[EM] True, the SD example is possible.

[MIKE OSSIPOFF]

I guess Norm & Markus have shown that Blake's example is
definitely possible. It had seemed to me that Blake didn't
count the example correctly, but Norm probably used a computer
program, and errors are unlikely.

Since it now seems more certain that SD has Monotonicity failure
that's avoidable (since several other methods don't have one),
that does seem to say that Tideman would be a better public
proposal, because it's less criticizable, by that criterion that's
so important to academic authors.

I'd say that SSD is intermediate in merit between Tideman &
SD. So, in terms of merit, maybe it's something like:

1. Schulze & Tideman(wv)
2. SSD
3. SD

That says that Tideman is the best public proposal, unless
it can be shown that SSD or even SD is much easier to propose.
As Blake showed, Tideman has a very obviously-motivated
definition.

Of course SD & Tideman both talk of either cycles or else
defeats that contradict or conflict with other defeats.
And it might be slightly more obvious to people to drop weakest
conflicted defeats and declare a winner when someone is
undefeated. Tideman gains top merit by solving all the cycles,
but some people might wonder why it's necessary to solve all the
cycles, to create a transitive ordering of all the candidates.

I'm not saying that to argue against Tideman as a public proposal;
I merely mention considerations that occur to me and which may or
may not turn out to be important.

Also, someone might ask what it means for a defeat to be
contradicted or for a defeat to contradict other defeats, and
then it seems necessary to talk about cycles. SSD can be presented
without talking about defeats contradicting other defeats.
An unbeaten set can be circled in a field of dots representing
candidates. It's natural that the winner should come from such
a set. A smaller circle drawin in that circle is also an
unbeaten set, an innermost unbeaten set. Obviously there's something
special about an innermost unbeaten set, whose members have
special qualification for winning. What could be more natural, then,
than to say that their defeats are the only ones that need to be
dropped?

I don't claim to have the answer about which proposal will be
accepted best, but I wanted to mention those considerations.

I'd add that just  because someone doesn't ask a question doesn't
mean that he isn't troubled by it, to the point that it could
affect his acceptance of the proposal.

Nonmonotonicity is of course a real embarrassment and a
vulnerability. But while IRV has been heavily promoted all around,
not one academic has publicly attacked an IRV proposal about
IRV's nonmonoticity.

Of course someone more cynical than I might say that's only
because IRV is known by the academics to be no good.

But imagine that academic up at the blackboard, with his
arrow diagram of 36 defeats, each arrow with its magnitude-label.
One has to question the effectiveness of a criticism that requires
that kind of proof. How would it stand up against a reply
that the guy is reaching pretty far to find a problem scenario, for
a method that has some powerful advantages--which are much more
likely to have effect. How patient would the audience be with his
proof?

It could also be pointed out to that audience that SD's
nonmonotonicity is nothing like that of IRV, which can be
nonmonotonic with 3 candidates, in a really obvious scenario,
and which has the particularly absurd embarrassment of
a group of voters being able to make someone win by moving him
from 1st choice to last choice in a 4-candidate example.

I think that audience would weigh SD's nonmonotonicity against
it's many big advantages over Plurality. As for SD vs IRV,
of course IRVies would know better than to bring up
nonmonotonicity anyway.

Again, I just mention that consideration, in case it turned out
that SD were the easiest BC complying method to get acceptance for.
When you're talking to someone, whether a friend or someone
walking up on the sidewalk, or a legislataor, you're going to
be worring more about how that person will react to your
method definition than about an academic coming to town with
a 36-defeat digram to show people.

***

I must apologize for my mistaken claim that SD acts like Schulze
under many-voter conditions. I still believe that SSD does, but
I've learned to not assert things like that.

If SSD acts like Schulze when there are no pair-ties or equal
defeats, that means that: 1. SSD is pretty good; and 2. SSD can
be used as a justification for Schulze, as has been suggested.
And that could make Schulze a viable public proposal, if that
indirect justification is enough for public acceptance.

I should probably say why I still believe that SSD does like Schulze
when there are no pair-ties or equal defeats, but that would
lengthen this letter even more.

Anyway, I still don't know which BC complying method I'd
use as a public proposal. Schulze, Tideman(wv), SSD, and even
SD are all good methods, but I accept that SD has an unnecessary
criticism vulnerability, due to its nonmonotonicity.

My inclination would be to first try those 4 proposals on
a number of people, to get their first impressions. It seems to
me that polls are more meaningful than "focus groups", because
the amount of discussion in a focus group won't be possible with
every voter. I'd just ask each person about one of the proposals,
to make it more realistic.

I'm going to ask my consultant what she thinks about Tideman
& SD, when "cycles" are replaced by conflicts or contradiction
among defeats. It's true that my polling sample has been limited,
but I can say that all of its results have been unanimous :-)

Mike Ossipoff







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