[EM] ICT definition. Presumed Kemeny definition.

[Kristofer Munsterhjelm]

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?