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.
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