[EM] Some unusual Condorcet STV methods

[Richard Lung]

On 15/09/2015 21:34, Kristofer Munsterhjelm wrote:
> On 09/15/2015 07:48 PM, Richard Lung wrote:
>> To all from one new to this group,
>>
>> I have been studying election methods for a long time,
>> including combining Condorcet method with STV.
>> As I believe I mentioned in my first e-mail, I have invented Binomial STV,
>> which does not disqualify any candidate before the (averaged) count is
>> complete.
> Could you describe your method here? I'd be interested in knowing how it
> works, and I imagine the other members of the list would as well.
>


Thankyou Kristofer for your interest.
I have evolved a transferable voting method, descriptively called 
(preference abstentions-inclusive keep-value averaged) Binomial STV.

Traditional single transferable vote is uninomial: it is just a 
preference vote count. Binomial STV also conducts a reverse preference 
count. The latter is an exclusion count to do away with the critique, 
"premature exclusion" of a trailing candidate, when the transferable 
surplus votes happen to run out.

The unfilled preferences or abstentions must also be counted, so that 
the relative importance of preference election count and unpreference 
exclusion count is conserved.
With Binomial STV, if you returned a blank ballot paper, that would be 
equivalent to None Of The Above. But partly unfilled orders of 
preference partly count also towards the quota for an unfilled seat.

A preference election and an unpreference exlusion is a first order 
Binomial STV count. The result is obtained by inverting the  exclusion 
keep values and averaging them with the election keep values (using the 
geometric mean).
Keep values were introduced by the computer-counted Meek method STV. 
However, I extended their use from candidates who are elected with a 
surplus of votes, to candidates still in deficit of an elective quota. 
This extra information is useful in Binomial STV, because winners are 
those who do best on average.

   Binomial STV is a preferential data mining system,which can be taken 
to indefinitely higher orders of election and exclusion counts.
If preference, p, plus unpreference, u, count is given in binomial 
theorem form, (p+u) then the second order count is given by (p+u)^2 = pp 
+ up + pu + uu. This is the formula for a second order truth table of 
four logical possibilities.

The algebra is non-commutative because "up" and "pu" represent two 
different operations.
The second order count qualifies the two first order counts with four 
counts: "pp" means that the most prefered candidate has votes 
re-distributed to next preferences; "up" means the most unprefered 
candidate has votes transfered to next preferences. The candidates keep 
values for these two counts are averaged for an election count. The 
process is repeated, with pu and uu, for an average exclusion count, 
which is inverted, and averaged with the average election count, for an 
over-all average result.

In turn, a third order count (p+u)^3 may qualify the second order count.

Normally it should not be necessary to determine an election result by 
higher order counts. In any case, the system requires an automated 
count, extending Meek method (which might be described as a sustained 
surpluses count). Binomial STV would not include the Meek method add-on 
of reducing the quota, as the preferences run out, because with Binomial 
STV, the abstentions are part of the whole preference information.

from
Richard Lung.
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