[EM] STV & Incompleteness theorem continued.

[Richard Lung]

STV & Incompleteness theorem continued.


The voting systems of the world aim for completeness. In other words, 
official voting systems aim to complete the election of all the 
available representatives. This is achieved despite inconsistencies in 
those voting methods. This is in accord with the Incompleteness theorem, 
which applies to algorithms in general and not merely democratic or 
would-be democratic procedures.

Thus, the incompleteness theorem is sufficient to explain the democratic 
inconsistencies of official elections.

The incompleteness theorem explains Binomial STV, in contrasting 
fashion. STV^, contrary to official methods, is a consistent system but 
an incomplete one. The incompleteness, however, is justified, not by 
logic, but by the evidence that voters may be incompletely satisfied 
with candidates put before them.

Therefore, it is not necessary to postulate an Impossibility theorem, to 
explain inconsistencies in democratic procedure. Indeed, Binomial STV 
shows that democratic procedure can be a consistent, tho incomplete, 
election to all the vacancies.

The negativity of the Incompleteness theorem is echoed in the so-called 
Impossibility theorem, theorem Arrow. A moral for the incompleteness 
theorem, man cannot live by logic alone, also demonstrates that 
mathematics is not enough to study elections. Mathematicians do not live 
in a logical vacuum but within a social context. The nineteen fifties 
was a particularly unfortunate time for electoral democracy in the USA, 
when the monopolistic city machines already almost exterminate STV/PR.

The Impossibility theorem attempts to show that an electoral system, 
based on a few reasonable principles, nevertheless falls into 
inconsistencies. However, the “skeleton key” or all-purpose epitome of 
election systems, set-up for analysis, is itself a flawed model, indeed 
an inconsistent correspondence of a vote to a count. So it is 
“impossible” to see how anything but inconsistencies of voting method 
could be deduced from the impossibility theorem. Kenneth Arrow adopts a 
multi-preference vote with a single majority count. But a single 
majority count follows from a single preference X-vote. And a ranked 
choice vote, an ordered choice or multi-preference vote, 1, 2, 3,…, 
elects a multi-majority count, of 1, 2, 3,…, Members per district.

A form of Alternative Vote, chosen by Arrow, may push some voters to 
elect their fifth preference, say, to a single-member monopoly. But that 
is not the purpose of many orders of choice, at all. Rather, it is to 
proportionally elect mostly highly ranked choices, mainly first 
preferences, to a district of many members. This may be called the 
Andrae principle, after the original inventor of vote-count consistency.

Many prestigious demonstrations, of the Impossibility theorem, appear to 
owe more to an Arbiter of Fashion, such as a bountiful prize-giving 
committee, than a credible proof. Generally, they consist of a handful 
of single-member voting methods (which monopolies are the least 
democratic) whose results differ, on the differing exactness of their 
respective counts. The impossibility theorem, as characterised, is not a 
theorem on the inconsistency of election methods. It is merely a 
demonstration of greater or lesser statistical accuracy in a count.

These alleged impossibilities of democracy amount to an academic echo of 
the Machine politics, that banished “effective voting” from American 
city elections, as it is banished from scientific consensus.

The New York Times published a petition of over 200 academics, calling 
for Congress to be elected by multi-member personal proportional 
representation, according to Voter Choice Massachusetts.

Regards,

Richard Lung.


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