And other answers to social choice theory.


Equilibrium STV (Hill Real-time PR).

Hill refers to Thomas Wright Hill and Rowland Hill and their early 19th century school childrens election by proportional representation.

 Mass election methods consist of procedural rules often put into computer languages for speed and efficiency of execution. But these formal rules of voting method are less flexible and efficient than the archetypal or original scenario of proportional representation.

Schoolchildren formed uniform queues or quotas behind their prefered candidates, till the given number of committee seats were filled. Candidates with too many supporters were elected but lost their surplus to next prefered candidates. And candidates with too few supporters were excluded but their voters went to their next prefered candidates needing more support.

 This is a real-time election in which all the voters can see what each other is doing and, thus fully informed, act according to their best interests, until the equilibrium of a final result.
Hence the suggested name of Equilibrium STV (Hill Real-time PR) where STV/PR stands for Single Transferable Vote/Proportional Representation.

In a mass election, formal rules do their best to achieve an approximation to the ideal of Hill Real-time PR. In a manual count, the procedure must not become too complicated and prohibitory of replication.

 But it would be possible to do a computer simulation of Hill Real-time PR for large-scale elections. All the voters would have access to a computer network. They would cast a vote for their most prefered candidate and the computer screen would show the lengths of queues for each candidate, in the form of bar charts.

 There would be a finishing line, kin to the finishing post. As in multi-member local elections, there needn't be just one winner. But the difference between first past the post in single or multi-member constituencies and Equilibrium STV is that the voters would be able to see on-screen whether their vote was not needed by a surplus candidate or would be wasted by a deficit candidate, with respect to the finishing line. If so, voters could transfer their vote to their next preference. This could go on till the required number of representatives, in the constituency, each had the required quota of votes.
Equilibrum STV prevents voters being cheated of representation by First Past The Post.

The required minimum is the Droop quota. But the on-screen bar chart, of queues of support for each representative, might show greater than minimal support for some representatives. That is anything up to a maximum of Hare quota support, in the final equilibrium of the election result.

Moreover, the count history of the bar chart would show how support oscillated between the candidates before representative equilibrium was reached. This history would reveal which candidates were the most popular but lost surplus votes to help next prefered candidates. Indeed, voters might consciously adopt this policy of first queing behind their favorite candidates before changing to help next prefered candidates.

In Equilibrium STV (Hill Real-time PR) the computer is programmed to become the eyes of the mass electorate so that all the voters know what each other is doing. This is essentially the same in principle as Hill schoolchildren STV.

This system cannot be criticised as a system of formal rules which every attempt to make more pedantically reasonable disproportionately makes more complicated.

 Instead, the result is arrived at by the direct consensus of all the voters. Die-hard critics may not be satisfied but the voters are: they have reached equilibrium; the result is settled.


Mistaking democracy for formal rules of mass elections.

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 A few years ago the social choice theorists gave themselves a 50th birthday celebration. In my opinion, a suitable after dinner speech might have been titled 50 years of going nowhere fast for democracy.

 It seems to me that social choice theory is based on misconceptions. Firstly it is not a refutation of democracy or even the limitations of democracy from a logical point of view. There is no basic critique of the original practice of proportional representation as described by Rowland Hill of the school of his father, Thomas Wright Hill. This was a real-time election by a limited number of children.
The problem was how to scale up this kind of election for
a large number of voters who can't see what each other are doing.

 The need to reduce the complexity of mass elections to a manageable set of rules resulted in the gradually improving STV system, which was bound to be less flexible and efficient than the original Hill scenario.
The main reason for inaccuracies is not attributable to the
admittedly crude rules themselves but to the use of disproportionately small constituencies. While STV algorithms are doubtless not completely rigorous, they are near enough to pass the tests of actual elections. Most peoples first preferences are elected with higher preferences accounting for nearly all the rest.
It shouldn't be forgotten that such
tests are as important as logical rigor in science.

Criticising a straw man method as democracy.

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 Now to the next basic misconception of social choice theory.
demonstrate the logical limitations of democracy requires at least to pick on the best democratic model available. Iain Maclean, in Democracy and New Technology, states the social choice assumptions as preference voting combined with over-all majority counting.

That is single-member majorities, which over-looks the rationalisation by the Droop quota into multi-member majorities. Single-member majorities of over half the voters generalise to multi-member majorities of two members with over one-third the votes each, giving a proportional representation of two-thirds the voters.
Three-member majorities give a PR of over three-quarters the voters. And so on.

The purpose of scientific theory is to generalise understanding. But social choice theory has confined itself to the special case.
No one
apparently but social choice academics believe that the alternative vote or something like it matches a generally adequate form of democracy. (AV wastes most first preferences and that from a much poorer choice than STV offers.)

It appears they have merely uncritically assumed a model of democracy

that is no more than a poor substitute of a straw man, just as the UKreferendum on the alternative vote was straw man referendum that

nobody asked for or really wanted, but was all the two-party oligarchy was prepared to offer before plunging into their coffers to snatch it back in propaganda terror of the most minor democratic improvement.



Mistaking information-deficient voting methods for lack of (reasonably) definitive method.

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Bob Richard said: Social choice theory is a branch of economics, not political science.

I agree that developments often are conditioned by their origins. Civilnuclear power hasnt escaped for fifty years from its military shackles touranium fission, when if the policy of keeping people alive, instead ofkilling them, had been in effect, the nuclear industry might have ahalf-decent thorium power model.

 Yet another serious error about social choice theory.
John Allen Paulos in Beyond Numeracy in the Voting entry uses an example of five different voting systems producing five different results. But the claim that this verifies the likes of Arrow's theorem is unsubstantiated.

What it amounted to was that the different systems used more or less voting information that left more or less leeway for error in counting the winning candidate.
This could be shown by substituting the Condorcet method with a more accurate version proportionly weighing by how much one of the pairings of candidates won. (I did that from my education in basic statistics. I didnt know that Kemeny had done something like it. At least I think it would be called the Kemeny-Condorcet method.) Anyway, the proportionly weighted Condorcet method agreed with the Borda method result. That is to say the two most informative counts did get the same result. (I showed the working on another web page.)

It appears that effective election methods are a function of the information they gather.

And this brings me back to a previous theme. That the single transferable vote uniquely follows the widely accepted four scales of measurement. This really is another way of saying that STV has by far the greatest power of information collecting.

Without rehearsing what that is - innumerable of my web pages have repeated it - it boils down to the fact that STV tells what the voters want comprehensively and in detail.

Politicians hate that. They want a "mandate" from the public do do what their mercenary hearts tell them to do and then tell us to live (or die)with it.

Brian Greene asked John Wheeler what he thought the coming thing of physics would be. He thought about it and replied: information.
Information could become the central theme of voting method.


Social choice theory in context of mathematical physics.

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Unqualified I admittedly am to discuss this.
Social choice theory with respect to Arrows theorem is essentially an adaptation of Godels incompleteness theorem. This was a qualification on the completeness of the rigor with which logical deduction could be carried out, in the context of the program of Russell and Whitehead in their Principia Mathematica, to base mathematics on logic from first principles.

Bertrand Russell tells in his Autobiography of the almost mystical enthusiasm that Newtons Principia gave him in his youth. Hence, his naming his own great work after Newtons. He says that he sought for certainty in knowledge. And it is characteristic of the Newton world view that given certain conditions, then certain consequences may be determined.

 Moving on from classical physics, quantum physics says that there is no unequivocal position for a sub-atomic particle. The particles are not stationary: they jiggle. Their measure of position is in terms of probabilities in one place or another.

On this analogy, notice how unsuitable the certainties of social choice theory may be, when it assumes that there is some definitive answer to which candidate is elected.

In particular, transferable voting does not assign voters choices to one definitive candidate or one preference position. Gregorys method means that voters choice is akin to a sum of probabilities of being for several more or less prefered candidates. The transferable voting system of representative democracy resembles statistical representation. In fact, the theorem I used to bring out the statistical nature of elections was the binomial theorem (invented by Newton) calling my method Binomial STV (amongst other things).

Nor does this system pretend to be more than a theoretical stop-gap (against premature  exclusion of candidates in an STV count) in the inevitable crudities of formalising preferential complexity.

If elections are implicitly statistical representations of choice, they do not measure the kind of definitive results, that the originally absolutist Newtonian world view behind the origins of social choice theory inappropriately insists on. Truly representative elections are at bottom probabilistic measures of voters choice.


Example of statistical character of STV:

Gregory method is a standard statistical technique for getting a more representative average from a range of data. It is known as weighting in arithmetic proportion.

Borda method of weighting also has a name as an assumed weighting in arithmetic progression. You would never use the latter if you had the information for the former.

Points systems like Borda method are only estimates of the relative importance of each interval in the range of data. Indeed JFS Ross in Elections and Electors thought weighting in geometric progression would be a better estimate, because arithmetic progression gives too much weight to later preferences. A third alternative is the compromise of weighting in harmonic progression (which was favored by Sir Robin Day!).


The point of this brief explanation is that transferable voting, using Gregory method of weighting in arithmetic proportion, as exemplified by routine statistical procedure is more accurate than points estimates. A social choice group did the reverse of good statistical practice, it banished the more accurate transferable voting system and promoted the makeshift points system - among other non-transferable voting systems.

Evolutionary transformation of count rules in transferable voting under real-time PR.

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The point about computer scaling-up the classic Hill playground PR to mass elections is that they become choice-led inter-active elections in which the count is taking place thru the transfering choices of the voters.

In formal elections, the voters choices are restricted by the rigidities of a pre-determined count. (Most election fraud derives from deliberately restricting the rules, in the first place.)

Some followers of social choice theory try to rule-out transferable voting on the assumption that the count rules must be pre-determined and these rules show up limitations, if not inconsistencies, analgous in election procedure to the Godel theorem of the incompleteness of what a systematic theory may deduce.

But in a Hill (real-time) PR election, there are a minimum of explicit rules determining the way children move about from queue to queue behind the candidates. I called the process Equilibrium STV because the transfers of allegiances resemble a damping oscillation of wave crests and trofs (surplus and deficit votes) about the equilibrium of the quota electing each candidate.

In other words, we do not know whether the voters are acting according to some set of fixed rules, which social choice theory might be justified in describing as irrational.

If we look for scientific inspiration not only from classical deterministic physics but from subsequent statistics, there are at least two new options. The implicit election rules of real-time elections may be too complex to determine definitively. Every election is more or less subtly different, dealing with complex inter-actions of complex individuals.

For most occasions, most of the time, the rules can be determined but there may be a residue of indeterminate behaviour, which it would be at least premature to label as irrational.

A stronger option is that voters transfers of allegiance in real-time may not only be a shade too complex to reduce to rule in practice but not completely reducible even in principle.

What on earth does that mean?
Well, it occurs to me to suggest, with some temerity, that real-time voter inter-actions may throw up spontaneous new choices arising from unforeseen, or perhaps unforeseeable, contingencies of the evolution of an election.

A real-time natural election, like natural selection, may throw up evolutionary surprises that cannot be pre-determined by sets of rules that know all there is to be known.

So far, ecologists do not know how to fully create sustainable eco-systems. Hence the Biosphere 2 blow-out of toxified atmosphere, where the inhabitants had to open the hatches on their self-contained would-be Moon or Mars dome! But that is no argument against such investigations.

Likewise, the limitations of formalised transferable voting systems are no argument for excluding them, modest as their defects are, compared to non-transferable voting systems (which might be likened to non-evolutionary biologies).



Foot-note 1, on simple formal procedure for STV mass elections.

The only really simple STV formalisation for mass elections is Cambridge (MA) elections, because surplus votes have their next preferences randomly selected.

This is a valid statistical technique, with a big enough poll, and provided the shuffling of ballot papers in the box is genuinely random.Cambridge (MA) STV even more obviously shows the character of STV as (statistically) representative system than Gregory method.

 Colin Rosenstiel, in the STV-voting group corrected me about Eire STV which is not quite as simple as Cambridge (MA). In his words:

All papers are sorted to their next available preferences but each parcel of papers is divided in proportion to the available surplus and the papers selected for actual transfer in each parcel are random selections from the totals of each parcel. So the random element only kicks in at all if the papers are transfered


Foot-note 2, on a purely exclusion count.

The problem with a purely bottom-up count of preferences is that it is anexclusion or negative election rather than the positive election of most prefered candidates from surplus transfers. Excluding candidates you dont want need not amount to including candidates you do want.

The candidates elected by bottom-up count may be those most successful incourting the voters whose first preferences are for the most unpopular candidates.

 In this respect, an exclusion count is too much like that most exclusive of counts, First past the post, which excludes candidates just on the accident

of which happens to have less votes than other candidate(s) at the first stage of the count. This undemocratic system can let an unpopular candidate thru a split vote between two more popular candidates. FPP should be called first-stage-only election counts.





From: "Bob Richard" <lists001@robertjrichard.com>
To: <stv-voting@yahoogroups.com>

Saturday, September 10, 20114:56 PM

Subject: Re: [stv-voting] Social choice theory.


The gist of his case might be that in economics, which social choice theory comes from, one may have to make a compromise choice that is the one best of several possible outcomes. But in politics, there is no one best outcome for the whole community, which is not that unitary or monolithic.

 Bob Richard says:

Voting is not a matter of aggregating individual preferences into a "collective preference" because there is no such thing as a "collective preference".




Richard Lung.
28 september; 14 november 2011.

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