[EM] Vote and count conservation laws

[Forest Simmons]

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 at 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.
>
>
>
>
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