Coombs meets LO2E-2

[Mike Ossipoff]

Steve Eppley writes:
> 
> Mike O wrote:
> -snip-
> >Of course any method that doesn't meet them already would be
> >improved if mitigated by requiring compliance with Condorcet's
> >criterion & GMC, or NPL & NML.
> 
> Is there a general way to require compliance?  I think that means
> stating the criteria as methods which select a subset of the
> candidates.  A method (like Coombs) could be the tie-breaker of 
> the criterion-expressed-as-method (like NML):  NML//Coombs

That would be a way of doing it, defining methods that eliminate
anything disqualified by certain criteria, such as NML & NPL,
or Condorcet's Criterion & GMC.

What I was saying, though this certainly isn't the only way,
would be to say: "Use method X, but nothing can win if it
has a pairwise defeat, unless everything has a pairwise defeat;
and nothing can win if it has a majority against it, unless
everything has a majority against it [I'd define "majority
against"].

> 
> BeatsAll and NPL are methods which express the Condorcet Criterion.

NPL, like my rule, above, is slightly more exclusive than the
Condorcet criterion, because it applies even when there isn't
anything that beats everything.


> Is NML a method which expresses GMC?  If not, what method does?

NML, likewise, is slightly more exclusive than GMC, because in
addition to disqualifying a majority-rejected alternative 
if there's something that isn't majority rejected, wasn't there
also something about favoring unbeaten alternatives?

NML is better than Condorcet's Criterion, in the small committee
elections where their results would differ, becauses it makes
an additional reasonable requirement. Likewise NML, if it has
that extra unbeaten-clause that I thought I remembered, would
be better than GMC in a small committee election.

Condorcet meets NML & NPL as well as Condorcet's Criterion & GMC.

NML & NPL, or Condorcet's Criterion & GMC could be added to a method
"lexicographically", as Steve or I worded it. I have no objection
to the use of NML & NPL instead, since they're somewhat stronger.

> 
> -snip-
> >I've defined LO2E-2 in full here, but a brief way of putting
> >it could be: A method meets LO2E-2 iff a full majority who
> >rank A over B have a way of voting whereby they can ensure
> >that B won't win, and this doesn't require that they vote
> >a less-liked alternative equal to or over a more liked one.
> >
> >That isn't my full & complete definition, which I've previously
> >posted on EM.
> -snip-
> 
> For those unfamiliar with the term "iff" Mike used above, it's a 
> shorthand which means "if and only if."
> 
> ---Steve     (Steve Eppley    seppley at alumni.caltech.edu)
> 
> .-
> 


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