[EM] Schrodinger's Candidate

[Richard Lung]

Schrodingers candidates would be a fanciful way of describing Binomial STV or FAB STV, because the candidates are in a superposition of election and exclusion, during the binomial count. The candidates might be both elected and excluded till an over-all count is reached by averaging the two counts.
Whether there is a deeper mathematical analogy is another question. The basic average used in Binomial STV is the geometric mean, which is an acceleration average, not a velocity average, like the arithmetic mean. (The Arithmetic Mesn is one of the four averages in FAB STV, tho.) Wave functions have an acceleration component, so it might be possible to transform the geometric mean into a wave function. -- I have not attempted this! 

Sincerely,
Richard Lung.



On 15 Oct 2021, at 2:55 am, Forest Simmons <forest.simmons21 at gmail.com> wrote:

Just as Schrodinger's Cat remains in a superposition of two states (alive and dead) until the decisive resolution of its wave function into a definite eigenstate occasioned by an observational "measurement" disturbance (opening and inspecting the contents of the box), so also Schrodinger's Candidate remains in a superposition of Good/Bad, Winner/Loser, until the ballots are voted and tallied.

In this method each voter chooses for  each candidate a mark from the range ...
Ultra Hyper Bad, Very Bad, Pretty Bad, Pretty Good, Very Good, and Super Dooper Good or UHB, VB, PB, PG, VG, and SDG, respectively... six judgments ... three each of negative and positive connotations that an English major could profitably standardize for our patriotic cause.

We cannot avoid numbers forever ... at very least we need to tally the ballots for and against each candidate X..... accordingly for each of the three gradations gamma of goodness let B(X, gamma) be the number of ballots on which candidate X is graded Better than or equal to gamma ... and for each of the three gradations beta of badness, let W(X, beta) be the number of ballots on which X is graded Worse than or equal to beta.

For each candidate X we form two polynomials in epsilon... one where the coefficients are the B for Better values, and another where the coefficients are the W for Worse values:

P+ = Sum (k = 0, 1, 2) of 
            Gamma(k)*epsilon^k,
and

P- = Sum (k in  Three) of
           Beta(k)*epsilon^k

Here "Three" denotes the set {0, 1, 2}, as in Von Neumann's construction of the whole numbers. 

Gamma(0, 1, 2 ) = 
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