Relativity theory and election method.


Since the 1970s, I could see that there was a relativity principle to elections, as well as to fysics. In 1981, I did a first paper on scientific models of the electoral process, which is on this website, in French with a UNESCO copyright, as Modèle Scientifique du Procès Electoral.

There was also a surplus of material to that paper, which eventually found its way in a more considered and complete form, on the web-page: A measure of evolution. Diffusion equation of natural selection and elections.

About 1984, I had another go at an analogy between relativity physics and relativistic elections. An American academic reviewer said he would not discourage the author from this endeavor but what was wanting was predictions generated by the model.

I salvaged some notes from about 1992, comparing election method with special relativity: Laws of Motion and Election. It is a more detailed, and, on the whole, better treatment than that which follows.

What follows was meant to be a simpler, more accessible re-run of that paper, put in the form of a fanciful story or science-fiction. But the electoral analogy is taken further to include basic ideas of general as well as special relativity.

I imagined the universe transformed from a physical to a moral (read: electoral) reality. But the very development of these ideas, especially in my web-page, Science is Ethics or “electics,” came to make fact look stranger than fiction.

I felt sorry for Ptolemy: Additional Member "epicycles."

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The moral transform (code-name heaven)
transforms the material universe
into a morality play.
(The cosmos, or our appreciation of it,
transforms as such.)
An equation, straight from the book,
has matter equal morality over time.
Energy develops an ethical vector.
If the moral transform takes place
(code-name heaven on earth)
fysics becomes ethics.

I felt sorry for Ptolemy. The master astronomer
rotated a heavenly shell about the Earth.
This was the firmament with all the stars
firmly in place, like speckles on an egg shell.

That is except for a few Wanderers
back and forth on the ecliptic plane.
Ptolemy explained away these rogue orbits
in terms of epicycles.

Then, zap!
(for want of a better way of describing it)
the universe suddenly turned upside down.
No permission for this cosmic revolution
was sought from us, puny humans
of vanishingly small importance
on the scale of things.

And why should earthlings be told,
grumbles the universal engineer.
All he had effected was a mere inter-
dimensional transposition of the fysical
and ethical axes of the cosmos.

The earthlings couldnt tell the difference,
anyway, not having any independent
reference for a re-orientation translation
from a fysical to an ethical basis of reality.

Poor Ptolemy (did he but know it)!
He found himself explaining a moral sense
to epicycles, by the ethics of elections.
What a come-down from fysics to politics!

A single-member election system is uniform
as the motion of the stars of the firmament.

But then there are the exceptions,
the Wanderers to be explained somehow.
The single member system has its own
Wanderers, who are not represented
in the firmament, yet to be accounted for.

These are the small party candidates
who win no seats or fixed positions
in the starry assembly, but wander
like lost souls back and forth
on the plane of the Milky Way.

A widely used election system
is Ptolemaic in its attempt to satisfy this
short-coming of a single member system,
namely an Additional Member System
(or Mixed Member Proportional system).

Localised single member constituencies
are modified by “epicycles” of list candidates.
Whole party lists of candidates have been
“rotated” or given a turn in parliament,
like epicycles within cycles of elections.

That is power to the parties, not the people.
Star-seers started partisans of planet Earth,
their single home. A moral of astronomy
is to see other points of view.

The heliocentric (sun-centred) theory
of Nicholas Copernicus hypothesised (guessed)
Earth is just one in a many-member constituency
of planets that is the solar system.

Political opponents of multi-member systems
of elections claimed they are too “remote,”
“breaking the link” with just one
representative per constituency.

They treat the single member constituency
as sacred as the Ptolemaic system
was once so viewed by Church hierarchy
with Earth as the sole representative,
the only astronomic point of view.

Politicians, like dogmatic high priests
of an earth-centred universe, treat
as heresy any challenge to their monoplies
on representation in single member system,
at most allowing additional members
in ad hoc "epicycles" of party lists.

Galileo & Newton: Passing motions as election counts.

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Isaac Newton felt like a child playing
with the pebbles on the beach beside
a mysterious ocean of knowledge.

That ocean throws up new kinds of pebbles,
less for their properties of motion,
than to be wished upon, namely votes.
And Newton system of natural filosofy
turned into a game of moral filosofy.

His third law of motion, in ethical terms,
states: For every left wing action there is
an equal and opposite right wing reaction.
Fysical masses have become political,
choosing sides in a "campaign"
with “victory” for the side with most votes.

War continued by political means left
about half the population unrepresented.
The campaigns losing half are laid to rest
as wasted votes. They might as well abstain.

In its original form, Galileo principle
of Relativity states the laws of motion
hold equally for observations on a bank
or in a boat: in rest frames or relative motion.

But the universal software engineer
translates Galileos book of nature
into the language of election counts.

In its translated form, physical motion
becomes the morality of choice.
Abstention (from unanimity) is rested choice
instead of "passing motions" on counts of votes.

Newton first law, of motion inertia,
suggests an ethical law of inertia of choice:
a vote follows a party line or remains at rest
(un-cast or wasted) unless acted upon
by an outside force of choice.

Under absolutism, force rules the masses.
And the masses may get votes, that restrict
to absolute choices for candidates.

Accelerating force of gravity or
decelerating force of friction take social forms.
The social gravity of crowd attraction
exerts conformity on individuals.
The man carries little weight against the mass.
Whereas the social friction of customs
and mores grind ruf ejes off individuality.

A force on a body changes its velocity,
in proportion to its mass.
This second law of motion, in ethical guise,
has a mass of votes given a proportional force
of partisanship in the electoral count.

This conserves proportion (but is not
truly proportional representation
but misrepresented as such).

Conversely, a non-proportional system
that elects individual majorities,
as in a simple plurality system, conserves
representation but not proportion.

Einstein conservation of mass-energy and PR.

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In his theory of Special Relativity,
Albert Einstein combined the conservation
laws of mass and energy
into conservation of mass-energy.

Translating fysics into ethics,
a better conservation both of Proportion
and Representation, properly combined
as genuine Proportional Representation
is by freely transferable voting
of most prefered individual candidates
for multi-member constituency representation
of a whole community in proportional elections.

Classical fysics seemed more universal,
than it was, because it did not include
experience of the more extreme conditions
under which Relativistic fysics operates.

Limited experience also gave the impression
that classical democracy, where all
represent themselves in small city-states,
was the only true kind of democracy.

In the forum of daily life, all count
as their own representative,
for an absolutely proportional representation.

The self-representative says “count me in”
for a quota count of ones own vote.
No election, or choosing-out, of one person
by another, much less a mass vote, takes place.

A fysical analogy is that light, at a maximum
constant speed, is pure energy in motion.
Compare pure self-representation without
electoral “mass” of support from other voters.

In mass elections, the (Droop) quota guarantees
a minimal level of proportional representation,
which approaches nearer and nearer
to complete representation of all the voters,
the more seats per multi-member constituency.

This increasing inclusion of the voters
or greater equality of representation
goes together with an increasing freedom
of effective choice in electing the most
prefered candidates by the most voters.

But the community, or universe
of the multi-member constituency,
would need an infinite number of seats
for completely proportional representation,
just as a body would need infinite energy,
taking-on infinite mass, to achieve light speed.

Special relativity of choice.

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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.

I felt glad for Einstein, as an ethicist,
instead of a fysicist with the atom bombings
on his conscience, that made him wish
he had been a plumber rather than a fysicist.

Einstein Relativity, in electoral terms,
considers a motion as a choice relative
to a co-ordinate system of the vote to the count.
An empirical order of (multi-)preference
1, 2, 3, etc corresponds to a rational order
of 1, 2, 3, etc (multi-)member majorities,
by the elective quota.

This is science as empirical rationalism
of the quota-preferential election system.
This is "Proportional Representation
by the Single Transferable Vote
in large constituencies."

This is the HG Wells formula, by which
his writings make a clear distinction
from the "scoundrelly impostures" of PR
employing party lists of political "gangs."

If democracy is relatively realised,
then the electoral law to be observed
is that of the majority preference.

Thus, a general law extends from
a single-preference vote for a single-majority count,
to many-preference vote for many-majority count.

The particular case of a majority preference
is a single-preference vote, or one order
of choice (not necessarily a first choice
when votes are split between over two candidates
but maybe a tactical vote for least unprefered
candidate with best chance of winning)
like simple X-marks-the-spot votes,
which sum up to a single majority count,
for one candidate prefered to some other.

Thus, election of one candidate, on over half
the votes in one-member constituency,
is one-preference vote for one-member majority.

The general case, exemplifying the general law
of majority preference, has many-preference
votes (usually just called "preference votes")
stating a whole order of choice between many
candidates (not just the minimum choice
between one of two candidates) which sum to
many-majority elections by proportional count.

For example, a multi-member constituency
of five seats is elected on five majorities,
each of over one-sixth the votes each,
(by the so-called Droop quota) therefore, each
a majority over the residual unrepresented
minority of up to one sixth the total vote,
for a proportional representation of at least
five-sixths the votes in the constituency.

The five prefered majorities are example of a many-preference vote for a many-majority count
in a multi-member constituency.

General Relativity in the equivalence of accelerated choice to social gravity.

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However, special relativity says fysical laws
only hold between observers in uniform motion,
rather than non-uniform, relative motion.
Einstein asked why should laws hold only
in a uniform, not a non-uniform, reference system
or for relative velocity not relative acceleration?

Albert Einstein used an imaginary model
of planetary gravitation to seek an answer.
This thought-experiment supposed someone let go
a weight, inside an upward accelerating "lift"
or spaceship, way out in outer space.

The spaceman in the lift sees the weight drop
to the floor as under the influence of gravity.
To an observer outside the lift, the weight stays
under its own inertia, while the lift left it
behind at an accelerating rate.

Einstein imagined a light ray, passing thru
the accelerating lift windows, would appear
bent slightly down, since the lift moved
slightly upward before a light ray reached
from one side of the lift to the other.

The accelerating lift, as gravitational field,
enabled Einstein to predict that light, passing
thru a gravitational field, would be curved.

This is Einstein "principle of equivalence"
of accelerated motion to a gravitational field.

Translate this fysics principle into ethics
or election science, and the question becomes:
why must the law of majority preference hold
only for a uniform reference system of choice,
such as a single member system, that is
with single-majorities of single-preferences?

Indeed, the same question would apply
to any uniform-member constituency system,
with equal number of seats in every constituency.

A vote for party, without individual preference,
moves voters by some mystical force
of partisanship, just as a mystical force
of gravity was assumed to drag a planet
out of a straight line into solar orbit,
because classical fysics only measured
with straight line geometry from Euclid.

A straight line may be considered as having
zero curvature, making Euclid geometry
special case of Riemann geometry of curvature.

A single (or any uniform) member system
has zero "curvature" or no variation in seats
per constituency thru-out the nation.

A flexible multi-member system compares
to Riemann geometry, as a more general
and convenient geometry, evidently based
on the geografy of real communities,
to allow for the varying "gravitational fields"
of population density “accelerating” choice.

Winston Churchill said: I would rather be
one-fifth of the Members for the whole of Leeds
than one Member for a fifth of Leeds.

Likewise, one could say:
I would rather make terms, of my choices
among many candidates, than have terms, of
my choices, made for me between few candidates.

This choosing among the choices (in ranges
of choice) rather than just choosing a given
(range of) choice, is an "acceleration” of choice.

This Ethical Equivalence Principle
is of an “accelerated” choice
equivalent to population “gravitation”
whose masses geometricly "curve" constituencies
from uniform to non-uniform member systems.

In the lift thought-experiment, the inside observer
becomes voters in the city, or citizens,
who feel the social gravity of mass opinion
influencing decisions and taking shape
in many quotas for the many seats
in a large multi-member constituency.

The outside observer, say, a rural on-looker
is free of the social gravity of the city,
only observing its acceleration of choice,
that allows city dwellers to choose among ranges
of choice, rather than just one range of choices,
the latter being zero acceleration of choice.

"Gravitational red shift" from pure self-representation.

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What of a plausible or realistic electoral analogy,
to the famous prediction of general relativity,
that light will bend in a gravitational field,
as when a light ray, from a distant star,
passes close to the mass of the sun?

The outside observer, of the light ray passing
thru the windows of the accelerating lift,
sees, in his frame of reference,
the light going in a straight line.

In his view, the fact, that the light passes
thru the out-going window at a lower level
than it enters the in-going window,
has nothing to do with the light being bent.
It is purely because the lift is accelerating
upwards during the time the light takes
to cross from in-going to out-going window.

But from the reference frame of the man inside
the lift, pressed to the floor by the upward
acceleration, as if being pulled down
by gravitational mass, the light ray is also
under this apparent gravitational downward pull.

Here, I hazard a most speculative translation
of fysics to ethics or electics.
A comparison has been made of light speed
with self-representation in the city state.

The out-side observer, of light passing,
from one window to other, thru the lift, compares
to a rural out-side observer of a city state,
with citizens being their own representatives.

The assembly of this city is self-representative
democracy, as distinct from representative
democracy in general, which requires a mass
of voting support for citizens to get elected
to the deliberative forum or meeting.

Outside observers or rural on-lookers of the city-
state see the electoral equivalent of light
moving in a straight line. That is to say
they see simply self-representing citizens.

Inside observers, citizens are differently placed
from the uninvolved view-point of the out-side
observer. True, the citizens self-represent
but they also feel the mass of others opinion.

You only have to attend a local meeting,
where anyone may speak, to feel the difference
in reception that greets each speaker,
whether a scatter of polite applause or
spontaneous cheer of unanimous support.

The inhabitants of the city-state,
tho they be all self-representative citizens,
completely equal in formal rights, still feel
a social gravity of their mass proximity.

Light speed, whch has constant velocity, measures
as frequency of vibrations times wave-length.
High frequency and short wave-length
(like blue) light is more energetic.
This is like the walker who takes short but quick
and energetic steps, yet walks at same speed
as someone taking longer but slower steps.

When light comes under the influence of gravity,
its pull slows down the light frequency
correspondingly lengthening its wavelength.
That is to less energetic red part of the light
spectrum or electro-magnetic continuum.
This is the famous "gravitational red shift."

To make the electoral analogy with fysics
yet more far-fetched, there is a corresponding
election formula to that for light speed,
as frequency times wave-length.

Basic formula for proportional representation
is given by the quota times number of seats
in the multi-member constituency.
Using the above example, a (Droop) quota,
of one sixth of the votes times five seats,
gives proportional representation of five-sixths
of the votes in the constituency.

The Droop quota is not the only possible
election quota but exemplifies the basic idea.
The Hare quota is more analgous to the formula
for light speed, because it is constant
at a maximum proportional representation,
just as light speed is a constant maximum
limit on speed of objects with mass.

The Hare quota is a constant, because simply
number of seats times number of votes per seat.
In theory, its PR always is of the total vote.

At its most basic, the Hare quota describes
self-representation of one candidate needing
only a quota of his own vote to elect him
as one representative. Thus, a quota of one vote
(ones own) times one seat (ones own) gives
a fully proportional (self-)representation
of one times one equals one.

The number of seats per constituency is akin
to the frequency of representation.
The quota corresponds to the wave-length.

Applying the analogy of gravitational red shift
to self-representation would slow its frequency
and increase its wave-length.
Instead of a frequency of one seat times
a wave-length quota count of one vote,
the frequency would become less than one seat,
with wavelength more than a quota of one vote,
to keep the balance of a constant
proportional representation of one vote.

Most simply, this situation may mean that
on average, each person needs a quota
of slightly more than one vote to be elected,
so there are not enuf votes to go round
for every-one to be self-represented.
A fraction of one seat would represent the ratio
of unrepresented to represented citizens.

A transferable voting system has no problem
dealing in fractional votes, as for instance
in Gregory method of transfering surplus votes
to a quota, needed to elect a candidate,
to next prefered candidates. This ensures
order of election determined by popular choice.

Thus, gravitational red shift suggests that
social gravity of citizens in close proximity
inclines many citizens to transfer their votes
to a better choice of more eminent candidates,
that the greater choice in cities may offer,
at the expense of asserting their self-worth,
as number one choice, giving themselves
a lesser ranking, in their ballot paper order
of choice, to some more able fellow citizens.

There is no doubt, that while an honest look
at oneself shows one to be frail and selfish.
we may recognise others are better
than ourselves for any number of tasks,
even within our specialities.

Richard Lung.
8 february 2015

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