# [EM] Representation form of Godel sentence and Binomial Meek

Richard Lung voting at ukscientists.com
Wed May 17 23:33:21 PDT 2023

```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.
>
>
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