Chris,
I'm sure that you are aware that in your example,
31: a|b
32: b|c
37: c|a ,
the UncAAO winner is c, so that DMC is not uniformly better than UnCAAO
in the three candidate case, assuming that c should win.
But I'm not so sure that c should win. In fact, I believe that more
likely than
Forest W Simmons wrote:
A candidate X covers a
candidate Y if and only if X (pairwise) defeats both Y and each
candidate that Y defeats.
So if X covers Y, then in a pairwise sense X dominates Y.
Now for UncAAO:
1. Write abbreviations for all of the candidate names on a big sheet of
Forest--
Alright, but the C voters are still truncating their approval, arent they?
They still need that strategy in order to put the choice to the A voters
about accepting the Nash equilibrium or else. True, the C voters dont have
to abandon A to the degree that theyd have to in wv. So
Forest W Simmons wrote:
UncAAO stands for Uncovered, Approval, Approval Opposition. Here's how
it works:
For each candidate X,
if X is uncovered,
then let f(X)=X,
else let f(X) be the candidate against which X has the least approval
opposition, among those candidates that cover X.
Mike,
That's right. The C voters still have to use defensive strategy, but
the moving the approval cutoff is sufficient.
When there are only three candidates, UncAAO is the same as Smith
Approval.
Here's another classical example:
49 C
24 BA
27 AB
Under wv, this is not a Nash Equilibrium,
Chris,
For the benefit of those who are just joining us, I'll start a little
more basic than you would need.
We need to know the meaning of cover. A candidate X covers a
candidate Y if and only if X (pairwise) defeats both Y and each
candidate that Y defeats.
So if X covers Y, then in a
Forest W Simmons wrote:
Here are the main advantages of UncAAO over other Condorcet methods:
1. It is resistant to manipulation ... more so than Beatpath or Ranked
Pairs, if I am not mistaken.
2. It always chooses from the uncovered set.
3. It is at least as easy as Ranked Pairs to
Forest had correctly said:
Under winning votes the C faction can take defensive action and
truncate to 20 C. The resulting position is a Nash Equilibrium.
Chris writes:
Taking such defensive action causes B to win, so why would they want to do
that when they
prefer A to B? And I don't see
Jobst,
You've probably already figured this out, but here goes:
UncAAO fails IDPA to the same extent that Approval does, because it is
possible (however unlikely) for a Pareto Dominated alternative to get
as much or more approval than an alternative that dominates it.
But note that if Y'
IEVS 3.22 now implements Forest Simmons' latest UncAAO voting
method [Uncovered, Approval, Approval Opposition]
Warren D Smith
http://rangevoting.org
http://rangevoting.org/IEVS/IEVS.c
election-methods mailing list - see http://electorama.com/em for list info
UncAAO stands for Uncovered, Approval, Approval Opposition. Here's how
it works:
For each candidate X,
if X is uncovered,
then let f(X)=X,
else let f(X) be the candidate against which X has the least approval
opposition, among those candidates that cover X.
Start with the approval winner
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