The HG Wells formula.

“The problem that has confronted modern democracy since its beginning has not really been the representation of organised minorities – they are very well able to look after themselves – but the protection of the unorganised masses of busily occupied, fairly intelligent men from the tricks of the specialists who work the party machines.”

HG Wells, 1918: In The Fourth Year.

Quoted by George Hallett with Clarence Hoag: Proportional Representation. The key to democracy. (1937 ed.)

The law of electoral entropy proposes that the organised few (as in parties) forestall the organisation of the many (as for government) by disorganising the electoral system.

First and most decisive degrading or disorganising (of the Andrae and Hare system) was to omit the preference vote from most proportional elections, leaving “The Vote” as a stub vote, a mere X vote, or one-preference vote to count only for the organised few, the parties, rather than the disorganised many, or all the people.

By 1918, HG Wells already was having to avoid misunderstanding, by defining the organised voting system, as opposed to its relentless disorganising by the meanest interests (so vividly described by Hallett and Hoag).

“The HG Wells formula” is proportional representation by the single transferable vote in large constituencies.

For, confining the vote to one preference, an X vote, no longer freely transferable in a proportional count, and confining the choice of representation, to one or few seats per constituency, enfeeble the information value of a general election.

and “HG Wells principle” (1916).

If there is no true election method, then no election method can truly choose an election method.

If there is a true election method, then, the truth being one, there is no choice of true election methods.

Without knowing the right election method for electing an election, there is no way of knowing how to elect it. If you do know, the election of an election is superfluous.

The widespread assertion that there is no such thing as right and wrong, in election methods, is a paradox.

If this statement were right, it would contradict itself, and is therefore wrong.

If this statement were wrong, then there is such a thing as right and wrong, in election methods.

This demonstrates (in The Elements of Reconstruction) “HG Wells principle” (1916) of scientific treatment – in this case – of voting method: voting method is “not a matter of opinion but a matter of demonstration.”

]]>I call my demonstration of this identity, the mirage demonstration.

A mirage is a scene of deceptive proximity (caused by atmospheric lensing).

In the context of elections, I define a mirage as a deceptive (ap)proximation.

The idea that there is a proportional count of parties or groups is a mirage that progressively recedes the more proportional the count is made, as more parties win less seats between them.

The more proportional the count, the more particular the extra parties become.

Taken to its extreme, every individual would be their own party. This is the reduction to the absurd (reductio ad absurdum) of party proportional counting for representative democracy.

Even a mirage has a basis in reality. Electorally, that reality is freedom of individual choice. That is the moral of the mirage. As John Stuart Mill said: “Proportional Representation” is “Personal Representation” (by “Mr Hare’s system”). His posthumous Autobiography explicitly accepts both terms.

Recently, I realised that second order or higher order Binomial STV could be subjected to another error-minimising averaging of recounts. Formerly, I assumed that recounts from redistributing the vote could be done on a plurality basis. The most prefered or the most unprefered candidate would have their votes redistributed to modify candidates keep values (according to the binomial theorem patterns of preference and unpreference counts).

I modify this method by redistributing the votes of each candidate, in turn, and then taking the arithmetic mean of the candidates keep values for each redistribution count.

This means that Binomial STV can be subject to three error-minimising averages: the geometric mean of election and exclusion keep values; the arithmetic mean of possible redistribution recounts; as well as the Harmonic Mean quota to neutralise the respective undemocratic shortcomings of the Hare and Droop quotas.

]]>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 ]]>