[EM]Re: AWP versus AM (and DMC)

[Chris Benham]

James,
This is Jobst Heitzig's table again:

"Perhaps it is helpful to look at the defeat strength
like this: When A defeats B, then the defeat strength
is composed as a linear combination
of the following three components:"

                                                     
AM  AWP  DMC
                   
no. of voters approving A but not B    +   +   +
                 
no. of voters approving A and B        0   0   +
             
no. of voters approving B but not A    -   0   0



You wrote (Fri.Apr.8):

> "A method should never elect the 'least-approved'
candidate." Yes, that's a normative criterion. 

It is, but it isn't exactly  one that any of the
proponents of   AM or DMC have proposed. Instead they
propose:
"A method should never elect a candidate that is
pairwise beaten by a more approved candidate", 
which of course implies:
"A method should never elect the 'least-approved'
candidate,  unless   that  candidate  is the CW"
You continued:

> "A method should overrule defeats consisting of
fewer strong preferences before it overrules defeats
consisting of more strong preferences." That's another
normative criterion.

I find the phrase  "defeats consisting of..." an odd
formulation with an unclear meaning. Arguably "defeat"
is just a label for a result which just is, and so
doesn't really "consist of"  anything.  If  soccer
team A defeats soccer  team  B   3-2,do we say that
the defeat  "consists of"  purely   A's  3 goals,  or 
of  the one goal  in excess of  B's 2 goals, or  of
the fact that B didn't  score more than 2 goals, or 
what?
In my last post in this thread I wrote:
Recently I wrote strongly in favour of the Plurality
criterion, which says that if candidate y has more
first-preferences than
candidate x has above-last-preferences,then x can't
win. Electing x gives those voters who prefer y (to x)
a very strong,virtually unanswerable complaint.
You wrote:

> Okay... So, a lot of good methods fail the Woodall
plurality criterion, right?

No. Of  the single-winner plain ranked-ballot methods
that fail that criterion, IMO the only good ones are 
CDTT,IRV  and CDTT,DSC (and maybe some other CDTT
method).

> Which ones pass, and which ones fail?

Some methods that pass the Plurality criterion:
FPP, IRV, Approval, Winning Votes (RP,BP,River,MM),
DSC, DAC, QLTD, Bucklin, Raynaud (Gross
Loser),SCRIRVE,
Point Count (e.g.Borda), Black

Some methods that fail the Plurality criterion:
CDTT methods, Any pairwise Margins method,
Raynaud(Winning Votes), Young, Condorcet-Kemeny,
Descending Half-Solid Coalititions, SC-DC

> AWP and AM both fail, right? 

No. AM and DMC definitely meet it, and I'm pretty sure
AWP does too.

> Are you saying that AM passes under conditions of
strict full rankings, whereas AWP fails under these
conditions?  

Any non-absurd method  "passes under conditions of
strict full rankings". 

One of the original justifications of the Plurality
criterion was about inferring (conservatively) 
approval from rankings.  This is somewhat redundant if
 the voters can enter their explicit approval cutoffs.
Repeating myself again: 'Compared with failing the
Plurality criterion, electing a candidate that is
pairwise beaten by a more approved candidate can give
more voters an even stronger,irresistible complaint.
There isn't available the comeback: "This method
encourages full ranking and so sometimes seems unfair
to truncators. The winner's supporters didn't
truncate, and you shouldn't have", because in AWP
(as in your two examples) the failure can occur when
all the voters fully rank and use their cutoffs.'

So what I'm saying is that in plain ranking methods,
failures of the Plurality criterion are very difficult
to justify; whereas in hybrid ranking/approval
methods failing the somewhat similar "Don't elect a
candidate that is pairwise beaten by a more approved
candidate" criterion is IMO impossible to justify. I
know that this is an idea of Forest's, but not if it
has an official name. He calls the set "P".  For the
time being I'll refer to it as  the "Approval
Plurality" (AP) criterion.

> There is no extra cost of AWP over AM or DMC.  

The  "cost"  I was referring to is not meeting AP.

> AWP is not hard to explain. For example: "If there
is a majority rule cycle (A beats B, B beats C, C
beats A), then we overrule the defeat that
> consists of the fewest strong preferences. (If you
approve of candidate A but not candidate B, then your
A>B preference is a "strong preference".)"
> This explanation is perfectly intuitive.

No, to me this sounds like a  slick but vain attempt
to make something quite weird and unintuitive sound
otherwise by using the vague and unclear phrase "the
defeat that consists of.."

> There is no need to talk about approval scores

It  would be very normal for all the participants in
the election to take a great interest in the
candidates'  FP and  approval scores as well as the
results
of the pairwise comparisons.

> AWP doesn't pay attention to approval scores;
rather, it uses approval cutoffs to provide a defeat
strength definition that I consider to be more
> sensitive to preference strength and more resistant
to strategic manipulation.

In this context "preference strength"  seems to be a
bit vague and abstract. But aside from that, how  does
using half as much approval information as
AM  make it  "more sensitive to preference strength"?
Maybe AWP  is a bit more strategy resistant than AP,
but only at the huge cost of  flouting AP.

AWP is a  clever and sophisticated idea, but when you
are using it to try to justify the election of the
least-approved (and pairwise beaten) candidate,
it will sound like "mumbo-jumbo"  to many fair-minded,
not-stupid voters.


Chris Benham








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