<div dir="auto">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!</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Sep 15, 2022, 6:28 PM Richard Lung <<a href="mailto:voting@ukscientists.com">voting@ukscientists.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<p><font size="5">Vote and count conservation laws</font><br>
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<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>Self-representation is the case of a minimum Hare
quota, where one vote elects to
one seat.</span></p>
<p class="MsoNormal"><span>(It
may be useful to compare energy quanta with the election quota,
tho the
individual perhaps correlates better to the atom than the
quantum.)</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>Hence,
the Droop quota, which adds one unit to the denominator of the
Hare quota:</span><span> 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. </span>
</p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>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.</span></p>
<p class="MsoNormal"><span>Thus,
a law of conservation of (preference) vote information
corresponds to a
conservation law of a liberty-equality count. <br>
</span></p>
<p class="MsoNormal"><span><br>
</span></p>
<p class="MsoNormal"><span>Regards,</span></p>
<p class="MsoNormal"><span>Richard Lung.<br>
</span></p>
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