[Election-Methods] RELEASE: Instant Runoff Voting (Chris Benham)

[Chris Benham]

Abd,

 "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candidate withdrawal, are no longer valid.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."
The utilities I gave were not normalised, they were absolute.  The only
"prepostrous assumptions" I made were that in a 2-candidate election
the voters would  'strategically' only approve the candidate they prefer
to the other, and with 3 candidates the voters might approve the 2 candidates
they  like nearly the same and much better than the third candidate.
"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. "


That is right.  But interpreting Range and Approval in the way needed
for it to meet IIA  means that it fails  even 2-candidate Majority Favourite,
so it doesn't magically evade Arrow's Impossibility Theorem.


"So does Approval satisfy the Majority Criterion?"

No, as stated in Kathy Dopp's paper.
"However, Woodall, it seems, may have thought differently, since, if I 
recall correctly, he considered Plurality as failing Majority."
As has been pointed out to you more than once, Woodall's version of 
"Majority" is equivalent to  Majority for Solid Coalitions (aka Mutual
Majority) which FPP ("First Preference Plurality") can't meet because
it only considers first preferences. 
Chris Benham


Abd ul Lomax wrote  (Sun Jun 22 10:01:40 PDT 2008 ):
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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