Re: [EM] Representation form of Godel sentence and Binomial Meek
On 18/05/2023 07:29, Richard Lung wrote:
Representation form of Godel sentence and Binomial Meek
A Kurt Godel sentence is of the form: This sentence is unprovable.
Its representation form would be: Representation is unprovable. Of
which its truth is simply proved.
The proof is that representation is a contingent relation. Innumerable
chance factors, known and unknown, influence the voters choice of
representatives, which is thus indeterminate, beyond not always
reliable approximations.
A determinate analysis cannot be deduced from an indeterminate basis.
There is no observable “collective consciousness” or “divine right” of
representation.
The Godel sentence that representation is unprovable must, therefore,
be true. According to the Godel Incompleteness theorem (completeness
is inconsistent with consistency) this follows from a formal
(election) system that is consistent.
However, the generality of election systems are complete, in their
election to all the seats. But they are inconsistent two-truth
systems, in their differing election counts to their exclusion counts.
The exception to the generality is Binomial STV. An acceptable
alternative name for this election method is Binomial Meek (method).
This is because Binomial STV uses Meek method of surplus transfer, not
only for the election count, but also for the exclusion count. The two
counts are symmetrical, with the order of preference counted in
opposite directions. The exclusion count is an iteration of the
election count, with the preference order reversed.
The over-all count procedure has to be incomplete however, because
abstentions remain to be counted, in order to establish the degree to
which voters like or dislike the candidates, from the relative
importance of abstentions in the election count and the exclusion count.
Completeness, in the count, requires conservation of (preference)
information.
Whereas, the generality of voting methods leave out abstentions, as a
(consistent) source of information, or bench-mark, of the true weight
of support for, or disenchantment with candidates.
The guaranteed complete election of all the candidates is at the
expense of complete information conservation. This amounts to an
inequitable count of preferences which violates consistency.
Thus, Binomial STV or Binomial Meek method consistency of election and
exclusion counts has also to be complete with respect to conservation
of preferential information, or else it would not be consistent, in
that respect.
This suggests to mathematicians that the incompleteness theorem needs
qualification, with regard to degrees of completeness. For, it may be
the case, that just as there are degrees of infinities, so there may
be degrees of completeness. So, it is true that Binomial STV is
consistent of election and exclusion counts, and incomplete with
respect to always filling all the seats.
But it also seems to be true that Binomial STV has to be complete with
respect to conservation of information or it would be inconsistent in
that respect. In qualification of the incompleteness theorem, it would
seem that some degree of completeness is required for consistency,
while allowing for another degree of incompleteness.
(Five Golden Rules, by John L Casti)
Regards,
Richard Lung.