[EM] Re: "inconclusively-dominated sets", IRV-completed Condorcet

[Chris Benham]

James G-A,
I've been looking at  your  Sun.Jul.25 post in this thread. You wrote:

>I wanted to talk about Condorcet completed by IRV (CCIRV) a bit more
>here, beef up the proposal a bit. 
>	First of all, if there is a top cycle in the pairwise result, I'd like to
>eliminate the non-members of the Schwartz set (union of minimal
>undominated sets) before moving on to the IRV tally.
>
A little further you write:

>My proposal for IRV-completed Condorcet is to eliminate every candidate
>outside the UMID set before proceeding to the IRV tally.
>	Okay, so the UMID set is like the Schwartz set, but a little different,
>because it takes into account whether a candidate is beaten by a majority
>or a minority. If there is a set such that no candidate within the set is
>majority-beaten by any candidate outside the set, then it's an
>inconclusively-dominated set. If it doesn't contain other
>inconclusively-dominated sets, then it's a minimal
>inconclusively-dominated set. So the union of minimal
>inconclusively-dominated sets consists of all the candidates who belong to
>a minimal inconclusively-dominated set.
>
The  UMID set it seems to me is the same as  "Condorcet Non-loser 
(Gross)", or  the "Schwartz (Gross)" set; which could be
defined as the smallest non-empty set  of candidates for which it is 
true  that none of  the members are pairwise beaten by a
majority of  ballots by any non-member. Or have I missed something?

If  I am right, then doesn't  your definition of  this method need to 
include something about restricting winners to members of the
Schwartz set?  Because otherwise couldn't it be possible for there to be 
a (net)CW  who  is not in the "UMID" set, and who doesn't  
go on to win the IRV count?

Chris  Benham

http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-July/013450.html