On 04/23/2012 10:32 PM, Michael Ossipoff wrote:
ICT:
Kevin Venzke proposed ICA. Improved-Condorcet-Approval.
ICA passes FBC. The part of ICA that ICT uses is the Improved Condorcet
part. But instead of completing IC with
Approval, it completes it by electing the IC winner ranked top on the
most ballots.
ICT was introduced by Chris Benham. He gave it a longer name with longer
abbreviation-initials. I'm calling it ICT,
consistent with Keven Venzke's naming of ICA.
What's the advantage of ICT over ICA?
It's recently been said on EM that Kemeny's properties are like those of
Condorcet, except that it meets one
additional criterion, called the Reinforcement Criterion. I don't know
what that criterion says.
Kemeny meets Condorcet. This is easy to see when you consider a
transformed Condorcet matrix (wv, margins, whatnot) such as would be
used by Kemeny. If there's a CW, you will always get fewer disagreements
by putting him at top than by not putting him at top. Similarly, Kemeny
meet Smith.
The reinforcement criterion is this: say you have two precincts that,
when their ballots are run through a method, both precincts report the
same ordering. Then if you run the combined ballots of both precincts
through the method, it must return that ordering in order to pass
Reinforcement. Basically, it's Consistency, but with an ordering, not a
winner.
Kemeny fails FBC.
Unless someone can show otherwise, prudence dictates that we assume that
Kemeny is not defection-resistant.
A tangential question: is Condorcet and defection resistance incompatible?
(If so, we wouldn't have to go on prudence. Simply knowing Kemeny is
Condorcet would be enough.)
According to the recent (maybe still ongoing) discussion about VoteFair
and Kemeny, VoteFair is quite similar
to Kemeny, and gives the same result under some, but not all,
circumstances. Kristofer says that, at least probably,
VoteFair doesn't meet both Condorcet's Criterion and Reinforcement--two
criteria met by Kemeny.
I'm pretty sure VoteFair meets Condorcet even when it starts going
outside the boundaries where it matches Kemeny. But if the paper's right
about Kemeny being the only method that can meet both Condorcet and
Reinforcement, and VoteFair departs from Kemeny at some point, then it
can't meet Reinforcement beyond that point.
I don't consider Kemeny or Condorcet suitable proposals, because FBC
failure, and lack of defection-resistance.
I said more about that in my previous post.
Yes, Approval isn't defection-resistant either, but I expect more from a
rank method. To significantly improve on Approval
requires defection-resistance. No rank method should be considered
unless it is both FBC-complying and defection-resistant.
Another question: do you know of any method meeting strong FBC and
defection resistance?
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