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<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">STV and the Incompleteness theorem</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"">Mathematicians would understand this much better
than I. Apparently, no algorithm or step-by-step procedure can
be both consistent and complete. This appears to be the case
with traditional or conventional Single Transferable Vote
compared to Binomial STV (STV^).<br>
</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">All the established forms of STV might be
characterised as returning officers counts. That is to say the
returning officer is expected to return winning candidates to
all the available seats in the constituency. Meek method
computer count goes out of its way, even more than the
traditional hand counts, to achieve completeness, in its
completely returning contestants to all vacant seats. But in the
extra attempt to ensure completeness, Meek method only adds an
extra inconsistency. This inconsistency is the reduction of the
quota, as voters use up all their preferences. The entire board
of the Electoral Reform Society, which knowledgeably ran a
ballot services, in those days, opposed quota reduction. It was
a breach of principle. Those who expressed more preferences,
accordingly had fuller use of their vote, which breached the one
person one vote principle, or voter equality.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">(This is true, but on balance, Meek method is a more
consistent system than STV hand counts, because
post-quota-achieving preferences continue to be counted, in the
so-called keep value. So it was a blessing that Meek method has
some use in official New Zealand elections.)</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">The more basic inconsistency of both traditional STV
and Meek method </span><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""><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold";
mso-fareast-font-family:SimSun;mso-bidi-font-family:"Times New
Roman";
mso-ansi-language:EN-GB;mso-fareast-language:ZH-CN;mso-bidi-language:AR-SA">(as
well as all other official elections!) </span>is the
inconsistency of their election counts with their exclusion
counts. The election procedure is rational but the exclusion
procedure is only ordinal; a sort of exclusion by “last past the
post,” as the election surpluses run out.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">I would call these former STV methods zero order STV
(STV^0). Binomial STV (STV^) is at least first order STV
(STV^1). Binomial STV, however, is consistently rational both in
its election count and its exclusion count, which are indeed
symmetrical, merely proceeding from last preferences to first,
instead of first preferences to last.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">As the Kurt Godel theorem states, the consistent
system is not complete. In this case, STV^ cannot achieve the
completeness that former STV systems achieve by sacrificing
consistency.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">However, incompleteness, with Binomial STV, is
justified, as there undoubtedly are elections in which the
voters are not satisfied with some or all of their would-be
representatives. Not only NOTA is counted but every single
abstention. Binomial STV allows or suffers the widest
preferential evidence, previously prevented in not counting
abstentions. Abstentions are consistent with allowing the
possibility of incomplete elections, but empirically consistent
with or true to the level of voter discontent.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Man cannot live by logic alone. Albert Einstein
followed the philosophy of the principle theory or reasoning
based on deductions from a firm foundation of evidence.<br>
</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>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
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