At 11:48 AM 6/20/2013, Jameson Quinn wrote:
Separately: I don't understand why you insist that "D" is an
unapproved grade. I have never treated it as anything but just
another grade. Obviously, any candidate who won with a "D" rating
would have a very weak mandate.
...It's a mess. Keep it simple.
Right. That means, no special separate rules for "D".d
Like, no "D."
GPA ratings.
Right. That means D is a 1.
And that would mean that, on a 4-point range scale, 1 is the approval
cutoff. Not good.
1 is below an "expected result approval cutoff."
Wrong.
First, you're the one insisting that the system be analyzable using
Score/Average.
Yup. The one. Do you have any idea who I am?
I'm saying that Bucklin *is* analyzable as using a Range ballot, with
all ratings being approvals. It makes complete and easy sense of the
system, how it works.
But analyzing any set of ballots using a system other than the one
they were cast under is always going to be a questionable
proposition. If it doesn't work, let it go; keep it simple.
No, Jameson, you have not understood. I am not analyzing Bucklin
using Range Voting strategy. I am analyzing Bucklin considering the
basic Bucklin ballot to represent a sincere Range ballot controlling
a series of simulated approval runoffs.
Range *ballot*, not Range voting system. As a single ballot, in an
approval voting system, it does not make sense to vote for a
candidate if one is not willing to approve of the candidate. Bucklin
*is* approval voting, only with approvals staged, for obvious
reasons. Classic approval strategy suggests approving all candidates
above the expected election value. We've seen that advised again and again.
So ... arrange the candidates on a Range spectrum, with the middle
representing the election expectation. So the range represents
utilities above the middle and below the middle. These are Von
Neumann-Morgenstern utilities, i.e., those studied by Dhillon and Mertens.
The system and translation you are proposing, Jameson, has the
utility of a D, an approval, being very close to the utility of the
worst possible candidate. It's radically unbalanced. Nobody would
actually approve of a candidate with such a poor utility, unless they
*know* that this is needed, that everyone else they prefer must lose.
Just realize this: most Bucklin elections are likely to collapse all
the approved ranks. The election will become pure approval.
Second, if you believe that D will be the winning median, and there
is some candidate with three times the utility of your preferred
frontrunner, it is perfectly honest and rational and
utility-consistent to vote your preferred frontrunner at "D" as an
approved vote.
It becomes useful for Condorcet analysis, especially. And it can be
used in a tiebreak. It can be used in study of voting system
results. It can be used in runoff nomination rules.
Thank you for making my point. "D" has some value. And so does
keeping the rules simple.
It has a value, but it complicates the rules and explanation, and
allowing it to be an approved category vastly disrupts the simplicity.
Or it can be unused because unexpressed on the ballot, simpler
system. Tiebreak can still be sum-of-votes, among majority-approved
candidates.
This is better for honest votes, but worse for the chicken dilemma.
Yes. Slightly "worse." Remember, I don't consider the "chicken
dilemma" to represent an actual harm. The problem causes voters to
balance utilities, which is a *benefit*. Removing the dilemma
actually removes some information from being used by the system.
The system already does pretty well with honest votes, so fixing
the chicken dilemma is more important. And anyway, that would be a
different system.
It is *offensive* to disregard the additional approvals after
counting them. Counting them at fractional vote value allows them to
be considered at a deprecated value, which is accurate as far as
utility expression is concerned. That deprecation ameliorates an
*exactly appropriate amount of the chicken dilemma." The error from
overenthusiastic approval, which is what causes multiple majorities
to appear, is *reduced* to an accurate representation of preference strength.
So we have a hybrid between seeking majority approval, and seeking
utility maximization. Voters will be more likely to add votes at
lower preference, knowing that they are *less likely* to cause the
election of a more-preferred candidate.
If D votes are allowed, I'd complete the Bucklin amalgamation at D.
If no majority has been found, then if the election must complete,
I'd consider pairwise analysis using those D votes, or better, in
theory, sum of scores. Pure Range.
Be there or be square.
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