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

[Kevin Venzke]

(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.

Aha, I said, the 23 voters need to truncate D>B.  But that won't do it: That
does nothing to weaken set ACD (although it gives 23 strength to set ABC, not
that that helps).  Order-reversing as B>D doesn't elect A, either.

What I eventually did was have the 23 votes vote "A>B>C>D."  In other words,
raise B, in order to take advantage of the Majority-guaranteeing goodness of
the method, which would then ensure that A or B must win.

How it plays out: set AB has the greatest strength (52), eliminating C and D.
Three coalitions have strength 48: ACD, AD, and D.  They eliminate B, and A
wins (finally).  All the A supporters had to do was bury the nearest competition,
and try to mimic the rankings for a candidate who couldn't win but had a lot
of first rankings.

Did Woodall really think this was a good method?


 --- Markus Schulze <markus.schulze at alumni.tu-berlin.de> a écrit : 
> 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.


Kevin Venzke
stepjak at yahoo.fr


___________________________________________________________
Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français !
Yahoo! Mail : http://fr.mail.yahoo.com