Dear STV voting members.

Electoral meaning to Buffon's needle trials; Complex probability and
Infinitely perfect numbers.

The sine curve area is demonstrated as a probability function by Buffon's
needle trials.
I suggest these can be adapted to an electoral meaning to transferable
voting, whereby a random falling off of elective first preferences may
correspond to the falling-off of the sine value moving thru a uniform angle.

The hypothesis further suggests that, in total, about 64% of first
preferences being elective is the expected level. Much higher levels than
that, which are often encountered in STV elections, would be above chance.

The sine curve relates to a circular function, whose Cartesian axes may be a
function of transferable voting's keep values and transfer values.
My method of keep-value averaged STV (or "Binomial STV"), unlike
conventional STV methods, also makes use of the information afforded by
negative or deficit transfer values for candidates.
The single transferable vote allows each voter to have part of their one
vote to be transfered to next prefered candiates from elected candidates who
dont need all of it.
Probability theory with probability of success and failure equaling unity is
akin to transferable voting with transfer value plus keep value equal one.
From this comparison negative transfer values can be applied to a concept of
negative probability. And indeed the next step from imaginary transfer
values to imaginary probability can be taken, resulting in a concept of
complex probability numbers.

Infinitely perfect numbers arise from a simple modification of so-called
slightly defective perfect numbers, such as powers of two.
All one has to do is extend positive powers of two to an infinite series
including negative powers of two. It is well known that the latter are
convergent to the sum of unity, which is precisely by how much positive
powers of two are reckoned to be defective.

Hence slightly defective perfect numbers would better be called infinitely
perfect numbers when an infinite series of
the negative powers of two are included.
This conception offers algorithm for the generation of diffusion over time
in the diffusion equation.
Whereas the algebra of the calculus of finite differences over space is
simply given by the expansion of the binomial theorem to any given power.


My web page reference is:
http://www.voting.ukscientists.com/buffon.html



Yours sincerely,
Richard Lung.