[EM] STV and the Incompleteness theorem

[Richard Lung]

STV and the Incompleteness theorem

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^).

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.

(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.)

The more basic inconsistency of both traditional STV and Meek method (as 
well as all other official elections!) 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.

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.

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.

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.

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.

Regards,

Richard Lung.


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