At 03:58 AM 6/22/2008, Chris Benham wrote:
Kathy,
I choose my words carefully.
"You managed to invent a really bad voting method (asking voters for
ratings and then converting their ratings to approval/disapproval by
your new voting method) and applied your method of conversions to your
own example, but it has nothing to do with either range or approval
voting methods."
Apart from a passing reference to Range the only voting method I discussed
or referred to was Approval.
I didn't suggest that voters be "asked for ratings".
40: A100, B98
25: A98, B1
35: B100, A1
These numbers I gave represent nothing outside the heads of the
individual voters.
I'm sorry if I didn't make that clear enough. This corresponds with
the use in
EM circles of the word "utilities".
On one level, Chris is correct. However, that Kathy didn't
"understand" that points out a problem that may be obvious to a
relatively newcomer to the topic of alternative voting systems (Dopp)
but not so obvious to someone who has been immersed in the topic for
years. When you assume a set of ratings which are clearly normalized,
they are no longer independent and absolute, and conclusions drawn
from them, based on the introduction of a new candidate or a
candidate withdrawal, are no longer valid. By using normalized
utilities, and assuming that they remain the same, Chris has made a
preposterous assumption, so no wonder his results are defective.
Range and Approval do not violate IIA as originally interpreted.
However, it's possible to reinterpret IIA to apply it to
nonpreferential ballots, in a particular way, and Range and Approval
can thus be made to violate this new version of the criterion.
Essentially, if voters change their votes as a result of the
introduction of new candidates, a different result may occur that
doesn't involve that new candidate being a winner. Chris and I have
had this discussion many times as it relates to the Majority Criterion....
If a majority of voters express their strict preference for a
candidate in Approval, that candidate must win. But if they dilute
that expression with approval of another candidate, that candidate
might lose (to a candidate with a *larger* majority). So does
Approval satisfy the Majority Criterion? It depends on the definition
and, problem was, the original criterion did not contemplate equal
approval of candidates at the "top of their preference lists," and
there was no distinction made between preference lists and actual
votes in the election. A complete ranking was simply assumed.
However, Woodall, it seems, may have thought differently, since, if I
recall correctly, he considered Plurality as failing Majority. I'd
have to review this to make sure I got it right....
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