[EM] Re: Woodall's "Descending Acquiescing Coalitions" method

[Chris Benham]

Kevin,
On  Thurs.Sep.11, 2003, you wrote:
"(This is in regards to the article that Markus recently uploaded, and 
mentioned
in the "Theoretical Justification for WV" message.)

I read this article, and particularly noted Woodall's method of "Descending
Acquiescing Coalitions" or "DAC," which he says is "the first election rule
that I am really happy with."

It started interesting enough. It looks superficially like RP, except
locking sets of candidates (thereby barring candidates outside the set from
winning) instead of pairwise defeats. The votes for a set are counted as 
the
number of voters who do not prefer anyone outside the set to anyone 
inside of
it.

Woodall says the method meets Plurality, Majority, certain types of
Monotonicity,
Participation, and later-no-help; he says it fails Condorcet, later-no-harm,
and other types of Monotonicity.

I did a few experiments with this method and it seems astonishingly bad 
to me.
There's great incentive to bury and order-reverse. I have a hard time
believing
the method meets Participation.

I'll give an example:
23 A>C>D>B
29 B>A>D>C
48 D>A>C>B

The CW is clearly A. "DAC" sees set ACD (strength 71) and kills B, sees 
AD and
D
(both strength 48) which make D the winner".

CB: Describing his DAC method, Woodall writes:
"In DAC, one first lists the sizes of  all the acquiescing coalitions in 
decreasing order..., and then works
down the list from the top, eliminating candidates until only one is left."
It has occurred to me that the method  might be improved by after the 
first round of eliminations (determined
by the second largest acquiescing coalition), then  ignore the 
eliminated candidate(s) in determining the next
largest acquiescing coalition; and after each subsequent round of 
eliminations likewise ignore the eliminated
candidates.
So to take your example, after  B is eliminated,  the next biggest 
 acquiescing coalition is  AD (77) so C is
eliminated, and then the next biggest  is A (52)  so  D  is eliminated 
and A wins.
Is there any problem with this idea?
In his article, Woodall claims that Condocet is incompatible with 
Participation, 4 out his 7 versions of
Monotonicity, Later-no-harm and  Later-no-help.  For the Condorcet 
die-hards,  would DAC  (either version)
be a good Condorcet-completion method?

You also wrote:
In this paper, Woodall introduces the so-called
 "plurality criterion":
 
 Plurality: If some candidate x has strictly fewer votes
 in total than some other candidate y has first-preference
 votes, then x should not have greater probability than y
 of being elected.

"I do like this. It seems to acknowledge meaning in being ranked non-last."

CB: While I of course know what  "first-preference votes" are, I  am not 
at all clear on exactly what the
phrase "strictly fewer votes in total" means (in a ranked-ballot 
context). What does it mean ?

Chris Benham.