[EM] Re: Definite Majority Choice, AWP, AM

[James Green-Armytage]

James G-A replying to Ted, on the subject of AWP, DMC, and AM...

Ted:
>Summary of discussion:
>Ted (AKA Araucaria) thinks AWP could do a better job of resisting
>strategic manipulation in some cases, but doesn't think it is as easy
>to explain to the public.
>James thinks they are equally difficult to explain and that relative
>merit should rule the discussion.
>I think we are two different planes that can never intersect.  But all
>of my posts thus far have been directed toward finding a strong public
>proposal, so I can't let the methods stand on their technical merits
>alone. I can explain DMC in three simple sentences:
>   Eliminate any candidate defeated by any other higher-approved
>   candidate.
>   The remaining candidates form what we call the Definite Majority
>   Set.
>   The winner is the single undefeated candidate in the Definite
>   Majority Set.

	Would you like me to give a similarly-simple explanation for AWP? I'd be
happy to try. Below is a provisional attempt.

(1) We say that those who approve A but do not approve B have a "strong
preference" for A over B.
(2) We say that a defeat that consists of more strong preferences is
stronger than one that consists of fewer strong preferences.
(3) If there is no unbeaten candidate, we drop the weakest defeat that's
in a cycle (e.g. X beats Y, Y beats Z, Z beats X) until there is an
unbeaten candidate.

	The above definition is for "sequential dropping (AWP)". For other
completion methods (e.g. ranked pairs, beatpath, river), you just have to
replace (3) with something else. For example, here's something which could
be called "Smith sequential dropping (AWP)", and which is probably
equivalent to beatpath in a public election. Parts (1) and (2) are the
same as above.

(1) We say that those who approve A but do not approve B have a "strong
preference" for A over B.
(2) We say that a defeat that consists of more strong preferences is
stronger than one that consists of fewer strong preferences.
(3) We call the set of candidates who beat all the other candidates the
"top cycle". 
(4) If there is no unbeaten candidate, we drop the weakest defeat within
the top cycle until there is an unbeaten candidate.

	The difference in results between these two methods shouldn't be
significant. "Sequential dropping" may have one step less in the
explanation, but "Smith sequential dropping" would please the
mathematicians more. So, either way. Keep in mind that the amount of lines
it takes to write a definition is not the sole determinant of how easy it
will be to explain to someone new to voting methods, although of course
there is a correlation.
>
Ted:
>This is, IMO, simple and comprehensible to most people, though they
>may argue the benefit of such a procedure and may worry (possibly with
>just cause) about its vulnerability to manipulation.
>Before replying once again with the same restatement of your opinions,
>could you address these points?
>- Approval Sorted Margins (AKA Approval Margins Sort?) appears to pick
>  the same winner as Approval Margins or Approval-weighted Pairwise,
>  at least in the examples given by you and Chris Benham.  But it has,
>  IMO, a simpler implementation.  Could you examine that method in
>  comparison to AWP?
>      http://wiki.electorama.com/wiki/Approval_Sorted_Margins

	That's a bit of a tall order for now... I might have to get back to that
one. But are you saying that ASM gives similar results to AM, or that ASM
gives similar results to AWP? If it gives similar results to AM, my
previous comparisons of AWP to AM should be helpful...

Ted:
>  Just to be clear on why I think ASM might be marginally more
>  feasible but not AWP or CWP:  it's the extra pairwise array.  Do I
>  have to explain further?  Chris Benham's Approval Margins proposal
>  doesn't have an extra pairwise array, but I have yet to see an easy
>  explanation for it.

	I don't think that you have to explain further. AWP and CWP use two
arrays in the counting. From the standpoint of being easy to implement in
a technological sense, I think that this is not a big deal, assuming that
the tally system is computerized anyway.
	When it comes to being easy to explain to non-technically-inclined
citizens, there is no need to talk specifically about arrays or matrices.
Probably better to represent defeats in a graphic form, e.g. arrows going
from one candidate to another.
>
>- The Definite Majority Set has a nice ring to it.  It gives a
>  favorable standing to non-winning members of that set, which always
>  includes the Approval Winner.  The AWP Smith Set won't always
>  contain the Approval Winner.  Can you find some alternate definition
>  of the AWP winner that allows higher approved candidates (including
>  the Approval Winner) to 'lose with honor'?

	I agree that DMC and DMS have a nice ring to them, but I'm not convinced
that it is very important for a candidate to get any specific type of
honorable mention if they lose. The important thing is who wins, not who
gets honorable mention. After the election, the pundits are welcome to
call attention to the members of the DMS, if they like, even if AWP is
used.
>

>- James, I read your paper on CWP, about 6 months ago.  I appreciate
>  that you put a lot of work into them.  But their technical nature
>  and PDF format render them somewhat inaccessible to even
>  election-methods list members.  

	Sorry about the pdf thing. I thought it was really cool for awhile, but
now I'm over it, and I'm gradually phasing it out. Here's a link to the
short version of the cardinal pairwise paper in html:
http://fc.antioch.edu/~james_green-armytage/cwp13.htm
	I don't think that the language should be too difficult for EM people. At
least it's almost entirely written in English, rather than math-ese.

>I think your technical ideas have
>  great merit, but you still need to sell me on implementation.  Why
>  not try putting together an electowiki page.  

	I'd like to do that... maybe you can help me. I like the new electowiki
pages. They are new, right?

>If you're going to
>  promote CWP, then design a ballot to go with the page.  

	I imagine the CWP ballot as being an interactive touch screen interface.
There are many different ways that it could work... all of which are
beyond my programming capacity (which is basically nil).

my best,
James