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<div class="moz-cite-prefix">On 18/05/2023 07:29, Richard Lung
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:cfb157b0-3c94-0b5a-406b-66d05cd49603@ukscientists.com">
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<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Representation form of Godel sentence and Binomial
Meek</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">A Kurt Godel sentence is of the form: This
sentence is unprovable.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Its representation form would be: Representation
is unprovable. Of which its truth is simply proved.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">A determinate analysis cannot be deduced from an
indeterminate basis. There is no observable “collective
consciousness” or “divine right” of representation.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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. </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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. </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Completeness, in the count, requires conservation
of (preference) information.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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. </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">(Five Golden Rules, by John L Casti)</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Regards,</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Richard Lung.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
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