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
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