[EM] Descending Acquiescing Coalitions versus Nested Acquiescing Coalitions

[C.Benham]

Forest,

This NAC method suggestion of yours fails my Descending Solid Coalitions 
bad example:

49: C
48: A
03: B>A

NAC, like DSC and FPP, elects C while DAC  elects the MDT ("Mutual 
Dominant Third") winner A.

DAC goes AC96 (disqualify B), AB51 (disqualify C), A wins.

NAC skips AB because that includes an already disqualified candidate and 
next goes to C49 and
disqualifies A.

> Which of the good properties of DAC are retained by NAC?


I think Majority for Solid Coalitions and probably Clone Independence 
and maybe some others.
I'd be surprised if it meets Participation.


Chris Benham



Forest Simmons wrote (9 Nov 2011):

DAC (descending acquiescing coalitions) disappointed Woodall because of 
the following example:

 03: D
 14: A
 34: A>B
 36: C>B
 13: C

The MDT winner is C, but DAC elects B.

DAC elects B even though the set {B} has a DAC score of zero, because 
the "descending" order of
scores includes both the set {C,B} (with a score of 49) and the set 
{A,B} (with a score of 48), and the
only candidate common to both sets is B, so B is elected by DAC.

But suppose that we change DAC to NAC (Nested Acquiescing Coalitions) so 
that sets in the sequence
of descending scores are not only skipped over when the intersection is 
empty, but also skipped over
when the set with the lower score is not a subset of the previously 
included sets.  Then, in the above
example, C is elected.

I want to point out that this NAC method also solves the "bad approval 
problem" by electing C, B, and A
respectively, given the respective ballot sets

49 C
27 A>B
24 B,

and

49 C
27 A=B
24 B,

and

49 C
27 A>B
24 B>A .

Which of the good properties of DAC are retained by NAC?

Thanks,

Forest