[EM] Vote and count conservation laws

[Richard Lung]

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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