Overstated Problems

[Mike Ositoff]

In a recent message to an individual that was inadvertentlyk
posted here, due to a problem of the mailer, I admitted that
Condorcet(EM) has problems with order-reversal. But it's important
to keep that in perspective by pointing out that all the other
simple methods, except for Schulze, have considerably worse
problems. Simpson-Kramer is almost as good.

And if some members of an electorate were sophisticated & devious
to use order-reversal, others would be sophisticated & well-informed
enough to deter it by defensive strategy, as I've described.

Plus, Tom Round, Steve, & I have also discussed enhancements
that could be added to simple methods, to gain better strategky
protection. That future sophisticated electorate could choose
to adopt some of these enhancements.

Tese include a candidate withdrawal option, a 2nd balloting
(in methods such as BeatsAll//Approval & Smith//Condorcet///Approval),
and an option for the voter to indicate his specification of
what the believes to be the 1-dimensional ordering (such as a
political spectrum) that he believes the candidates or alternatives
to have. I've already described that option here, and this letter
probably isn't the place to describe in detail this or the other
enhancements.

In that previous letter, I also said that, if there's a subcycle,
then that could cause Condorcet(EM) to require a defensive strategy
of ranking a less-liked alternative equal to a more-liked one in
order to protect a Condorcet winner. But it must be pointed out that
a Condorcet winner would never be in a natural cycle of any kind,
so we're talking about a _strategic_ cycle, engineered by
impossibly sophisticated offensive strategy, using impossible
predictive information.

Say it's a Green,  a Democrat, & several Republicans. You're
a Green. The Democrat is Condorcet winner. You want to steal his
win by order-reversal, but you know that defensive truncation is
probably being used against the Green, making it impossible for
you to make the Republicans as beaten as the Green is. So, if you
still want to try the order-reversal, you have to do more than jkust
make a fake main cycle--you must also engineer a fake subcycle among
the Republicans, making each of them beaten by as big a majority
as the Green is. Bigger, actually. For that, you must have 
very good information about how the Republican & Democrat voters
rate the various Republicans with respect to eachother, and make
use of that information to make a cycle among the Republican
candidates such that everyk Republican has a bigger majority
against him than the Green does.

What? You wouldn't want to try that? Neither would anyone else.
It sounds impossible, to me, due to the predictive information it
needs.

So I can safely say that Condorcet(EM) doesn't require ranking
a lower-ranked alternative equal to a more liked one in order
to protect a Condorcet winner. Of course it also never requires
ranking a less-liked alternative _over_ a more-liked one either.

***

I've been a little unfair to Saari's point systems. What I was
arguing was that, by the standards that I've said are important
to many people, including us, point assignment systems can't be
as good as Condorcet(EM) or Schulze. I stand by that claim, but
point assignment methods are better than the _worst_ rank balloting
methods such as IRO.

I've recently advocated a point-assignment method on ER: Approval.
You give each candidate either 1 or 0 points. Though, with a
flexible point system like the ones that Saari proposes, one
could calculate strategies to optimize one's statistical expectation,
it would be a difficult calculation, based on one's utility ratings
for the candidates and some probability estimates. Voting an
Approval strategy is simpler. Weber, in the Winter 95 issue
of _Journal of Economic Perspectives_, describers an Approval
strategy calculation. Of course most voters aren't going to do
that either, any more than they do a similar calculation with
Plurality. What most will do will be to just vote for the candidate
they expect to need as a compromise, the Condorcret winner (though
they might defect on the CW if they believe that someone they like
more will get more votes than all those whom they like less), and
for everyone whom they like more.

My point, then, is that the added flexibility of the methods that
Saari proposes would just confuse people, and only a few mathematicians
would actually be qualified to calculate strategies that would make
use of that flexibility. But I do agree that, as far as basic merit
goes, Saari's methods are as good as Approval--though they're 
unnecessarily complicated and confusing for voters. The advantage
of Approval over Condorcet(EM) & Schulze is its _simplicity_, ;and
ease of implementation. Saari's flexible methods would lose that
advantage.

However, the best of the methods that are already familiar to the
public, in my opinion, is the Olympic 0-10 method:

Voters may give anywhere from 0 to 10 points to any alternative.

Again, the flexibility would be difficult for nonmathematicians to
use, but this method has the very big advantage of prior familiarity
to the public.

Mike