[EM] Re: fixing DMC page on electowiki

Wed May 11 10:19:18 PDT 2005

On 10 May 2005 at 19:56 UTC-0700, Abd ulRahman Lomax wrote:
>At 01:25 PM 5/10/2005, Araucaria Araucana wrote:
>>It appears that you are reading my comments out of context, and are
>>also misunderstand the intent of a wiki -- it is a *collaborative*
>>site.  See these links: [deleted]
>
> Perhaps it doesn't matter, but I operate several wikis, and I've
> contributed to Wikipedia (though I'm certainly not a wiki expert). I
> don't know why Mr. Araucana got the idea that I didn't understand
> this basic concept.

Please, call me Q (see sig).  And please don't take offense [there's a
bit too much of it on the list at present!].  I've heard it said that
written language is only 7% effective -- much more is conveyed in
intonation and body language.  Email has a long time-lag, so to avoid
too many separate messages, I tend to err on the side of too much
information.  You may choose to interpret this as being patronizing,
but it isn't meant to be.

I do apologize for underestimating your abilities, but it was your
first posting, and I didn't have anything else to go on.  My default
assumption is that posters to this list usually are stronger at
theoretical math than web skills.

> So the least-approved candidate ... is the winner? Explain this
> thing to me....

Okay, here goes:

First, a Condorcet method is a procedure for holding a set of
one-on-one elections simultaneously, using ranked ballots.  Some on
this list have proposed calling it Instant Round Robin.

   http://wiki.electorama.com/wiki/Condorcet_method

Ranked ballots (equal ranking allowed) are tabulated into a pairwise
matrix (call it M).  A vote in location M(i,j) means a vote for
candidate i against candidate j.  So if the total M(i,j) is greater
than M(j,i), candidate X(i) defeats candidate X(j).

   http://wiki.electorama.com/wiki/Condorcet_method#Counting_with_matrices

Because the final total can sometimes be cyclic (i.e., no candidate is
undefeated), we are interested in finding a satisfactory completion
method.  There are several strong methods (e.g. Ranked Pairs, CSSD,
River) that use ranked ballot information alone, but they may be too
complex for an initial reform proposal.  Therefore, some have proposed
combining Condorcet with Approval Voting.  Here's some background on
Approval:

   http://wiki.electorama.com/wiki/Approval_voting

To combine approval with a ranked ballot, we use an approval cutoff:

   http://wiki.electorama.com/wiki/Approval_Cutoff

When both pairwise and approval information are available, it is
possible to reorder the pairwise array in descending order of
approval.  Here is an example of an election with approval cutoff
ballots, before and after reordering:

    http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting#Example

I'm excerpting the ballots and reordered pairwise matrix from that
example.  A winning off-diagonal score is 461 and greater.

 98: Abby >  Cora >  Erin >> Dave > Brad
 64: Brad >  Abby >  Erin >> Cora > Dave
 12: Brad >  Abby >  Erin >> Dave > Cora
 98: Brad >  Erin >  Abby >> Cora > Dave
 13: Brad >  Erin >  Abby >> Dave > Cora
125: Brad >  Erin >> Dave >  Abby > Cora
124: Cora >  Abby >  Erin >> Dave > Brad
 76: Cora >  Erin >  Abby >> Dave > Brad
 21: Dave >  Abby >> Brad >  Erin > Cora
 30: Dave >> Brad >  Abby >  Erin > Cora
 98: Dave >  Brad >  Erin >> Cora > Abby
139: Dave >  Cora >  Abby >> Brad > Erin
 23: Dave >  Cora >> Brad >  Abby > Erin

+-----------------------------------------------+
|            |             against              |
|            |----------------------------------|
|            | Erin | Abby | Cora | Brad | Dave |
|------------+------+------+------+------+------|
|     | Erin | 708  | 410  | 461  | 298  | 610  |
|     |------+------+------+------+------+------|
|     | Abby | 511  | 645  | 461  | 458  | 485  |
|     |------+------+------+------+------+------|
| for | Cora | 460  | 460  | 460  | 460  | 460  |
|     |------+------+------+------+------+------|
|     | Brad | 623  | 463  | 461  | 410  | 312  |
|     |------+------+------+------+------+------|
|     | Dave | 311  | 436  | 461  | 609  | 311  |
+-----------------------------------------------+

There are no undefeated candidates ==> there is no Condorcet winner.
So, using DMC (aka Ranked Approval Voting), let us begin by ignoring
the row and column of the least-approved candidate, Dave.  We then see
that Brad defeats all remaining candidates.  We're done -- Brad wins.

As it happens, there are several candidates who are undefeated by
other candidates with higher approval.  Erin, Abby and Brad all
qualify.  In DMC, we call this set the definite majority set.  Among
the definite majority set, Brad defeats all others. 

*** It is a corollary of the definite majority set's construction that
*** the winner is the least-approved member of that set.

Compare with this idea:

   http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

See also the various criteria that have been proposed for voting
methods.

IMO, DMC/RAV may not be the best possible single-winner election
method, but it has enough strong features that it will discourage
insincere voting and give much more satisfactory results than
single-vote or IRV.

> Actually, even stupid and ignorant comments can be very useful.

Yes, Socratic method, etc.  But it's kind of a flimsy excuse for not
doing your homework. ;-)

>
> I do have comments to make, lots of them. But not yet.
> www.beyondpolitics.org
>

I now see you have your own political agenda.  I would be interested
to see, when you are ready, how your Free Association - Direct Proxy
ideas compare with other similar proposals such as Direct Democracy or
Candidate Proxy.

BTW, does ul-Rahman means "the merciful and compasssionate one"?

Q
-- 
araucaria dot araucana at gmail dot com
http://www.metafilter.com/user/23101
http://wiki.electorama.com/wiki/User:Araucaria
Q = Qoph = "monkey/knot" -- see http://www.ship.edu/~cgboeree/alphabet.html