Laws of motion and election.


This web page was written in about 1992, from what I can make out of the scraps of paper it was written on. In 1981, I attempted a coherent comparison of electoral method with relativity, which is also a method of choice of observations and their co-relation. This was almost, tho not quite, the first attempt. In 1985 I made a more ambitious attempt, including again some comparisons with general relativity, so far as my rudimentary knowledge allowed. I have not included the latter below. Indeed, the early nineties version only attempted the special theory and much of that has been cut from the text shown below.

The reason for the editing is that I was still grappling with a quantitative comparison between scientific method of elections and special relativity theory. When that eventually came about a decade later ( on my page, An Electoral Model Of Special Relativity ) it was a correction of my earlier quantitative attempts.

In the end, I think only sheer stubborness kept me trying to come to this quantitative formulation that made reasonably consistent sense. I had a vague idea, of what I was searching for, but it kept evading me and my failure to close with the problem was wearing me down. People may say, if they say anything at all, that I wasted my time. Fortunately, that is not for me to decide. They are entitled to their opinion. I have only to satisfy my own judgment that I have done enough to justify a comparison of physical theory and electoral method.

Also, I cannot say that the qualitative comparisons below contributed very obviously to my finding out the simple mathematical structures that electoral method and the special theory seem to have in common. Nevertheless, I think the intuitive analogies made on this page remain interesting, perhaps all the more because they remain a thing apart from the more mature mathematical formulations.

Intuition does matter very much, tho. It was obvious that absolute versus relative motion compared to absolute versus relative choice, and so on. By the late nineteen seventies, perhaps earlier, when I tried to make comparisons, it stood out that Minkowski's Interval was reminiscent of the Senatorial Rules of transferable voting.

But it wasnt till much later, the turn of the century, that I tried to explain the Interval to myself on a web page. And the improved understanding was a necessary preliminary to drawing a good analogy with voting method. Indeed, it is only the other day that I put up a simple quantitative comparison ( in a postscript on the page, An Electoral Model Of Special Relativity ). This tardiness owed to the fact that I could not make the comparison till transferable voting method developed the concept of a negative surplus transfer. And I only did that this year of 2004 on my pages about the Retransferable Vote and Binomial STV.
The concept was needed to develop STV method, it was not contrived to make STV fit with Special Relativity, which, anyway, has not been a final word in theory for a century.

Physical theory and electoral method are both structured enough to show diverse similarities. Analogies need only be good and suggestive of further similarities between different systems. Analogies, like science in general, dont have to be perfect, only progressive.

My early gloss, below, on special relativity includes the conventional wisdom of a constant maximum speed of light merely as a basic postulate based on the accumulation of evidence. My newer page, on A Statistical Basis For Special Relativity, says rather that this postulate appears to follow from light speed appearing constant because variations average out, in the case of large scale relativistic physics, as they are not so prone to do, in the case of very small scale quantum physics.

That idea came about because I needed a statistical interpretation of special theory to make good my analogy with electoral method. On looking for this, I realised that the special theory could be considered as a statisticly-based theory more reasonably than as a "because-it-is-so" theory based on the just given, or arbitrary, fact of a maximum light speed.

Electoral analogies of Galileo's and Newton's laws.

In my comments, on the fourth review page of Julian Barbour's The End of Time, I suggested that relativity theory made Newton's laws more consistent with the study of measurement scales.

Here I would like to point out that a similar sort of thing needs to be done with respect to the world's election laws. In The Discarded Image, C S Lewis reminds us that the idea of natural laws owes to man having to make his own laws for society.

We dont have to seek an understanding that reduces men to machines, in the name of ( mechanical ) science. But it is instructive to note that physical motion enters the language in a moral sense.
Passing a motion means voting on a choice of action. The advocate ends with: 'I rest my case.' The physical terms, motion and rest, which appear in Newton's first law, are morally shadowed.

This law of inertia comes from Galileo and states: A body at rest, or in uniform motion in a straight line, will remain so, unless acted upon by an out-side force.

The simplest elections are such an all-or-nothing affair, to choose or not to choose a given candidate. You are moved to put a mark by a name in the ballot and then must rest from further options. The spot vote offers a straight choice, typicly between one of two uniform groups or parties.

The two party system gains inertia from people's fear that the side, to which one does not belong, comes to power, if one does not vote for the other main contender. The spot vote or one-shot vote moves a main contender or rests as a 'wasted vote' on minor party candidates and independents, unless acted upon by an 'out-side force' of tactical voting for a second or lesser choice, to stop the least prefered candidate from one of the two main parties.

To hang in the two-party balance of power, voters polarise in a system of divide and rule. Newton's third law of motion says: For every action, there is an equal and opposite reaction.
Politics of the dual lends itself to the parody that for every left wing action, there is an equal and opposite right wing reaction.

The first law states uniform motion, like rest, has inertia. Velocity, as speed and direction in a straight line, goes on but for friction's external and decellerating force, or gravity's external and accelerating force.

To measure a body's motion over a space of time, the exact position of a body of any size, at a given time, is at its centre of gravity. So, the body is treated as a 'mass particle'. In classical physics, this mass is an absolute quantity, not related to the positions of other objects.

Likewise, x-marks-the-spot votes can but prefer one candidate absolutely, saying nothing about any voter's relative weight of support for other candidates, as if they were all equally out of the question.

Galileo's great break-thru was that force does not cause a body's velocity but change in its velocity, in proportion to how massive the object may be. This is stated in Newton's second law of a body's motion, that its mass is proportional to the accelerating force on it.

Acceleration is observed. And, in terms of the third law, the ( inertial ) mass of any body measures as a constant factor in collisions between bodies. But unobserved force is merely defined in terms of mass.

Election law may also be less than evident. Party list systems are a proportional count of spot votes for parties, rather than persons: the mass of spot votes is presumed under a proportional force of partisanship.
But parties are defined by their members. Only people are real, 'the observables', that voting really should be in terms of.

The notion of force, as distinct from mass, might be an arbitrary distinction between the active and passive parts of an inter-action.
Rulers and ruled might be arbitrarily put into active and passive categories, to excuse the lack of inter-action there should be between them.

A moral of astronomy is learning how to see other than our own point of view. Star-seers started partisans of the Earth naturally from the position we were put in. Aristarchus of Samos saw our home as just one of the planets circling the sun.

Two milleniums elapsed before the issue could not be ignored. Church authority forced Galileo to back down from the helio-centric hypothesis of Copernicus.

The geocentric theory of the planets' motions was propped-up by supposed 'epicycles' to account for 'reverses,' from Earth's out-look, of planets traveling the ecliptic plane.

Mixed Member Proportional ( MMP ) or Additional Member Systems ( AMS ) have a 'geocentric' out-look, in the sense of being conditioned to the local out-look of single member elections, modified by 'epicycles' of list candidates. ( Whole lists have been 'rotated' or given a turn in parliament, like epicycles within the cycles of general elections. )

The 'heliocentric' theory identifies Earth as just one in a multi-member solar system of planets. Singles-centred supporters claim multi-member constituencies much too 'remote,' 'breaking the link' with representatives, as if their monopolies were a local monotheism over Earthly constituents, as patronised by the holy church of party.

Going a step further than Copernicus, Herschel guessed the sun in a disk of stars but honestly admitted he hadnt proved the shape. That took till the twentieth century. The sun Catherine wheels two-thirds the way to the rim relative to the hub of a spiral galaxy, the Milky Way.

Newton didnt abandon the idea that the universe is absolutely at rest at some fixed point relative to all movement. He only considered relative motions as convenient and 'sensible measures'.

Einstein made a scientific virtue of motion as an observation of the changing motions of things relative to each other: Einstein's relativity principle kept physics within observable bounds. The classical belief, that the law of inertia held thru-out the universe, could not be proved, and so was metaphysics not physics.

Electoral analogies with special relativity.

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Albert Einstein took up the Galilean relativity principle that the same laws of motion hold for observers whose relative motion is a constant speed in a straight line. The special theory of relativity goes on to say that all natural laws, including the laws of optics and electricity, unified by Clerk-Maxwell, also hold for observers in this so-called uniform relative motion.

Clerk-Maxwell's electro-magnetic waves moved at light speed, so he guessed light is this kind of wave. Sound and water waves are a traveling disturbance thru a material medium. Light waves were supposed to transmit thru an 'ether', universal even to the vacuum of space.

The universal ether was thought to be a frame of reference, absolutely at rest compared to all others. Only therein would the speed of light be constant all ways. Other reference points, moving with or against the ether, such as the Earth, should add to, or subtract from, the speed of light.
But the Michelson-Morley experiment always measured light speed at a constant value ( of about 300,000 km / sec. ).

In politics, people fall into certain assumptions about 'the People' similar to those about 'the Ether'. H G Wells described a belief in

the People one and indivisible, a simple mystical being, which pervades and dominates the community and determines its final collective consequences.

One could substitute 'the Ether' for 'the People' and 'the universe' for 'the community' in that phrase. The people should not be a corporate concept.

The ether was thought-up merely to make light seem less mysterious as a wave but only created another mystery that could not be observed or even infered. Instead of an elusive ether, the special relativity principle is based on the evidence of light's constant speed.

Observers cannot see the speed of light differ with respect to a velocity difference of their own. So, the way they see each others velocities must vary in keeping with both seeing the same constant speed of light. Velocity is only distance traveled in a given direction over a period of time. Therefore the measures of space and time, as well as velocity, will be mutually affected between observers, in the context of light velocity.

To go to extremes, if one observer could move at light speed, his measures of space and time, rod and clock, would be seen at zero by another observer. This is because no speed can be added to light's maximum motion.
As one observer approaches light speed, to another, his ruler or rod would contract and his clock slow down. The formula for this process is the 'Lorentz transformation' of respective observations, so that their measurements, of a given event, correspond.

Only at earth-bound speeds can common sense safely assume that different observers effectively work within the frame-work of one absolute space and one absolute time.

Dimensions of proportional representation.

Classical physics and Relativity compare to classical democracy and Representation. We are used to acting for our-selves, rather than being represented, and so tend to think of absolute self-representation as true democracy, like the Greek city state.

Like classical physics, classical democracy is thought to be universal when it is only an adjunct of our limited experience. In the forum of our daily lives, every one counts as their own representative, for an absolutely proportional representation.

The self-rep says 'count me in' for a proportion or quota count of one's own vote. No election, or choosing-out, of one person by another, much less a mass vote, has taken place.
This count is by the Hare quota, which divides total votes by number of representatives. In this case, one is a voter for one representative, oneself. Therefore, one is bound to achieve the Hare quota of ( one over one equals ) one vote, to 'elect' oneself.

Light is a maximum constant speed, because pure energy in motion, needing no impetus. Whereas bodies imply the possession of mass. Likewise, pure self-representation has no electoral 'mass' of support from other voters.

The self-rep compares to an observer at light speed, in that others observe neither vote of preference nor ( the transfer of preferences to the self-rep in ) proportional counting. Thus the self-rep is observed to have zero proportional preference, analgous to a zero space-time.

There are three dimensions of space and one dimension of time. Electorally, there are perhaps three dimensions of proportion. One dimension is expressed in the requirement of equal constituencies or proportional representation between constituencies.
( The Hare quota ensures that electorates have the same number of representatives. )

In 1979, the British Tories, behaving like one-dimensional democrats, instructed the Boundary Commission to fulfil this objective to the exclusion of the other two dimensions of equal representation, namely proportional representation within constituencies and across constituencies.

Within constituencies, proportion, defined as an equality of ratios, applies to voters per representative, given by the ( Droop ) quota. That is the proportion of the votes, in a multi-member constituency, that each of the most prefered candidates needs to take a seat.
This dimension of proportion is usually called proportional representation, out of context from the other two dimensions.

From 1979, much local protest was also caused by over-ruling the third dimension of proportional representation across constituencies, in uniform member constituencies. J F S Ross showed a single member system had to allow a proportionate variation from equal representation to best keep local communities together as representative units.
I suggested a 'Ross quota' for uniform systems not only of one seat per constituency.

For a fourth electoral dimension, analgous to time, we are left with the number of candidates that voters choose to prefer. Voters must prefer at least enough candidates to take the number of seats to be filled in a given constituency. That is the average number of candidates, that voters prefer, must be proportionate to the number of seats in the constituency.

Electoral conservation law.

The Hare quota was used to show an analogy between the maximum limit of representation and light's maximum limit on velocity. The Droop quota supplies an electoral analogy to massive bodies not being able to reach light speed.

As a body approaches a significant fraction of the speed of light, it significantly gains mass. This mass would have to become infinite to reach the limiting speed of light. All the energy in the known universe would not be enough.
Mass and energy are gained together and may be considered as equivalent terms. Physicists commonly measure mass in energy units.

The Hare quota tells how many voters are to be shared between representatives. The Droop quota tells the least number of voters needed to elect a candidate, relative to the remaining votes other candidates may have amassed. The Hare quota allocates representation to the voters. The Droop quota elects representation from the voters' relative majorities.

These relative majorities start with half the voters prefering one candidate to the others. Then, in a two-member system, two relative majorities, of one third the voters, prefer two candidates over any others. That is a PR of two-thirds the voters. In a three member system, the PR is three-quarters the voters, and so on.

Thus, the Droop quota achieves a high degree of equal representation together with great freedom to prefer the candidates. But the community, or universe of the constituency, would need an infinite number of seats for completely proportional representation.

The residual portion, of however few unrepresented voters, is a function of the right of relative majorities to prefer candidates. This infinitely extendable freedom of choice is a limit on absolute equality of representation. But the more seats, the more choice and proportion, the more freedom and equality of representation. Like energy and mass, they are commensurate, being gained and lost together.

The conservation of mass and energy were two basic but separate laws of classical physics, united by special relativity theory, into one conservation law of mass-energy.

Analgously, different political cultures have followed implicitly basic but separate conservation laws of electoral practise. At least till recently, English-speaking countries mainly kept to a law of the conservation of ( individual ) representation. But equal electorates in a single member system merely give proportional representation between constituencies.

The first past the post system is irrational. Time warped politics are the result. Old parties are over-represented for too long till their support dips below a certain level, when they are suddenly exterminated as an effective force. Conversely, new parties have to wait too long to put into effect urgent policy messages.

First past the post is prone to taking snap-shot elections, often foto-finishes, which give undue recognition to short-term fluctuations of support. The undue power this gives to one of the main parties ushers in a new era, that is not in keeping with the times.

Continental Europe turned to a conservation law of proportional partisanship. Party list systems involved constituencies so large that they became unimportant as assemblages of locally known individual representatives.

Till recently, there was a trend for states to copy the German ( MMP ) system, with two votes. One is for a single member system, the other for a party list system. These nations thus combine election laws of individual representation and of partisan proportion.
Their election law compares to a classical physics that recognises the conservation laws of mass and energy but has not learned that they are one conservation law of mass-energy.

That is to say additional member systems are not truly a system of proportional representation, in which freedom and equality grow together, but one in which they are at monopolistic cross-purposes with each other. Individual representatives monopolise single seats: no equality of representation there. And party candidates on lists monopolise the proportional count: no freedom of choice there.

Generalisation of relative choice.

The single transferable vote proportionally elects, by the Droop quota, the most prefered individual candidates as representatives. STV thus provides a unified conservation law of proportional representation, properly speaking, as a rationalised liberty.

A majority is not simply one member's majority. The single member majority count is generalised by the Droop quota into a multi-member majority count.
The vote generalises in a similar way from a one-preference spot vote to a many-preference vote, in order of choice.

The simple majority system is sometimes called a relative majority system. But it is only the most limited kind. First past the post elects one candidate on a majority relative only to the runner-up. Therefore, most voters may go unrepresented. Transferable voting elects as many candidates as constituency seats, each with the same majority, relative to all the runners-up put together. Then, the overwhelming majority is represented.

A majority means 'greater than,' being relative to what it counts as greater than. Choice is also relative, in that voters more or less favor some candidates in relation to others. This is allowed expression in a preference vote from greater to lesser choice. So, magnitude of choice transfers from the vote as preferences, into the count as majorities. The count of the community corresponds to the vote of individuals, in greatness of support for candidates.

Einstein favored Relativity as a 'principle theory', which makes logical deductions from a firm empirical base, that motion is relative to a co-ordinate system.
Similarly, choice is relative to a co-ordinate system of the vote to the count. An empirical order of preference 1, 2, 3, etc corresponds to a rational order of 1, 2, 3, etc member majorities.
This is the view of science as empirical rationalism.

Richard Lung.
c1992; 30 November 2004.

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