[EM] Representation form of Godel sentence and Binomial Meek

[Richard Lung]

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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