[EM] To Steve re: criteria, Plurality, majority, etc

MIKE OSSIPOFF nkklrp at hotmail.com
Wed Mar 6 20:57:34 PST 2002


Steve Barney said:

DEMOREP1 at a...:

Your point is well taken. Our exchange seems to illustrate a problem with 
axiomatic approach in general, where you may find the procedure which 
the fulfillment of this or that fairness criterion. The problem is that you 
overlook the fact that it seriously violates other criteria.

I reply:

So don't overlook other criteria that you consider important. I mean,
wouldn't it be pretty silly to advocate a method because it passes
one criteria that you like, though it fails other criteria that
are very important to you? And if you do overlook that, then hopefully
someone will point that out to you.

It makes no sense at all to criticize the use of criteria because
it's possible for a method to pass one criterion that you like, while
failing others that you like. If you don't notice the failures, don't
blame the criteria.

Steve continued:

That was
illustrated by my highlighting of the fact that the plurality vote is the 
positional voting procedure which always elects a majority candidate when 

I reply:

What do you mean by a majority candidate? If you mean a candidate
who is favorite to a majority, then Plurality doesn't always elect
a majority candidate when one exists. Not unless you stipulate sincere
voting, which would be fantasy in Plurality.

If you mean a candidate whose vote total exceeds half the number
of voters, Approval & CR always elect a majority candidate when
they exist.

But we can say this for Plurality: It's the only method that always
elects the candidate voted the most favorite. Yes, that's almost
a repetition of Plurality's definition, but it's still true, and it
still sounds more desirable than undesirable.

Obviously that criterion conflicts with most of those that are
important to most of us, and so we politely pass up Plurality and
choose methods that meet criteria more important to us.

Still, it's worth pointing out that IRV can fail to elect a sincere
CW or a voted CW even if s/he is the voted favorite of more people
than any other candidate, and that even Plurality won't do that.

In Runoff, a sincere CW can't lose if s/he comes in 1st or 2nd in
the primary. That's a very big advantage for Runoff compared to IRV.

Steve continued:

So, you
see, the axiomatic approach [by which I assume Steve means the use
of criteria]...

...may provide insufficient information for a proper
evaluation of voting procedures.

I reply:

...if you only consider a method's score on some but not all
of the criteria that are important to you. But that's only your
fault, and it's only your problem.

Criteria are the way to say something definite about what a method
will do. But it looks as if now Demorep has an ally in opposing the
use of definite statements about what a method will do.

Steve continued:

Saari's approach, on the other hand, seems to
differ in that he attempts to describe ALL possible problems with large 
of voting methods.

I reply:

I hope he does so with more clarity than is had by that sentence.
So Saari describes all possible problems of voting systems? That's
odd, I hadn't heard of him discussing the strategy problems that
have been discussed here. If he did, it would be difficult for him
to advocate Borda, perhaps the only proposed method that can
fail to elect a candidate who is the voted favorite of a majority.

Borda creates co-operate/defect dilemmas where even Plurality wouldn't.
Borda fails Myerson's corruption-encouragement test in the
most ridiculous and extreme way, in a way that no other method
approaches. Does Saari discuss these problems of voting systems?

Mike Ossipoff

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