John Pyke, Vice-Pres, Proportional Representation Society of Australia

]]>STV Evolves.

I have evolved a transferable voting method, descriptively called (abstentions-inclusive keep-value averaged) Binomial STV.

And a new quota: the Harmonic Mean quota.

An explanation (which will later be in my e-books) is here:

Binomial STV and the Harmonic Mean quota.

http://www.voting.ukscientists.com/kabstv.html

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 have run out.

Unfilled preferences or abstentions must also be counted to preserve the structure of the relative importance of greater to lesser preferences. (The abstentions may achieve a quota that leaves a seat vacant.)

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 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. And so on.

Binomial STV can be used on any STV count but would require a computer program and its level of analysis would only make sense in conjunction with Meek method, but without the quota reductions to help fill all the seats. Since Binomial STV includes preference abstentions in the count, it makes no sense to worry about any seats left vacant when the preferences run out.

Now you dont need Binomial STV for ordinary elections. Traditional (uninomial or zero order) STV is by far the best method compared to the anarchy of rotten voting methods in politics.

For systematic analysis of preferential data, Binomial STV might interest the data-mining community.

Harmonic Mean quota.

The Hare quota (votes/seats) and the Droop quota (votes/(seats plus one) are respectively maximum and minimum range limit quotas. Since they are harmonic series, the average of their range is the harmonic mean, which works out at: votes/(seats plus one-half). Hence, this is the Harmonic Mean quota.

The HM quota is justified because the Droop quota may deliver statisticly insignificant margins of victory, and the Hare quota may require levels of support only possible with deferential voting.

Ive just published the first of two free e-books on electoral reform and research:

“Peace-making Power-sharing” can be obtained free from Smashwords here in epub format:

https://www.smashwords.com/books/view/542631

It is also available from Amazon, which makes the author charge at least $0.99 until they find out it is free elsewhere.

The Amazon kindle (mobi) format is available here:

http://www.amazon.com/dp/B00XM3CE2O

From

Richard Lung.

http://en.wikipedia.org/wiki/Electoral_reform_in_New_Zealand ]]>

http://www.atheistnexus.org/profiles/blogs/proportional-representation ]]>