Count "votes against" in pair-ties? (was Re: I don't contest pre

[Mike Ossipoff]

You have a point that A is more disliked than C in that example
where A, the only unbeaten alternative ass 50 against it in its
tie, while C only has 2 against it in its defeat, & 35 against
it in its victory.

I haven't found any strategy problem that would be caused by
counting votes-against in ties. Or anything wrong with the outcome.

But, as you said, it wouldn't matter in public elections, where there's
virtually never a pairwise tie. And so, for public proposals, 
including vote-against in the (there nonexistent) pairiwse ties
would merely complicate the language, and raise unnecessary questions,
and perhaps provide a target for criticism.

There's something intuitive about an unbeaten alternative being
in a different class than a beaten one. I'm not saying that
a votes-against comparison can't show that the unbeaten but
tied alternative is more disliked. But for public acceptance,
a method could be criticized if it let a beaten alternative
beat an unbeaten one. It's like the Smith criterion, & the
various related candidate-counting criteria that a method
meets if it meets the Smith Criterion. I don't consider the
Smith criterion necessary, but it would be prudent to 
observe it, to pre-emptively thwart flak.

***

But say we were recommending a method for an organizational committee
where pairwise ties were likely? Still, the natural appeal of
an unbeaten alternative dominating the beaten alternatives seems
important for acceptance by whatever committee the method is
being recommended to. Besides, again, it simplifies the wording
of the rule if it doesn't include ties in its votes-against
count.

***

What about votes in EM? Well, unless there's compelling reason to
the contrary, it's simpler to stick with what we're proposing
to others. I don't know of a serious reason, in terms of results
or standards, basic principles or criteria, for doing it one way
or the other. So maybe it's best to stick with the simplest way
, the way that we propose for public elections.

Or maybe not. I've suggested the Schwartz set for EM votes, and
a list of tie-breakers that we wouldn't want to suggest to any
committee not made up of mathematicians or serious conscientious
electoral reform advocates. So if it's felt that counting votes-
against in ties is aesthetically more appealing, then maybe
that's how it should be done in EM votes. I don't know for sure
if it's more aesthetically appealing to me. I like the idea of
counting votes-against, & not leaving any out unless there's a
good reason to. So maybe that could be the basis for a case
to count votes-against in ties. But there's also aesthetic appeal
in the simplicity of looking only at defeats, keeping it like
the public proposal.

That's one of those things where I'd go with whatever proposal is
made.

***

This discussion of votes-against, other than just in defeats,
has brought it to my attention that, when tie-breakers are 
needed, I'd rather stick with votes-against for a while before
going to other standards. So, as my 1st tie-breaker, I'd rather
use Simpson-Kramer, the relative of Condorcet that goes by
an alternative's greatest votes-against, over all of its
pairwise comparisons.

Then I'd use Beat-Something, and then Fishburn, and then
Stepwise-Plurality.

So my tie-breaker list suggestion would be:

1. Simpson-Kramer
2. Beat-Something
3. Fishburn
4. Stepwise-Plurality

***

Of course when recommending to an organization, other than
mathematicians or detail-tolerant electoral reformers, I'd
suggest just recommending Bruce's Plurality.ext as the
only tie-breaker. It has the advantage of combining decisiveness
with simplicity.

I re-emphasize that, for public elections, there's no need to
even bring up tie-breakers. If they already have one enacted for
Plurality, then we'd leave it in. Otherwise, if they don't consider
that they need one for Plurality, then they don't need one for
Condorcet either. Of course if there's a tie-breaker for Pluralilty
it would be something like drawing lots, or letting the city
council choose the mayor, or holding a 2nd election, etc. It
doesn't matter. A tie is so unlikely that it matters not at all
which of those methods is used.

***

The discussion of votes-against in ties also brings out the
issue of Smith//Condorcet vs plain Condorcet. 

Just as the unbeaten alternative gets its status from what beats
what, so do the members of the Smith set.

Say that there are several alternatives in the Smith set, and they
circularly beat eachother by huge majorities. And say that there's
an alternative not in the Smith set, and only a few peo
ple ahve

That paragraph got garbled by my editor, so let me start over:
Say there are several alternatives in the Smith set, and they
all circularly beat eachother by a huge majority of all the
voters. And say there's another alternative that isn't iln
the Smith set, and that the Smith set alternatives barely
beat it, around 50/50, and that, additionally, the "turnout"
for those pairwise preferences is somewhat less, due to
equal rankings.

So if someone says the Smith set alternatives should get the
election, since every one of them beats everyting else, I
could say that everything in the Smith set has a big majority
of all the voters who say that something else is better. It's
not like they aren't beaten. They're beaten worse. The 
non-member is the only alternative that doesn't havew a
majority saying that something else is better.

I'm not claiming for sure that plain Condorcet has more merit
than Smith//Condorcet, but it seems to me that there isn't
a _conclusive_ case for limiting the choice to the Smith
set. At least not a conclusive case based on merit. I agree,
as I said, that it would be good to include the use of the
Smith set to pre-empt criticism from the opposition in public
initiatives.

Mike






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