A More Attainable LO2E-2

[Mike Ossipoff]

Steve once mentioned that it would be better if LO2E-2 were
replaced with something that Condorcet & Smith//Condorcet
can strictly meet, because it's an embarrassment to have
to say that Condorcet only meets LO2E-2 "for all practical
purposes", instead of being able to say that it strictly
meets that criterion. Incidentally, Bucklin, Stepwise-Plurality
& Coombs do strictly meet LO2E-2, though they don't meet
GMC. Anyway, I'd like to change the name of the LO2E-2
that I've previously defined to "LO2E-2a", and define
another criterion as "LO2E-2". A method meets LO2E-2 iff:

If a majority of all the voters vote A certain particular
alternative A over alternative B, then there's a way that
the members of that majaority can vote that will ensure
that B can't win, and that doesn't require anyone to vote
A equal to or over anything that s/he prefers to A.

[The words "certain particular" are intended to avoid
challenges like Bruce's, that the criterion requires
several majorities to simultaneously achieve that
against different alternatives. Though not strictly
necessary, this wording goes out of its way to 
deter that kind of objection]

This new LO2E-2 criterion is met by Condorcet & Smith//Condorcet
& Simpson-Kramer, & of course Smith//Simpson-Kramer. No one's
proposing Simpson-Kramer, except that I've proposed it as the
1st tie-breaker for small committee elections, in the event
that Condorcet returns a tie. Of course no one at all has
proposed Smith//Simpson-Kramer.

This new LO2E-2 is a slight easing-up of the previous LO2E-2,
enough that the best methods can meet both LO2E-2 & GMC.
And of course LO2E-1. It's in order to have a criterion that
shows another reason why those methods are better. If anyone
is going to criticize the idea of loosening LO2E-2 just enough
so that Condorcet can meet it, I point out that, as I just
said, it shows a way that Condorcet is better than other
methods (other than Bucklin, Stepwise-Plurality & Coombs--
it's better than them in other respects, like GMC &
LO2E-1).

I should also add that it's still true that for Condorcet
to fail LO2E-2a (the previous version of LO2E-2) would
require cheaters who are phenomenally lucky & have the impossible
predictive ability needed to know when that rare lucky chance
occurs. I should also admit at this point that I was mistaken
when I said that the subcycle rule would enable Condorcet to
strictly meet LO2E-2a. I found a situation where not only
can the subcycle rule be circumvented, but where it can also
be taken advantage of. Condorcet is better without the subcycle
rule, which is a good thing, because the subcycle rule added
much complication to Condorcet's definition. Of course
the subcycle rule isn't needed for Condorcet to meet the
new LO2E-2, or any other criterion, such as GMC or LO2E-1.

Mike




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