Vote and count conservation laws
Vote and count conservation laws
When all the preference votes are counted in an election method, like
Binomial STV, the law of the conservation of (preference) information is
fulfilled. In physics, energy concepts are being translated into
information concepts. The conservation law of mass-energy is translated
into conservation of information.
Election method or electics may have a corresponding conservation law to
information conservation of the vote. As JFS Ross said, every election
has a vote and a count. So, the corresponding conservation law would be
a conservation of the count. The vote is summed or aggregated to the
count, so vote information conservation should cross-over into a
conservation of mass action.
In physics, the basic unit of energy is that minimum packet of energy
called the quantum. Energy is never transfered in lesser amounts than
these discrete quanta. In electics, these quanta are analogies to the
quota count. Candidates are proportionally elected on discrete equal
ratios of votes to seats.
The minimum elective vote is the one vote of self-representation,
associated with the ancient Greek city-state. Here, the vote
conservation law merges with a count conservation law.
Self-representation is the case of a minimum Hare quota, where one vote
elects to one seat.
(It may be useful to compare energy quanta with the election quota, tho
the individual perhaps correlates better to the atom than the quantum.)
It is a bit confusing talking about a minimum Hare quota, because the
Hare quota gives maximum proportional representation. Indeed, even a
minimum Hare quota of one vote gives maximum (proportional)
representation to one self-representing voter: one seat for one vote.
But suppose two voters contesting one seat. The Hare quota is powerless
to elect either, unless one or the other transfers their vote. The
transferable vote is indeed a possibility, that should be tried, but it
may not break the dead-lock.
Hence, the Droop quota, which adds one unit to the denominator of the
Hare quota:2/(1+1) = 1. The Droop quota gives either candidate voter an
elective quota. This minimal case would be decided on a random tie-break.
The Hare quota offers maximum proportional representation, but it does
so at a price. To take the extreme case, of a single vacancy, a
representative elected, on the Hare quota, has to win all the votes. For
example, 100 voters, for a single vacancy, would all have to vote for a
single candidate, to be elected. With the Droop quota, a candidate would
need only half the votes, to be elected. A double vacancy requires two
candidates to each win one third of the votes each, giving two thirds
proportional representation. In general, the Droop quota combines a
minimal or least proportional representation with voter choice.
The more seats per district or constituency, the closer that the Droop
quota approximates to the Hare quota. But as the seats increase, the
increase, in proportional representation of the Droop quota, is at an
increasingly slower rate. A triple member constituency ensures
three-quarter or 75% representation. That is up from nearly 67%
representation of a double member constituency, an increase of over 8%.
However, that 8% increase was already less than the nearly 17% increase
of representation, between a double and a single member constituency. A
four-member constituency gives 80% representation, but that is only up
5% from a three member constituency with the Droop quota.
This (Droop quota) decelerating increase of representation with more
seats is formally the same as found in high-energy physics of special
relativity theory. As the motion of a physical object significantly
approaches light speed, the increasing energy, put into that motion,
increases the mass of the body, and only has a decelerating increase in
the body speed. In theory, the body would have to achieve infinite mass
before it could reach the maximum speed limit of light. Light itself has
no rest mass but is pure energy.
It is possible to make a formal comparison between the motions of
massive and massless particles in physics, and minimum and maximum
proportions of representation, in election method. The Hare quota, which
gives maximum proportional representation, compares to light, which
moves at maximum speed. Droop quota representation compares to the
motion of massive objects, significantly approaching light speed.
The Hare quota gives maximum equality of representation. Its analog is
light, at maximum speed. The Droop quota sacrifices some of that
equality for liberty of choice. Its analog is motion of objects with
rest mass. To put the analogy at its most spare, energy compares to
equality, and mass compares to liberty. So, the conservation of
mass-energy formally compares to a conservation law of liberty-equality.
Thus, a law of conservation of (preference) vote information corresponds
to a conservation law of a liberty-equality count.
Regards,
Richard Lung.
As a mathematician I love formal analogies among apparently disparate
fields of inquiry ... the greater the apparent disparities, the more
interesting ... and the greater the potential for cross fertilization!
On Thu, Sep 15, 2022, 6:28 PM Richard Lung voting@ukscientists.com wrote:
Vote and count conservation laws
When all the preference votes are counted in an election method, like
Binomial STV, the law of the conservation of (preference) information is
fulfilled. In physics, energy concepts are being translated into
information concepts. The conservation law of mass-energy is translated
into conservation of information.
Election method or electics may have a corresponding conservation law to
information conservation of the vote. As JFS Ross said, every election has
a vote and a count. So, the corresponding conservation law would be a
conservation of the count. The vote is summed or aggregated to the count,
so vote information conservation should cross-over into a conservation of
mass action.
In physics, the basic unit of energy is that minimum packet of energy
called the quantum. Energy is never transfered in lesser amounts than these
discrete quanta. In electics, these quanta are analogies to the quota
count. Candidates are proportionally elected on discrete equal ratios of
votes to seats.
The minimum elective vote is the one vote of self-representation,
associated with the ancient Greek city-state. Here, the vote conservation
law merges with a count conservation law.
Self-representation is the case of a minimum Hare quota, where one vote
elects to one seat.
(It may be useful to compare energy quanta with the election quota, tho
the individual perhaps correlates better to the atom than the quantum.)
It is a bit confusing talking about a minimum Hare quota, because the Hare
quota gives maximum proportional representation. Indeed, even a minimum
Hare quota of one vote gives maximum (proportional) representation to one
self-representing voter: one seat for one vote.
But suppose two voters contesting one seat. The Hare quota is powerless to
elect either, unless one or the other transfers their vote. The
transferable vote is indeed a possibility, that should be tried, but it may
not break the dead-lock.
Hence, the Droop quota, which adds one unit to the denominator of the Hare
quota: 2/(1+1) = 1. The Droop quota gives either candidate voter an
elective quota. This minimal case would be decided on a random tie-break.
The Hare quota offers maximum proportional representation, but it does so
at a price. To take the extreme case, of a single vacancy, a representative
elected, on the Hare quota, has to win all the votes. For example, 100
voters, for a single vacancy, would all have to vote for a single
candidate, to be elected. With the Droop quota, a candidate would need only
half the votes, to be elected. A double vacancy requires two candidates to
each win one third of the votes each, giving two thirds proportional
representation. In general, the Droop quota combines a minimal or least
proportional representation with voter choice.
The more seats per district or constituency, the closer that the Droop
quota approximates to the Hare quota. But as the seats increase, the
increase, in proportional representation of the Droop quota, is at an
increasingly slower rate. A triple member constituency ensures
three-quarter or 75% representation. That is up from nearly 67%
representation of a double member constituency, an increase of over 8%.
However, that 8% increase was already less than the nearly 17% increase of
representation, between a double and a single member constituency. A
four-member constituency gives 80% representation, but that is only up 5%
from a three member constituency with the Droop quota.
This (Droop quota) decelerating increase of representation with more seats
is formally the same as found in high-energy physics of special relativity
theory. As the motion of a physical object significantly approaches light
speed, the increasing energy, put into that motion, increases the mass of
the body, and only has a decelerating increase in the body speed. In
theory, the body would have to achieve infinite mass before it could reach
the maximum speed limit of light. Light itself has no rest mass but is pure
energy.
It is possible to make a formal comparison between the motions of massive
and massless particles in physics, and minimum and maximum proportions of
representation, in election method. The Hare quota, which gives maximum
proportional representation, compares to light, which moves at maximum
speed. Droop quota representation compares to the motion of massive
objects, significantly approaching light speed.
The Hare quota gives maximum equality of representation. Its analog is
light, at maximum speed. The Droop quota sacrifices some of that equality
for liberty of choice. Its analog is motion of objects with rest mass. To
put the analogy at its most spare, energy compares to equality, and mass
compares to liberty. So, the conservation of mass-energy formally compares
to a conservation law of liberty-equality.
Thus, a law of conservation of (preference) vote information corresponds
to a conservation law of a liberty-equality count.
Regards,
Richard Lung.
On 9/16/22 05:05, Forest Simmons wrote:
As a mathematician I love formal analogies among apparently disparate
fields of inquiry ... the greater the apparent disparities, the more
interesting ... and the greater the potential for cross fertilization!
I still find it very hard to extract useful information from any of
that. But then I have got Richard plonked for a reason :-) With my email
client automatically ignoring his posts, I don't have to wrack my brain
parsing them.
I wonder if any of the early STV theoreticians focused very much on the
count, because I see this sort of "algorithm-based approach" (where
exactly how the algorithm works matters) both in Richard's posts and
James Gilmour's program instruction view of ranked ballots.
It's very different from my "ranked ballots are preferences, and
criteria that are used to evaluate voting methods are entirely
implementation agnostic" view -- which I have the impression is a later
American perspective, although I couldn't say just how I've come to that
impression.
-km
Some of my best ideas have been triggered by trying to understand comments
that were somewhat or tonally mysterious to me:-)
On Fri, Sep 16, 2022, 2:07 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 9/16/22 05:05, Forest Simmons wrote:
As a mathematician I love formal analogies among apparently disparate
fields of inquiry ... the greater the apparent disparities, the more
interesting ... and the greater the potential for cross fertilization!
I still find it very hard to extract useful information from any of
that. But then I have got Richard plonked for a reason :-) With my email
client automatically ignoring his posts, I don't have to wrack my brain
parsing them.
I wonder if any of the early STV theoreticians focused very much on the
count, because I see this sort of "algorithm-based approach" (where
exactly how the algorithm works matters) both in Richard's posts and
James Gilmour's program instruction view of ranked ballots.
It's very different from my "ranked ballots are preferences, and
criteria that are used to evaluate voting methods are entirely
implementation agnostic" view -- which I have the impression is a later
American perspective, although I couldn't say just how I've come to that
impression.
-km
In my experience, unfamiliarity is more an obstacle to understanding, than lack of intelligence. :-)
My post a 12 tone score to you! The unconventional scoring of the "bark brod" symfony 4 by Sibelius had an orchestra misplaying unexpected turns. It may have been Kutovitsky - can't remember the spelling -- who said he would keep on playing it till audiences liked it -- familiarity, you see.
I know nothing about music, as mathematicians also realise.
On 17 Sep 2022, at 7:21 pm, Forest Simmons forest.simmons21@gmail.com wrote:
Some of my best ideas have been triggered by trying to understand comments that were somewhat or tonally mysterious to me:-)
On Fri, Sep 16, 2022, 2:07 AM Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 9/16/22 05:05, Forest Simmons wrote:
As a mathematician I love formal analogies among apparently disparate
fields of inquiry ... the greater the apparent disparities, the more
interesting ... and the greater the potential for cross fertilization!
I still find it very hard to extract useful information from any of
that. But then I have got Richard plonked for a reason :-) With my email
client automatically ignoring his posts, I don't have to wrack my brain
parsing them.
I wonder if any of the early STV theoreticians focused very much on the
count, because I see this sort of "algorithm-based approach" (where
exactly how the algorithm works matters) both in Richard's posts and
James Gilmour's program instruction view of ranked ballots.
It's very different from my "ranked ballots are preferences, and
criteria that are used to evaluate voting methods are entirely
implementation agnostic" view -- which I have the impression is a later
American perspective, although I couldn't say just how I've come to that
impression.
-km
One of the deep questions is how the sciences seem to follow the same
structure of measurement, notably given by SS Stevens and widely
accepted. I wrote a book about it, Science is Ethics as Electics, and
made some progress since.
To continue, on a different tack:
Scientific statements are conditional statements. They are of the
nature: If…, then… The Andrae/Hare system expresses the scientific or
knowledgeable condition: if given the same number of orders of choice,
in a preference vote or ranked choice, as the number of seats,
thenelective proportions or quotas of votes may be personally determined
by the electorate.
In the mid-nineteenth century, the Andrae system and, independently, the
Hare system, or quota-preferential method, thus established electoral
equality, as a condition of liberty.
This was half a century before physics united the conservation laws of
mass and energy, into a single mass-energy conservation law.
The continent of Europeand its colonies disunited the liberty-equality
condition of the Carl Andrae law, by abolishing the preferential
suffrage of a number order vote. The illiterate x-vote, which only
expresses a single order of choice, cannot determine a proportional
count, which is a multiple equality of ratios of votes to seats. The
X-vote for a representative was demoted to a vote for the abstraction of
a “party.” The Andrae system was demoted from a scientific or
knowledgeable statement of an observable conditional relationship, to a
“metaphysical” statement. Of this, David Hume held: “commit it to the
flames.” Or, such a statement, is, as Karl Popper would grandly say:
“outside the realm of scientific discourse.”
The English-speaking countries electoral reform also did not fare well.
The irrational count of simple plurality has been retained. In recent
decades, electoral reforms, to so-called proportional representation,
have seen a preponderance of x-voting party dogmatism.
The history of electoral reform has not been so much progress as
regress. Whereas physics has united its conservation laws of mass and
energy, politics has dismantled electoral liberty in equality.
The modest gains, against great adversity, of the quota-preferential
method, or single transferable vote proportional representation, have
demonstrated that STV possesses the character of a good scientific
theory. This is its explanatory power, whose range is not possessed by
the usual electoral methods. For example, STV, the quota-preferential
method, possesses the power of primaries, and prefered coalitions,
within general elections.
However, the democratic advantages of STV are not desired where they are
dimly appreciated, and not dimly appreciated where they are desired. The
Andrae/Hare system perhaps was half a century ahead of its time. At a
conservative estimate, its progress must now be over a century behind
the times, causing an unstable imbalance between the natural and the
moral sciences.
Scientific progress is not sufficiently regulated by effective elections
in the common interest. There is a real possibility that parasitic
vested interests kill the host body of humanity.
To name only two cases, both full of propaganda, the fossil fuels
industry threatens an irreversible greenhouse effect, like Venus. And
nuclear fission threatens, at least, all vertebrate life with
radioactive fall-out, thru the military extermination industry, or its
pseudo-civil atom plants by-product, at present, terrorising the world,
in Zaporizhzhia
On 16/09/2022 04:05, Forest Simmons wrote:
As a mathematician I love formal analogies among apparently disparate
fields of inquiry ... the greater the apparent disparities, the more
interesting ... and the greater the potential for cross fertilization!
On Thu, Sep 15, 2022, 6:28 PM Richard Lung voting@ukscientists.com
wrote:
Vote and count conservation laws
When all the preference votes are counted in an election method,
like Binomial STV, the law of the conservation of (preference)
information is fulfilled. In physics, energy concepts are being
translated into information concepts. The conservation law of
mass-energy is translated into conservation of information.
Election method or electics may have a corresponding conservation
law to information conservation of the vote. As JFS Ross said,
every election has a vote and a count. So, the corresponding
conservation law would be a conservation of the count. The vote is
summed or aggregated to the count, so vote information
conservation should cross-over into a conservation of mass action.
In physics, the basic unit of energy is that minimum packet of
energy called the quantum. Energy is never transfered in lesser
amounts than these discrete quanta. In electics, these quanta are
analogies to the quota count. Candidates are proportionally
elected on discrete equal ratios of votes to seats.
The minimum elective vote is the one vote of self-representation,
associated with the ancient Greek city-state. Here, the vote
conservation law merges with a count conservation law.
Self-representation is the case of a minimum Hare quota, where one
vote elects to one seat.
(It may be useful to compare energy quanta with the election
quota, tho the individual perhaps correlates better to the atom
than the quantum.)
It is a bit confusing talking about a minimum Hare quota, because
the Hare quota gives maximum proportional representation. Indeed,
even a minimum Hare quota of one vote gives maximum (proportional)
representation to one self-representing voter: one seat for one vote.
But suppose two voters contesting one seat. The Hare quota is
powerless to elect either, unless one or the other transfers their
vote. The transferable vote is indeed a possibility, that should
be tried, but it may not break the dead-lock.
Hence, the Droop quota, which adds one unit to the denominator of
the Hare quota:2/(1+1) = 1. The Droop quota gives either candidate
voter an elective quota. This minimal case would be decided on a
random tie-break.
The Hare quota offers maximum proportional representation, but it
does so at a price. To take the extreme case, of a single vacancy,
a representative elected, on the Hare quota, has to win all the
votes. For example, 100 voters, for a single vacancy, would all
have to vote for a single candidate, to be elected. With the Droop
quota, a candidate would need only half the votes, to be elected.
A double vacancy requires two candidates to each win one third of
the votes each, giving two thirds proportional representation. In
general, the Droop quota combines a minimal or least proportional
representation with voter choice.
The more seats per district or constituency, the closer that the
Droop quota approximates to the Hare quota. But as the seats
increase, the increase, in proportional representation of the
Droop quota, is at an increasingly slower rate. A triple member
constituency ensures three-quarter or 75% representation. That is
up from nearly 67% representation of a double member constituency,
an increase of over 8%. However, that 8% increase was already less
than the nearly 17% increase of representation, between a double
and a single member constituency. A four-member constituency gives
80% representation, but that is only up 5% from a three member
constituency with the Droop quota.
This (Droop quota) decelerating increase of representation with
more seats is formally the same as found in high-energy physics of
special relativity theory. As the motion of a physical object
significantly approaches light speed, the increasing energy, put
into that motion, increases the mass of the body, and only has a
decelerating increase in the body speed. In theory, the body would
have to achieve infinite mass before it could reach the maximum
speed limit of light. Light itself has no rest mass but is pure
energy.
It is possible to make a formal comparison between the motions of
massive and massless particles in physics, and minimum and maximum
proportions of representation, in election method. The Hare quota,
which gives maximum proportional representation, compares to
light, which moves at maximum speed. Droop quota representation
compares to the motion of massive objects, significantly
approaching light speed.
The Hare quota gives maximum equality of representation. Its
analog is light, at maximum speed. The Droop quota sacrifices some
of that equality for liberty of choice. Its analog is motion of
objects with rest mass. To put the analogy at its most spare,
energy compares to equality, and mass compares to liberty. So, the
conservation of mass-energy formally compares to a conservation
law of liberty-equality.
Thus, a law of conservation of (preference) vote information
corresponds to a conservation law of a liberty-equality count.
Regards,
Richard Lung.