More Standards

[Blake Cretney]

On Tue, 20 Oct 1998 21:02:32   Mike Ositoff wrote:
>
>Blake proposes a Marginal Majority Criterion, but, except for
>the fact that any pairwise proposition can be called a
>"majority", his criterion isn't about majority. It's about
>margins. It should just be called "Margins Criterion".

Maybe I should have called it the Margin of Majority Criterion

>
>Though I've already told why "random fill" isn't a problem,
>I'd like to add that in Margins, when nothing is known about
>other voters, a voter can gain by random fill. 
>
>He can gain by random fill in Schulze(VA), but he can also
>lose by it. So it isn't clear how that consideration is
>supposed to distinguish between Margins & VA.
Because random-fill works on average in VA, even if no information
about how other voters voted is known.  And the average case is what
motivates a rational voter.  I know you don't think this is an 
important difference, but that isn't the same as saying there is 
NO difference.

>
>As for finding the best candidate or the worst candidate,
>I believe that Blake is chasing a rainbow when he speaks 
>of finding the best candidate.  We can try to avoid specified
>strategy problems, and majority rule violations, but it's
>rather overambitious to speak of finding the best candidate.

Of course, I don't think we can expect to find a method that finds
the best candidate ALL the time.  After all, much of the time the
voters themselves will be wrong.  However, I think our goal should
be a method that finds the most likely best candidate based on the
ballots.

For a simple example, if there are only two candidates A and B, and
all we know is that 60 people vote for A, and 40 for B, then we have
to conclude that the best guess for best candidate is A.  To me, this
seems pretty clear.

Of course, the conclusion here is the same as that from the principle
of majority rule, but starting from a more basic premise.  Everybody
would agree that we should be looking for the best candidate (where
they agree that it is possible), but not everyone will agree with 
majority rule.

In more complicated examples, not everyone even agrees on what 
majority rule means.  In fact, we all seem to have our own 
definitions to fit whatever method we advocate.  And it is impossible
to prove that anyone's definition is wrong.  People can define words
any way they wish.

Our arguments take on the character of scriptural debates, where
people all agree that a particular phrase must be true, but
disagree widely on what it means.  When I say that
I support majority rule, I do so because I think that the
majority will give the best guess for the best candidate, and
my argument for majority rule frames my definition of it.  I
would be interested to hear arguments for majority rule that
do not derive it from the search for best candidate.

So, I think that best guess for best candidate is in fact a 
more realistic goal than a direct search for arbitrarily 
defined majority rule.

And you can make strong arguments that certain methods do not
find the best guess for best candidate, at least in some
situations.  For example, methods that violate monotonicity.

>l've replies several times to the arguments regarding
>to reversal of rankings. I refer Blake to the archives.

Perhaps even more obvious is the argument against methods that
are reverse-inconsistent.  That is, consider a method that says 
the  best candidate is candidate X for some ballots.  Now reverse
the candidate order on all ballots, so they are now ordered to 
determine the worst candidate.  If the worst candidate is found 
to also be X, the method is reverse-inconsistent.  That is, it 
can't possibly be right both ways because it contradicts itself.

Of course, this isn't a strategy problem.  But we should be
concerned with more than just strategy problems.  There is
little benefit to a method that forces everyone to vote
sincerely, if the method gives bad results even when they
do so.




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