Chris Benham wrote:
31: A>>B
32: B>>C
37: C>>A
Leaving aside the approval cutoffs, methods that don't elect C here
must fail mono-raise.
With these rankings and also C being the most approved candidate, for
me a method needs
a good excuse for not electing C.
DMC and also "Approval-Weighted Pairwise" both elect C.
The last line is wrong. I meant to write
DMC and also "Approval-Weighted Pairwise" both fail to elect C.
They both elect B. Sorry if I caused any confusion.
Chris Benham
Peter Barath wrote:
And what about the method (I don't know the name) in which
the least approved candidate is eliminated until there is
a Condorcet-winner?
That is called "Definite Majority Choice". It has some alternative
algorithms.
http://wiki.electorama.com/wiki/Definite_Majority_Choice
Does it also fail FBC?
Yes. All methods that meet the Condorcet criterion fail FBC. Condorcet
is incompatible
with FBC. Kevin's "adjustment" of Condorcet//Approval to meet FBC
causes it to no
longer strictly meet the Condorcet criterion.
Did somebody
analyse the strategy incentives then?
Yes, it has been discussed a lot at EM. It used to be my favourite.
31: A>>B
32: B>>C
37: C>>A
Leaving aside the approval cutoffs, methods that don't elect C here
must fail mono-raise.
With these rankings and also C being the most approved candidate, for
me a method needs
a good excuse for not electing C.
DMC and also "Approval-Weighted Pairwise" both elect C.
http://wiki.electorama.com/wiki/Cardinal_pairwise
I like "Approval-Sorted Margins".
http://wiki.electorama.com/wiki/Approval_Sorted_Margins
I also like using that method to find the lowest-ordered candidate,
eliminate that candidate, and then
repeat the process until one remains, each time interpreting ballots
that make no approval distinction
among remaining candidates as approving all except those they rank
(among the remaining candidates)
bottom or equal-bottom. (I think that is also good for plain ranked
ballots that allow truncation but not
an explicit approval cutoff.)
An algorithm that is equivalent or nearly equivalent to ASM is to use
one of Beatpath, River or Ranked Pairs
measuring the 'defeat strength' by the difference between the two
candidates' approval scores. I proposed this
a while ago as "Approval Margins".
Chris Benham
By the way, electing from the Condorcet top tier using approval
would be called Smith//Approval or Schwartz//Approval depending on
which top tier is used. I don't typically consider these methods
because they are more complicated than Condorcet//Approval and
can't be adjusted to satisfy FBC.
And what about the method (I don't know the name) in which
the least approved candidate is eliminated until there is
a Condorcet-winner? Does it also fail FBC? Did somebody
analyse the strategy incentives then?
(And here I don't think of a method in which all ranked
candidates are considered as approved, but a whole preference
order with a cutoff mark somewhere between.)
Peter Barath
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