if the winning-votes methods beat the margins methods
in the CR poll.  I get the feeling that most margins supporters, including me,
see winning-votes as silly but rather harmless.  But I feel justified in using
the word "vicious" to describe Mike's attacks on margins.  He seems to see
margins methods as betraying all that's good about Condorcet methods.  Given
the importance he ascribes to his strategy criteria, I admire him for sticking
to his guns, and I certainly admire his careful criterion-based approach.

There are a lot of really smart people on this list.  It's a shame mutual
respect isn't more apparent.  By the way, any women here?!?  :)

Keep those ballots rollin' in!

=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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