This is going crazy, but I cannot now resist.
On Jun 7, 2009, at 1:45 AM, Paul Kislanko wrote:
Let's go back to the original post. Mr Smith called me an idiot for
pointing
out that his claim that approval ballots contain as much information
as
ranked ballots or range ballots do.
This much should have ended it, but this idiocy goes on and ON!
I point out that given a range ballot I can create a ranked ballot,
and
given a ranked ballot (truncation allowed, equivalent to assigning a
zero
for a range) I can create the approval equivalent.
Slipping a bit. If approval was truly equivalent to ranking one would
be able to reconstruct any ranked ballot from an approval ballot that
contained all the ranking information - but approval cannot include
ranking information other than which candidates were approved.
Now, in a 3 alternative ballot with alternatives A, B, and C, I
approove B
and C. Knowing only that, Mr Smith asserts their is as much
information as
there would be if I'd ranked the candidates. I ask him publicly to
derive
from my approval of B and C which one of them I'd prefer, using only
the
knowledge that I approve both of them.
Weak in that Paul has not (and could not have) indicated via approving
B and C, which of them he preferred - but Paul is pointing out that,
with ranking, he could have indicated a preference.
He can't do that, but he calls me an idiot.
That ranked ballots provide more informations than approval ballots
is not
a myth, it is a fact. Mr. Smith can evidently tell from my {B C} >
{A} what
my preference between B and C is. If he can't provide an algorithm
for that,
his assertion that my explicitly telling him provides no new
information is
certainly not correct.
Does not matter whether information in an approval ballot requires the
same length of statement as in a ranking ballot - what matters is that
all that can be said via approval can be said via ranking, but ranking
can say more.
If "ranked ballots provide more information than approval ballots"
is a
MYTH, then Mr. Smith should be able to decide from {B C} > {A} which
of {C
B} is preferred by the approval voter over the other.
Saying it another way, by approving one or more candidates approval
divides them into two groups, but is unable to say anything more about
either group. Ranking, of course, approves B&C , and can indicate
which is most preferred.
Dave Ketchum
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